Simplex algorithm — primal or dual?

Question: As far as I know there are two simplex algorithms – primal and dual. They have different halting criteria etc. Before using simplex I have to make a standardization of the LP. So, when do I use primal, and when dual simplex?
Comment: Related post from OR.SEs: [When should I use dual Simplex over primal Simplex?](https://or.stackexchange.com/q/282/491) and [Guidelines for Linear Optimization approaches?](https://or.stackexchange.com/q/421/491)
Answer: In general, if the primal problem is too difficult to solve (i.e. put into standard form and use the Simplex method), then likely it is easier to solve the dual problem. If you have to add a lot of artificial variables for solving the primal, then you are probably better off writing the dual of the LP and solving it using the Dual Simplex method. Keep in mind that when using Dual Simplex, you're sort of solving the primal within the dual due to complementary slackness and the Strong Duality Theorem, which is awesome. Note that this theorem has a necessary condition that the LP is bounded and has a feasible solution to it. See the related question here regarding solving the primal within the dual. Here is also a reference on the Strong Duality Theorem.
Consider the problem below (borrowed from here) for a good example of when to use dual simplex.
$$\mathrm{Min} \  Z = 2x_1 + 3x_2 + 4x_3 + 5x_4 \tag{0}$$
s.t.
$$x_1 - x_2 + x_3 - x_4 \ge 10 \tag{1}$$
$$x_1 -2x_2 + 3x_3 -4x_4 \ge 6 \tag{2}$$
$$3x_1 -4x_2 + 5x_3 -6x_4 \ge 15 \tag{3}$$
$$x \ge 0 \tag{4}$$
If we instead had all inequalities that were $\le$, the normal Simplex method would work great. The two-phase method would be a bit of work.  However, since all of the coefficients in our OF (objective function--namely, Z here) are all non-negative, we can use the Dual Simplex without any problems.
Comment: The number of artificial variables between the (P) and the (D) problem need not be the same I believe because the whole point of using Dual Simplex method is so you choose an IBFS (initial basic feasible solution) so there are no artificial variables. The process in general of finding such an IBFS is what makes Dual Simplex to be used less because there is an easy way if you have all $\ge$ constraints, but can be difficult (and time consuming) otherwise. I'll look into the algorithms that computers use to determine whether it is better to do Simplex or Dual Simplex--I'll keep you updated.
Comment: I don't understand a couple of things here. Primal simplex for LP gives the same result as dual simplex for its dual LP? But if both methods need standard form (min objective function) then how do I know if it's primal or dual?
Comment: And why adding a lot of artificial variables for the primal doesn't imply adding them for the dual? In both cases I need an identity matrix, so artificial variables would be the same, isn't that right?
Comment: In your example I get an identity matrix ($x_{5},x_{6},x_{7}$) but with two $-1$, so can't I just use primal and multiply two rows by -1?
Comment: From what I've experienced, the canonical notation is using $x$ for the primal ($u$ for its corresponding slack variable) and $y$ for the dual problem ($v$ for its corresponding slack variable). See the link I added on Strong Duality Theorem which shows that if $y^*$ is an optimal solution to the dual, then there exists an $x^*$ such that both yield the same OF value.
Comment: Ok, thanks! And what about the 3rd comment?
Answer: Adding to what was said above, the dual simplex algorithm is also very useful in cases where you might need to $\textbf{insert new constraints}$ as you go.
Using the "regular" simplex method, you would have to solve the problem from the beginning every time you introduce a new constraint, and using the dual you will only have to make some (relatively) minor modifications.
See example here.
BTW, using the dual simplex method is equivalent to taking the dual and then using the simplex method on the dual. See example here.

Simplex algorithm — primal or dual?


Como excluir apenas um determinado dado de um estado React

Question: Hoje tenho a seguinte constante:
const alunos = [{
 id: 1,
 nome: 'Julia',
 curso: 'Enfermagem',
}, {
 id: 2,
 nome: 'Isabela',
 curso: 'Veterinária'
}]

porém eu precisaria apagar apenas o dado do id, que está setado no state e atualizá-lo.
Comment: Thales, acho que você precisa ser um pouco mais claro. Você quer atualizar ou deletar? O que você tentou até agora? Deu algum erro? Porque o que você tentou não está funcionando?
Comment: Acrescentando a resposta do "Douglas Teles" você pode fazer o uso do `map` no lugar do `FOR`. https://developer.mozilla.org/pt-BR/docs/Web/JavaScript/Reference/Global_Objects/Map
Answer: Varra o array e busque pelos IDs, então remova utilizando delete

const alunos = [{
 id: 1,
 nome: 'Julia',
 curso: 'Enfermagem',
}, {
 id: 2,
 nome: 'Isabela',
 curso: 'Veterinária'
}];

for (var i =0; i < alunos.length; i++){
      delete alunos[i].id;
}

console.log(alunos);
Answer: Amigo, sua pergunta está um tanto quanto difícil de entender, talvez até por que você ainda não entende muito bem React.
Você disse que quer apagar um item do 'Estado React'. Isso para mim significa que você deseja apagar de this.state, correto? Se for, por qual motivo mostrou uma constante de array com 2 objetos e não o this.state?
Além disso, no this.state você nunca deleta nada, nem atualiza nada diretamente (this.state.attribute = 'some value'). Você sempre deixa que o React atualize para você através do this.setState({}). Por exemplo, para apagar um atributo basta defini-lo como undefined: this.setState({ foo: undefined })
Melhore o enunciado de sua dúvida para conseguirmos ajuda-lo mais.
Answer: Basta você usar o método filter para manter na lista somente as propriedades que tenham um ID diferente daquele que você deseja excluir.
Por exemplo:

const state = [{
  id: 1,
  nome: 'Julia',
  curso: 'Enfermagem',
}, {
  id: 2,
  nome: 'Isabela',
  curso: 'Veterinária'
}]

// ID que desejamos excluir:
const id = 1

const newState = state.filter((data) => data.id !== id)

console.log(newState)

Para saber mais sobre esse método, leia a documentação Array.prototype.filter no MDN.
Answer: Você pretende deletar o item que está guardado no estado?
Poderia:
 const alunos = [{
 id: 1,
 nome: 'Julia',
 curso: 'Enfermagem',
}, {
 id: 2,
 nome: 'Isabela',
 curso: 'Veterinária'
}]
 const index = alunos.findIndex( i => i.id == this.state.alunos.id);
 alunos.splice(index, 1);
 // Ou se for somente o id
 delete alunos[index].id;

Answer: Como o nosso amigo Gleidson Henrique Comentou sua pergunta não esta clara mas eu vou tentar ajudar pelo que eu entendi.
Você tem uma constante dentro do Estado Certo ?
Tome como exemplo esse meu estado button
{this.state.buttons.map((button, index) =>
        delete button[index]
)}
Espero ter ajudado


What does a wave with all even harmonics sound like?

Question: So most synthesizers provide us with four standard wave forms:

A sine wave which has a single fundamental
A sawtooth wave which has a fundamental and a range of odd and even harmonics
A square wave which has a fundamental and a range of odd harmonics
A triangular wave which also has a fundamental and a range of odd harmonics

My question is twofold:
Why is a wave with a fundamental and all even harmonics not included in this canonical set of waves, and what would one sound like?
Comment: I'll leave the full answer to someone with more knowledge, but I think it's worth noting that, in this context, the fundamental *is* the first harmonic, so it's actually already included in the phrase "wave with odd harmonics." A wave that has the fundamental plus even harmonics would actually be a wave with one odd harmonic and the rest even, which might in part explain why it doesn't come up as a fundamental wave very often. Anecdotally, I've created even-harmonic waves and found them to sound a lot like regular square waves, but I might be misremembering.
Comment: @MattL. Oh wow, you are totally right, I feel stupid—divide everything by two and its indistinguishable from a higher overtone series. Fascinating, however that, with the right choice of odd fundamental, a single additional frequency would immediately drop the octave. Thanks for the correction, I should have thought it through.
Comment: Thanks. Yes that is a strange contradiction - that something is only even in relation to a fundamental which by its very nature is always odd.
Comment: Of course, only the even harmonics would still sound like the fundamental, even if that frequency isn't literally present.
Comment: @PatMuchmore: If you only have the even harmonics without the fundamental, the perceived fundamental frequency would be twice the original fundamental. You would need at least one odd harmonic for the wave to have the original fundamental frequency (without the fundamental actually being present).
Comment: @MattL. That is not necessarily correct, thanks to difference tones.
Answer: On most synthesizers with two oscillators this is easily achieved by setting one oscillator to a sine wave (to produce the first harmonic) and setting the other oscillator to a sawtooth wave and tuning it one octave higher (to produce the even harmonics).
As mentioned in the comments, hearing just the second oscillator will simply sound like a saw wave one octave higher, but adding any of the odd harmonics will tell your brain that the saw is in fact the even harmonics of a sound one octave lower.
You can use this as a trick to play sounds that appear to be lower than what the synthesizer is capable of producing. E.g. if you tune one oscillator to the lowest setting, and then tune the second oscillator one octave and a major third higher, you get the ratio 1/2.5, which your brain then interprets as the ration 2/5, and that makes it sound like the even and multiple-of-five harmonics of a note one octave lower than the lowest setting. This is especially effective if the synth has a ring-modulator; e.g. try it on the Korg MS-20 with oscillator one set to 32' and oscillator two set to 16' and tuned up from C to E.
You can also create a sound where you have all harmonics, but can mix the balance of odd and even harmonics, by setting one oscillator to a square wave (to produce the odd harmonics) and a second oscillator to a sawtooth wave one octave higher (to produce the even harmonics). The volume balance of the two oscillators then controls the odd/even harmonic content of the sound. This is also what happens when you switch on the sub-oscillator on a synth like the Roland Juno-106.
There are even synths that use stacked square waves, each one octave higher than the previous one, to achieve a sort of additive synthesis. E.g. on the Roland SH-7, there is a section in oscillator one where you can set the level of five square waves. These five sliders then effectively control these harmonics:

32' -> 1   3   5   7   9  11  13  15  17  19  21  23  25  27  29  31  33  35  37  39  41...
16' ->   2       6      10      14      18      22      26      30      34      38
 8' ->       4              12              20              28              36
 4' ->               8                              24                              40
 2' ->                              16
Comment: IIRC, the phantom low note you described is used in real pipe organs to get a 32' sound on an organ that only has room for 16' pipes.
Answer: With what you have it's actually easy to generate what you're looking for. I think what you want is a periodic signal (wave) with a given fundamental frequency f0 and harmonics at 2xf0, 4xf0, etc. This is equivalent to generating a wave with odd and even harmonics (e.g., a sawtooth wave) at twice the desired fundamental frequency, i.e. at 2xf0, and adding a pure sinusoid at frequency f0. This will give you frequency components at f0 and at its even multiples.
One simple example of a wave with only even harmonics (apart from the fundamental) is a half-wave rectified sinusoid:

This is quite easy to see: it is equal to the sum of the fundamental sinusoid and a full-wave rectified sine, which has twice the fundamental frequency.
Answer: The square wave has the first harmonic with an amplitude of one, the third harmonic with an amplitude of 1/3, the fifth harmonic with an amplitude of 1/5 and so on...
If you in a similar way take only the even harmonics, that is: the second with amplitude 1/2, the fourth with amplitude 1/4 and so on... You get a triangular wave with double frequency of the fundamental.
If you, in a similar way, takes all the harmonics, you get a triangular wave with the same frequency as the fundamental.
Comment: A triangle wave /\/\/\ contains all odd harmonics at levels 1/n², not 1/n. Do you mean a sawtooth wave |\|\|\ ?
Comment: You are right. It should have been sawtooth.


Update Policy for Low-Quality Answers: Citations Required

Question: Abstract: "Back It Up" Policy for Answers
In this post, I propose updating the policy on Economics.SE for deletion of low-quality answers. While there has been some recent discussion regarding our site's policy regarding deletion of low-quality answers, this question has come up on this site multiple times (reference provided below). A recent post has demonstrated that there is significant community support to develop more detailed guidelines for deletion of posts. Here, I review the policies adopted by other Stack Exchange sites and the rationale behind these policies and review criteria for how these policies might be successfully adopted on this site. In the end, I propose a stricter set of guidelines specifically for the deletion of answers. Specifically, I propose that we adopt the "back it up" principle adopted by over a dozen other stack exchange sites: a non-mathematical answer (or similar) must be backed up by citations or is subject to deletion. Here is an example. This policy reduces the amount of subjective judgement needed to determine whether a post needs to be deleted while also significantly increases the quality of posts on the site.

The question portion of this post reviews the policies of other sites and discusses the rationale for them. Upvote this question if you support a revision of our policy.
The answer portion of this post will contain specific policies that we might adopt. I post a specific policy based on an assessment of other sites' policies. Upvote my answer if you support the specific policy that I propose. Also, feel free to submit alternative proposals.

Reviewing Answer-Deletion Policies Across Sites
On this site, we have discussed the problems associated with low-quality answers several times. I list these here.

Bad in my opinion vs. low quality
Post Removal and Rules Reminder
What to do about heterodox answers in low-frequency questions?
Preemptive protection
Wikipedia Referencing and Content Rules - Is this time for me?

A common thread among these posts is the tension arising from the inherent subjectivity of determining whether an answer is of low quality. Fortunately, this problem has been already been solved (or at least mitigated) on many other Stack Exchange sites through the adoption of the so-called "back it up" principle. For most sites, this means that an answer must be backed up with a citation of some sort. On our site, it might mean something slightly different. For example, an answer to a question of a mathematical nature must be backed up with mathematical argumentation (obviously). A question of a more "wordy" nature must be backed up with a reference or citation to, say, a peer-reviewed journal. As argued on another site,

"For anyone who is trying to do actual research, answers without
sources are useless. I'm not even going to talk about how answers
without sources are often inaccurate, but I've noticed that people who
know where they got their information from usually don't misremember
things or post incorrect facts."

The rationale, summarized in an oft-cited blog post by Robert Carataino is that "opinion, by itself, is noise." If an answer is not backed up, it should be subject to deletion. See here for a list of sites that have adopted a policy of this nature: How widespread is the "back it up" principle?
Criteria for a Successful "Back It Up" Policy on Economics.SE
The idea of "back it up" is universal. However, since each site on Stack Exchange is different, the particulars of implementing such a policy are subtly different. Here I review some criteria that such a policy should have to be as successful as possible.

Because Economics.SE contains mathematical and computational questions, as well as discourse-based "wordy" questions, simply requiring all answers to contain citations is not a sufficient policy. However, the principle of "back it up" should be universal---since mathematical answers, say, can be backed up by mathematical argumentation. A successful policy on our site needs to articulate this.
The policy should be effective! That is, it should reduce the visibility of unsourced answers and other answers of low-quality. One way to do this is to simply encourage users to downvote such answers. Given that this site attracts a lot of laypeople who are very willing to upvote unsourced answers, I believe that the policy should be to delete such answers.
Such a policy should put as little burden on moderators as possible. Deletion of answers can only be done by moderators, with the exception of answers with a negative score. Given this, the community should be vigilant to downvote answers that do not satisfy this policy. (A downvote can be undone if the author fixes the answer via edits.) When such answers do not get the necessary downvotes, enforcement of the policy rests with the moderators. Thus, the policy should be such that a moderator can decide whether or not an answer should be deleted almost instantly and without effort. To accomplish this, there should be a simple, nearly programmatic rule for this. An example that might arise, for example, is that a moderator wants to allow for some sort of grace period for the author to revise the answer. In this case, a programmatic rule would be that an unsource answer MUST be deleted if it is older than 3 days, for example. By tying the hands of the moderator in this way, we in fact make their job easier.
How should this policy be applied to very old answers? There are a lot of old, unsourced answers on this site. A successful policy must describe how to deal with these. My take is that they will either be fixed by the community slowly over time or that they will be eventually deleted. For example, over time community members edit them or will flag them to bring them to the attention of moderators and they will slowly be resolved. If we've tied the hands of the moderators, as described above, the solution will be simple. Remember, "opinion, by itself, is noise."
The policy should be short and simple. Short and simple policies are the most effective.
Comment: "Deletion of answers can only be done by moderators." This does not apply to answers with a negative score.
Comment: @MichaelGreinecker Oh. Thanks, this makes a pretty interesting difference. I've edited the proposal to reflect this. The new commentary that I've added is this: "Deletion of answers can only be done by moderators, with the exception of answers with a negative score. Given this, the community should be vigilant to downvote answers that do not satisfy this policy. (A downvote can be undone of the author fixes the answer via edits.) When such answers do not get the necessary downvotes, enforcement of the policy rests with the moderators. "
Comment: With apologies if I have missed something, where is a statement of the current policy on low quality answers that you propose to update?  In the Help Centre under "How do I write a good answer?" and "Why and how are some answers deleted?" there is only general guidance which does not appear specific to this site (unlike for questions where "What topics can I ask about here?" contains specific guidance for Econ SE).
Comment: Yeah. For better or for worse, a lot of site-specific policy lives in meta posts rather than on the FAQ. Here's a question that talks about it: https://meta.stackexchange.com/questions/279879/improved-help-center-site-specific-pages-and-site-specific-edits-to-all-pages. One comments on one answer talk about our situation: "some communities have a stronger back-it-up policy than others. It would be nice to let them create a page with that community-specific policy defined in one place that's more controlled and easier to find than a random Meta question."
Comment: @AdamBailey I think jmbejara refers to this: https://economics.meta.stackexchange.com/questions/2084/generic-response-to-unsourced-answers. Also note those help pages, except the ones for off/on topic cannot be edited by us they are generic, so it is common across sites to specify additional rules/policies on meta like for example here on skeptics: https://skeptics.meta.stackexchange.com/questions/1505/faq-welcome-to-new-users/2512#2512
Answer: Here is my proposed FAQ on answers, the text is based on mashup of ideas in and under the two other answers of HerK and Jmbejara, as well as putting them into appropriate FAQ format (i.e. this FAQ has to be new user friendly), please feel free to comment on the FAQ or provide further answers that could be incorporated in.  Once we agree on precise wording and policy we will create separate community wiki and update notices and other relevant materials with links to it.

FAQ on Answers:

I am a new user here on Economics.SE. What do I need to know about writing an answer here?

Welcome to Economics: Stack Exchange. Economics:SE is a question and answer site for those who study, teach, research and apply economics and econometrics. It's built and run by you as part of the Stack Exchange network of Q&A sites. With your help, we're working together to build a library of detailed answers to every question about economics.
Economics:SE is Different
Economics:SE  different to many online Q&A sites and forums (such as mailing lists, bulletin boards, and the commenting systems on blogs.) It is also fairly different to many other non-science web sites in the Stack Exchange family, such as Stack Overflow, that you may be familiar with.
As a result, the Economics.SE community can appear to be a little demanding on new users. Many — perhaps even most — first time users are surprised when their contributions are judged against an unexpectedly high set of standards. We urge you not to be disheartened by this. Have a look around, and you will quickly understand how we work. We hope that you will soon appreciate the value that these standards bring in ensuring that the answers on Economics:SE are of very high quality and reliability.
These standards can be summarized as simply as: "Back it up!" This means that answers on this site have to be supported either by references to reputable and/or scholarly sources or by formal (mathematical) model or by sharing empirical results backed up by replicable example of code and data.
1. Answers That Need References
The biggest surprise to new users may be our insistence on references in the answers. Many forums will appear to simply accept at face-value the word of a random internet denizen. Here, we expect to be able to independently check what you are saying, as we want to chase down the evidence, rather than relying on authority or personal expertise. You should expect that people will actually verify whether your references say what you claim they say. Ideally, we would like to see links to peer-reviewed evidence. This makes writing an answer harder, but the good answers are appreciated much more.
To be more specific,  answer that:

contains a claim of an empirical or theoretical nature that concerns primarily with inferred information  (i.e. information obtained as a result of some empirical or theoretical analyses), the sources cited must also be reputable and scholarly source;

addresses a data inquiry or data request, it must provide links or references to the data or to a data codebook or data guide;

claims about factual information (e.g. "Event X happened" or "So-and-so said this") be supported by reputable (or reputable and scholarly) sources.

What is reputable and scholarly source?

A source is reputable if its publisher or author(s) have the reputation within the economics profession for maintaining high standards of fact-checking, accountability, ethical reporting or production of high quality scholarly or professional work related to economics.
A source is scholarly if its publication requires a peer-review process.
Reputable and scholarly sources are:
a)  peer reviewed articles published in reputable journals (i.e. predatory journals are not allowed, if in doubt refer to Scimago Journal & Country Rank of journals in economics or other fields).
b) peer reviewed handbooks or books that could be cited in reputable journals (but not undergraduate textbooks, save for circumstances mentioned under "Are There Any Exemptions?").
c) curated working paper series (e.g. NBER or MPRA that undergo limited peer review but not SSRN which does not - with exception of SSRN articles from authors affiliated reputable high ranking university; please refer to top 200 universities in QS Economics & Econometrics ranking).
d) technical reports produced by widely recognized government or supranational organization which specialize or heavily participate economics research (e.g. IMF, World Bank, ECB, BoE, Fed, OECD etc.).

What is only reputable source?

a) News articles (but NOT opinion pieces) in a respectable news outlet such as Associated Press, Reuters, Bloomberg, etc.

Does that mean that popular books or blogs from economists are not allowed on this site?

No, but these do not count as a support for an independent claim. You should feel free to quote or use material from these and reference them but they should not be the only sources used to back up a claim. For example, if you think that certain blog provides excellent intuition behind a certain result you can use reputable and scholarly sources as a support for the result itself and blog as a source for intuitive explanation.
2. Answers That are Supported by Theoretical Model
These are answers supported by mathematical argumentation and derivation from certain premises. You should still provide reference for the validity of premises unless they fall under exceptions listed under "Are There Any Exemptions?" or if question requests you to use certain premises (please note that graphical analysis, done rigorously, is also form of mathematical analysis e.g. supply-demand charts etc).
3. Answers That are Supported by Empirical Model/Estimation
These answers should be explicit about functional form of their model and provide access to replicable code and data.  Note code and data can be provided via link to external sites (such as GitHub) or link to external dataset (unless user combined several dataset or manipulated data in a way not reflected in the code).

Are There Any Exemptions?

Yes there are few exceptions from the rules above:

Common knowledge. What is common knowledge? Common knowledge is a knowledge that everyone or virtually everyone knows. Examples of common knowledge include: "Canada is country in North America", "USD is currency of USA", "1 is an odd number". Remember: whenever in doubt whether your statement is common knowledge, please follow the rules listed in previous sections!

Common knowledge in economics. What is common knowledge in economics? It is a knowledge that anyone who ever studied economics 101 should know. It is general knowledge you would find in introductory economics texts such as Samuelson: Economics, Mankiw Principles of Economics,  Krugman: Economics for AP and so on...  (e.g. statements like 'profit maximizing monopoly will produce quantity at a point where marginal revenue equals marginal cost').  Remember: whenever in doubt whether your statement or claim is common knowledge in economics, please follow the rules listed in
previous sections! (Note: you can provide citations to introductory
economics texts as a proof of claim being common knowledge, if
challenged).

Common knowledge in mathematics, statistics & econometrics. What is common knowledge in in mathematics, statistics & econometrics? It is a knowledge that anyone who ever studied in mathematics, statistics & econometrics 101 should know. It is general knowledge you would find in introductory texts such as Sydsaeter et al: Essential Mathematics for Economic Analysis or Newbold et al: Statistics for Economics and Business or Stock and Watson Introduction to Econometrics etc...  Remember: whenever in doubt whether your statement or claim is common knowledge in mathematics, statistics & econometrics, please follow the rules listed in previous sections! (Note: you can provide citations to introductory texts as a proof of claim being common knowledge, if challenged).

When you are writing an answer for question with soft-question tag references are encouraged but not required. Note:  soft-question  tag should not be abused and only used for informal questions about workings or practices within economics profession. Repeated abuses of  soft-question tag after warning might result in moderator intervention.

When you are writing an answer for question with reference-request tag and original poster specifies that they are looking for a reference to literature not mentioned in the previous section.

What Happens if I do not Follow These Rules?

Your contributions can get flagged and receive moderator post notice

Answers that are at least 3 days old and are still not backed up will be deleted.

What Should I do if I See an Answer That does not Follow These Rules?

Please consider either:

Edit the answer and add missing sources if you know sources that would support the answer.

flag the answer using:

low quality flag

or

needs moderator intervention flag and write in "needs support/references/sources" or an equivalent of that (feel free to specify which paragraphs lack sources).

I Flagged Old Question for Lack of Sources and the Flag was Declined, What is Going on?

We implemented this policy on insert date. Previously, we only encouraged the 'back it up!' principle but did not enforced it.
As a result this site might have some old but great answers that do not fully comply with these rules.  While we would ideally want to bring these old answers to our current standards, some of the past users might no longer be active and it would not be fair to delete their great contributions.
Consequently, moderators reserve right to apply the 'back it up!' policy on case by case basis for any answer posted before insert date (unless the post already received post notice in the past).
However, you should still feel free to edit these old answers and add sources that support the answer.
Conclusion
If you never visited Economics:SE these rules might seem a little bit demanding for an internet site. However, if you stay with us for a bit you will see that we take economics seriously and provide great answers and thoughtful answers. If you will stay with us longer, you will soon  start to be disappointed that other forums don't demand the same standards.

Some remarks

the FAQ above tries to be a compromise as such I think everyone will dislike some part of it but please let's not let perfect be the enemy of what can be done.

the FAQ above copies the scholarly and reputable definitions from HerrK but not authoritative. This is because I can foresee that there will be borderline cases where someone's favorite economist is not well known or heterodox economist  and there will be arguments about that. Unless we would wanna go the same way as Physics.SE and only allow mainstream science this might be bad idea and it might lead to fights and too much work for mod team to adjudicate who is authoritative and who is not.

it does not allow entry level textbooks (save as proof of common knowledge when challenged), this makes it bit more strict and in line with original jmbejara proposal even if it does not go as far).

it also allows for bit of ambiguity (one of the michaels points)

it changes wording to at least 3 days, I will strive and also encourage other mods to do it after 3 days but were are volunteers there might be days (summer vacation times) where our vacations might overlap or we might accidentally miss an answer in periods of high activity so I prefer having there at least 3 days to avoid complaints that someone's post got bit more time before deletion.

it allows for case by case dealing with old answers (I think this is only fair to past answers - especially for users that are not active right now but might want to come back to Economics.SE in the future).

EDIT:
I added provision for allowing use of graphs to support theoretical answer. In addition, I removed the right of moderators to delete very bad answers sooner than 3 days.
PS: This post is in essence just mash up of Herr K and jmbejara answers, thus credit should be yours guys. If this does matter to both or one of you, you can both post parts of this answer into community wiki which will record the contribution as being from you (community wikies allow for multiple contributors). Of course, this will be extended to any other users whose ideas might shape this FAQ.
Comment: I hope you don't mind that I made some cosmetic changes to some English expressions. But overall I like what you've written and I'd be happy to support your version.
Comment: @HerrK. I don't mind thanks
Comment: I like this alot. In particular, I think it does well in keeping an inviting tone even though the rules are strict. Two suggestions: I would soften the SSRN claim. To something "SSRN papers need not be reputable and scholarly." Often, there are other criteria such as authorship that clarify the scholarliness. Also, I would add a proviso that what can be taken to be common knowledge might vary with the context of a question.
Comment: @1muflon1 Maybe requiring authors of SSRN papers with affiliations from university or reputable research institution. Regarding the common knowledge thing, I was more worried about more advanced questions, where more things can reasonably be taken to be common knowledge. If someone asks how Bayesian Persuasion proofs with a compact metric type space work, the answer will utilize results that go beyond Sysaeter and Hammond's books.
Comment: @1muflon1 I don't think mods need to evaluate technical answers to advanced research topics. I can't imagine that such answers will cause much controversy. In the context of graduate microeconomics, the first welfare-theorem might well be assumed to be common knowledge. And if a reference is needed, good online lecture notes would be a more useful reference than sending the reader to a hard-to-find textbook.
Comment: @MichaelGreinecker thanks, I would not mind softening the SSRN policy, but can you suggest a way to do it? My issue is that while I think many SSRN contributions are good (and I myself have working papers listed there)  I seen people posting there literally just essays with very little scholarships and they somehow still listed. Perhaps I could add provision unless the SSRN paper is published elsewhere? Regarding common knowledge I would rather prefer to have some stated areas (although we can expand it if you think it is necessary), because I think that would be abused too much.
Comment: @MichaelGreinecker ok thats a good suggestion for SSRN, I will add that in. Regarding the common knowledge, I think in that case it is better to rather reference some handbook (non-entry level handbooks are still allowed) I would hope that would not be too troublesome. This is because in such cases it might be difficult to evaluate for us mods if it indeed is common knowledge and then that could lead to disputes if someone does not like an answer
Comment: @MichaelGreinecker well I would not mind also doing further adjustments but I dont like the wording of it being context specific because that will be definitely abused. I would even say perhaps let it be as it is. Just to be clear I do not plan to be a person who would just go from question to question and just wait for a 'gotcha' moment to past the post notice on a post, if there will be high quality answer people will likely not flag it and it will not have a problem and in rare cases if they arise  I can first just leave comment with gentle reminder I think this should not be too cumbersome
Comment: @1muflon1 I think that is reasonable; it should work out fine this way.
Answer: Definitions
The following definitions of terms are adapted from here:

A source is reputable if its publisher or author(s) have the reputation within the economics profession for maintaining high standards of fact-checking, accountability, ethical reporting or production of high quality scholarly or professional work related to economics.

A source is authoritative if its publisher or author(s) have established expertise in the relevant subject area(s) as evidenced by their past scholarly publications or comparable professional accomplishments in the said area(s).

A source is scholarly if its publication requires a peer-review process.

The idea for introducing these three definitions is to require

claims about factual information (e.g. "Event X happened" or "So-and-so said this") be supported by reputable sources, and
claims about inferred information, i.e. information obtained as a result of some empirical or theoretical analyses (e.g. "Most of X has property Y" or "X causes Y") be supported by either reputable-and-authoritative or reputable-and-scholarly sources.

The reason for accepting "reputable-and-authoritative" sources is that opinions of a well-established expert, on a topic of their expertise, deserve serious consideration by virtue of them being authoritative--a usually hard-earned status, even if we may end up disagreeing with them.  Moreover, if one day Al Roth comes here and answers questions on market design, his answers would carry weight even if they are not properly sourced. The reputability requirement is there to rule out self-proclaimed "experts" in some niche areas.
Likewise, scholarly sources should generally be acceptable, and I throw in a reputability requirement there to rule out articles from dodgy journals.
The definitions purposefully leave room for accepting good quality professional sources. If we are serious about including them as part of our core user base, non-academic professional economists, e.g. PhDs working in the "industry" --- banks, consultancies, think tanks, governments, international organizations, etc. --- may have a slightly different set of trusted sources than what academic economists deemed acceptable. While such trusted professional sources would typically not be scholarly, they should still pass some form of reputability and authoritativeness criteria --- or so I would think. Input from member professional economists on this point would be especially welcomed.
Examples satisfying the above definitions
For completeness, I provide examples for all possible combinations of the three criteria. I don't expect full consensus on my placement of the examples, but a lot of the potential disagreements won't matter for the purpose of formulating our policy, which only requires the distinction between being reputable, reputable-and-authoritative, and reputable-and-scholarly.
Reputable but not necessarily authoritative or scholarly:

News articles (but NOT opinion pieces) in a respectable news outlet such as Associated Press, Reuters, Bloomberg, etc.

Authoritative but not necessarily reputable or scholarly:

A working paper on a niche topic by an otherwise "well-established" economist (e.g. Bart Lipman's 12-year-old working paper)

Scholarly but not necessarily reputable or authoritative:

An article by a little known author in a very lowly ranked journal

Reputable and authoritative but not scholarly:

A "popular science" book by a well-known and well-established economist (e.g. Al Roth's book)

Reputable and scholarly but not authoritative:

The first publication by a young economist in a decent journal

Authoritative and scholarly but not reputable:

An article on a niche topic in a non-economics journal by an otherwise well-established economist (e.g. Arthur Robson's secret handshake paper)

Reputable, authoritative, and scholarly:

Many articles in decent journals
Many books by well-known academic publishers

Policy Statement
Given the above definitions and in light of @jmbejara's answer and the comments under it, I propose the following revised version of the "Back it up" Policy:

Effective on <date>, each answer on Economics.SE must be appropriately backed up; otherwise it is subject to deletion.  "Backing up" an answer means providing suitable support for the claims made therein. Specifically, if an answer:

contains a claim of a mathematical or theoretical nature, that claim must be supported by mathematical arguments or reference to reputable-and-authoritative or reputable-and-scholarly sources;
contains a claim of an empirical nature, that claim must be supported by referring to reputable sources; in addition, if the claim concerns primarily with inferred information, the sources cited must also be either authoritative or scholarly;
contains a claim of a computational nature, that claim must be supported by code or references to such;
addresses a data or reference request, it must provide links or references to scholarly or authoritative sources, unless explicitly requested otherwise by the asker.

Answers that are 3 days old and are still not backed up WILL BE DELETED.
Community members should flag posts that don't meet these standards as "low-quality answers" to bring them to the attention of moderators.

I should note that this version is itself subject to revisions and improvement.

Remarks

The inclusion of an "effective date" give us some leeway in dealing with "old violations".
The policy require claims to be supported, so an answer with multiple claims would call for separate support for each of them.
Newspapers are allowed for facts only.
On inferred information, the following "reasonable" examples would clear the bar:

most common journal articles
most working papers by professors tenured at major universities
NBER WP series
academic books and handbooks published by major academic publishers
papers presented at major conferences/workshops/seminar series
most graduate textbooks

Cases that require judgment/discussion:

widely adopted undergraduate textbooks (e.g. Mankiw)
reports by (trusted) government, industry or international bodies (e.g. IBIS World Industry Reports, publications by the IMF/World Bank/OECD)
trade journals
<...>
Comment: @1muflon1: Perhaps we can broaden the definition of "inferred info" to include theoretically derived statements as well? As in: "**inferred information (i.e. information obtained as a result of some empirical or theoretical analyses)**". Correspondingly, point 2 in the policy would read: "**contains a claim of an empirical or theoretical nature**..."
Comment: I prefer this version. But I think the phrasing in 1. and 2. needs some adaption. For mathematical claims, one needs to give a mathematical argument (1.), for theoretical claims, one needs a reputable source (2). These should really be exchangeable, and the dividing line is not clear.
Comment: I like a lot of that is written here but you somehow omitted also theoretical claims, claims about mechanisms (which are empirically testable but not necessarily empirical themselves), in that definition. There we should have rule as for that inferred information or that one should simply write out the model formally
Comment: Also additional issue if there will be user with nick Al Roth how do we verify it's actually the author, I seen several Keyneses, Walrases and so on here.
Comment: If the *real* Al Roth do become a member, I think it would be fairly easy to tell from the quality of their first few answers. More generally, my point is that if for example someone cites (correctly, not out of context) a blog post by Roth on a relevant issue, that citation, albeit not scholarly, should be given serious consideration.
Comment: @MichaelGreinecker: There is indeed some overlap between math and theoretical claims. But I think we shouldn't rule out "verbal" theories (à la [Coase (1937)](https://onlinelibrary.wiley.com/doi/full/10.1111/j.1468-0335.1937.tb00002.x)), even though they are few and far between nowadays.
Comment: More specifically, I intend for **mathematical claims** to be something like "[Cobb-Douglas function is concave](https://economics.stackexchange.com/a/42830/42)" and for **theoretical claims** something like "[Population diversity causes more conflicts](https://doi.org/10.3982/ECTA13734)" or "[Torture is ineffective](https://www.jstor.org/stable/26160244?seq=1)".
Comment: @HerrK. That makes sense. I still think one should allow references for a mathematical claim, at least references with actual proofs.
Comment: I tried to combine your answer with the other one into a compromise FAQ consider having a look
Comment: "Newspapers are allowed for facts only." will be abused to no end by trolls.
Comment: @MichaelGreinecker: I edited the grouping in the policy to reflect your suggestion. In any case, I think it's better to have overlaps than gaps in the coverage of citation requirements.
Comment: @KitsuneCavalry: Possibly. But trolls will abuse whatever policy we put out, and we should not expect trolls to abide by it. Policies are intended to bring clarity to moderators and site users with whom we can reason. Moreover, sometimes reputable news outlets may be the only source of reliable *factual* information. A very quick search only led me to [eg1](https://economics.stackexchange.com/q/19210/42) and [eg2](https://economics.stackexchange.com/q/1808/42), but I suspect answers that rely on factual info can probably be found somewhere under the `macroeconomics` tag.
Comment: You've made some good arguments for why "back it up" should include more than just strictly peer-reviewed articles. Thanks!
Answer: The "Back It Up" Principle on Economics.SE
Policy Specifics
Policy Statement: Each answer of Economics.SE must be backed up in some way, or it is subject to deletion. Answers that are 3 days old and are still not backed up WILL BE DELETED. "Backing up" an answer depends on the type of question. Questions of a mathematical or computational nature must be backed up by mathematical argumentation or code. Questions about data or data sources must be backed up by links or references to the data or to a data codebook or data guide. All other types of questions must be backed up by references to credible academic sources. Examples of such sources include articles from a peer-reviewed journal or high-quality working paper series (e.g. NBER); peer-reviewed handbook chapters; or advanced-level, scholarly textbooks. References to newspapers or similar publications do not count. If an answer makes several significantly independent claims, each must be supported by references. Community members should flag posts that don't meet these standards as "low-quality answers" to bring them to the attention of moderators.
Discussion of why the policy was formulated in this way

As discussed in the question, requiring deletion after the unsourced question is 3 days old makes the job of the moderator easier. If their hands are tied, they don't have to worry about offering grace periods or offending. Community members should be able to alert an author of the deletion policy and 3 days should be enough time to revise. Also, authors will still be able to see their deleted posts, so they can always repost later if they are able to find a citation later.
I have chosen 3 days specifically because it is a rather short time period. If the time period is longer, then the answer will likely get lost down deep in the feed. It is easiest to delete while the answer is fresh, so that moderators don't have to remind themselves to come back to it later.
Theoretically, the community will bring such posts to the attention of moderators. This means that a moderator can easily go through their queue of flags and quickly delete answers that don't meet our standards.
Note that moderators may always choose to delete an answer that doesn't meet these standards sooner than 3 days, subject to their judgement. This policy only requires the answer to be deleted after 3 days. However, this policy does not limit their ability to use their best judgement where appropriate.
For non-mathematical questions (and the like), this policy requires citations to credible academic sources. Newspapers and other such references do not count for the following reason, because such references are likely useless for the target audience of this site. This site is supposed to be a site for experts or those doing economics professionally. See this recent post. For a student, even a first-year graduate student and an advanced undergraduate, writing a research paper using references to newspaper articles is generally unacceptable. For graduate students, academics, and professionals, only peer-reviewed journals or high-quality working papers are useful. This also has the benefit of avoided discussions of bias among different news outlets. Technically, the one exception embedded in the policy is if the newspaper article is used as a citation for data. That is, the newspaper article contains a graph or figure that is used to back up the answer given.
Note that neither books nor Wikipedia should not generally count as peer-reviewed sources (unless the book is a reputable, scholarly textbook). Also note that high quality textbooks will include references to peer-reviewed articles. If you're using a textbook, this will make it easy to find the relevant peer-reviewed article to cite and it is encouraged that you provide the references to the underlying articles rather than the textbook itself.
The policy does not specify what happens to very old unsourced posts. My intention is that these will slowly resolve themselves over time. Either community members will slowly edit them over time or they will eventually be flagged by the community and will be deleted.
This policy complements a related policy for questions developed in another meta post regarding "expert-level questions".
The policy description that I have provided above is relatively short. It is one short paragraph that can be included in the help section of the site. It covers most of the cases that this site will encounter. Answers that don't fit any of the cases will be left to the discretion of the community and the moderators. The underlying principle is the same, though. All answers must be "backed up."
Comment: An excellent proposal, I was actually working on my own version of this yesterday but did not managed to finish it yet. I fully agree on the broad points. I further suggest that we learn from other sites off-topic on-topic statements and FAQ such as Physics.SE, Biology.SE or even from Skeptics.SE - Skeptics.SE have very good FAQ on citing, I actually already contacted Skeptics.SE moderators yesterday to ask for permission to copy **some parts** of that for our site since naturally here provision has to be made for mathematical answers, in addition, I think it has to be said publicly that
Comment: @jmbejara I think "references to credible academic sources" should be enough and required for empirical claims. But not allowing books would throw out the baby with the bathwater. Truman Bewley's book "Why Wages Don't Fall during a Recession" has more than 2000 citations on Google Scholar. If we exclude books, we basically exclude many areas close to other fields such as economic history or history of economic thought. I think the risk that people cite case studies from undergraduate econ textbook is rather minor.
Comment: PPS: here is link to physics.se help center: https://physics.stackexchange.com/help/on-topic. PPPS: I would also add provision not just for high quality working paper sites but also high quality books e.g. handbooks/textbooks. I dont see why citing Hamilton: Time Series Analysis or Romer Advanced Economics or Mostly Harmless Economics (books cited in many published papers should not be also included). Yes those books will include citations to papers directly but often they are more than just sum of the individual citations and they also offer knowledge in organized way
Comment: I agree with the proposal. Seems like a way to increase the quality of content on the site.
Comment: @1muflon1 If someone cites Hamilton or Mostly Harmless, my guess is that the answer will likely satisfy "back it up" by virtue of containing mathematical reasoning. E.g., an answer might discuss pitfalls associated with diff-in-diff identification without writing a bunch of equations. This would still be considered mathematical reasoning. An answer doesn't have to contain a full-on proof to be deemed "mathematical reasoning."  The requirement that an answer contain a reference to a peer-reviewed article applies only to those answers that are purely discourse---answers that are just "talk."
Comment: painstakingly going through old paper and retyping what is there for a quote especially where the information is not that different (and Romer book is citable). Next some knowledge was actually first published or properly organized in a book. Consider Friedman and Schwartz Monetary History of US, Keynes General Theory, Friedman Theory of Consumption Function. Yes in recent times books are bit sidelined and sometimes are just amalgamation of papers but there are exceptions like Woodford Interest and Prices or Gordon The Rise and Fall of American Growth, such books in my opinion might even have
Comment: References to handbook series ([eg 1](https://economics.stackexchange.com/a/27858/42) and [eg 2](https://economics.stackexchange.com/a/29086/42)) can be particularly helpful and sometimes sufficient to answer some `reference-request` type questions. Moreover, the [JEL](https://www.aeaweb.org/issues/606) regularly publishes  book reviews and listing of new books. It would be a bit ironic not to acknowledge---as a matter of site policy---the value of books catalogued by none other than the Journal of *Economic Literature*.
Comment: @1muflon1 I agree that we should tell users that theoretical answers need arguments and empirical claims evidence. If they lack this, they may be deleted. But the proposal is that any answer that does not mechanically satisfy the criteria needs to be deleted. I am primarily against such a mechanical deletion policy, moderation needs judgement and moderation.
Comment: @1muflon1 Thanks! I like what you describe about updating "off-topic" and "on-topic" statements and the FAQ. I'm looking forward to seeing that happen. Thanks for doing that!
Comment: Some arguments to not allow textbooks to count towards the requirement: (1) If the textbook is of high quality, you should be able to find the underlying peer-reviewed reference. (2) If you're writing a paper, textbooks references are not very helpful since peer-reviewed papers almost never cite textbooks. Answers on this site should be helpful for those trying to write quality research papers. (3) I'm afraid of people writing answers where they cite the "applications" section of their undergraduate econ textbooks. Such references don't meet the higher standard that I think we want.
Comment: @jmbejara yes that was good post. I think we will make FAQ like they have on skeptics because not all pages in help center are editable by mods
Comment: @1muflon1 Re: accessibility of articles for download. You mention that academics will have access but others will not. The counter-argument is that the ideal target audience for the site is academics, professionals, and graduate students. Enthusiasts probably won't care as much to actually look up the papers and read them. Even if they do, a motivated person can always find a way to download these papers for free somewhere. Often on the author's personal website.
Comment: Yeah, it gets difficult at that point. What constitutes an independent claim? I haven't addressed this, but again this leads to the "unwritten and unspoken" aspects to a policy. There is some inevitable subjectivity here.
Comment: @jmbejara well, I think you have me almost convinced but I still worry bit about users who might wanna abuse such unspoken policy. I think even if we go for your proposal fully we should at least provide some guidance on this in FAQ so the policy is not completely unspoken. I hope some other users will also share their opinion on this
Comment: @1muflon1 Sounds good. Trolls are frustrating for sure. I personally don't see this aspect of policy being a prime target though, but you can never know. Let's see what others suggest. As always, it's been very nice to talk/work through these things with you!!
Comment: @1muflon1 Yeah, I think that's reasonable! To make sure we're on the same page, I'd be curious to see examples of what this would mean. Regardless, I think we really need to assemble a list of answers that pass the test and don't pass the test. That's probably our next task.
Comment: @jmbejara that is a good idea, if you have some examples then please add them I will look for some as well (I personally would consider the 3 answers I linked above good examples)
Comment: How many references would one have to add to [this answer](https://economics.stackexchange.com/a/40851/1442) to save it from deletion? Asking for a friend.
Comment: @MichaelGreinecker very good example, just some notes 1. I like your answer there I would rather spend whole night tracking down sources for you and editing them in rather than deleting it. 2. Perhaps we could have provisions that this won't necessary apply to answers that did not get post notice before implementing this new rule? indeed I can imagine one making valid argument that people in the past were just operating under rules in place back then
Comment: I think we should use the criteria to eliminate bad questions but are less strict for sensible questions. Psychological explanations for the gender wage gap need a lot of sources; the statement that evolutionary game had its boom in the 90s does not.
Comment: @jmbejara I agree, but think that such questions are often the most useful for actual research. I see some danger that the site degenerates to well-sourced but ultimately pointless undergraduate term papers.
Comment: I think some books, especially those published by university presses or other academic publishers, do undergo a peer-review process. Though it may be true that the peer-review for books is not as rigorous as that for journal articles, disqualifying all such "academic" books could be a slippery slope, as by extension, we would also have to bar any article that appears in *AER P&P*, which does not go through a full-fledged peer-review process.
Comment: @MichaelGreinecker I dont think so. Consider this 1. Such policies are already in place in other science stacks + skeptics (this is not groundbreaking policy here). 2 Consider Physics.SE one of the most successful stacks here, their help center literary states: "Anything that couldn't be published in a reputable journal is not appropriate on this site" also note this meta answer from physics SE which is on point https://physics.meta.stackexchange.com/questions/564/citations-are-the-source-code-of-physics-stackexchange. Especially this answer https://physics.meta.stackexchange.com/a/568/291143
Comment: @MichaelGreinecker I sympathize with this. But this site is not really designed for what you have in mind. This was articulated [here](https://stackoverflow.blog/2010/09/29/good-subjective-bad-subjective/): "Questions that are not answerable — discussions, debates, opinions — should be closed as subjective.... We never claimed that subjective questions were horrible abominations that should never be asked. We simply choose to forego those subjective discussions, as there were dozens upon dozens of forums which already catered to them."
Comment: @HerrK. maybe we could actually use JEL or even better EconLit to define what (book) sources are acceptable?
Comment: @MichaelGreinecker I think you're right. Also, it sounds like there is plenty of support too. I've edited my answer to reflect this. However, I really like 1muflon1's answer and I'll support it. Let me know if I've missed anything.
Comment: what you propose is actually not controversial but common practice across virtually all science stacks. Economics.SE was quite unique for not having these policies and given how other sites such as Physics.SE, History.SE Biology.SE with these harsher policies thrive it can only help us. PS here is link to skeptics FAQ https://skeptics.meta.stackexchange.com/questions/1505/faq-welcome-to-new-users/2512#2512
Comment: I agree with basically this whole proposal. As for textbook references being a grey area, I think even if it's a really seminal work, you should be able to either find a direct citation that the textbook uses for a section, or one should give a page number AND give a brief explanation of the text in question, because this site is meant to provide answers that are accessible, and a textbook may be more difficult to find than a paper.
Comment: @KitsuneCavalry Thanks. That's a good point. For the reasons you describe, my original inclination was to simply not allow textbooks to count towards this requirement. How would you feel about this?
Comment: @jmbejara In the sense that it is hard to evaluate the quality of a textbook compared to a research paper that has been reviewed, I'm inclined to agree. I think people can still cite textbooks--but other reasoning must be given. This could be hard though, especially if the textbook has a valid point, but maybe doesn't citate a lot of other works.
Comment: @KitsuneCavalry I  think we should allow books at least provisionally. Lets allow it but lets make rule that if claim is challenged one should edit the answer and provide primary sources.
Comment: @1muflon1 I'm curious to see what your objective is that would make you want to allow textbooks. My guiding principle is this: suppose you're a graduate student trying to write a research paper and looking for help on this site. In that case, it seems that references to textbooks are of little use *if* you can't find the underlying peer-reviewed article citation. There is a time and place for textbooks. They're helpful for learning a subject and serving as references, but as you mentioned, peer-reviewed journal articles are the currency of science.
Comment: @1muflon1 What if we tried it without textbooks for a while and see how we like it? Also, do you have any examples of good answers where someone referenced a textbook but could NOT easily find a peer-reviewed article to back it up?
Comment: @jmbejara well, I just think that using textbooks can sometimes be useful shorthand and I am scared that if the policy is too strict there will be too much pushback.  1. Especially when talking theory many papers from 70s 80s or even earlier can still be valid or subject of question (e.g. permanent income hypothesis), often these papers are published online simply as a photos of pages. On the other hand Romers Advanced Macro is all there online for anyone who can google in pdf form fully searchable - just from practical perspective for older papers it would be better to just user Romer than
Comment: better scholarship in them than Q3-Q4 papers. In addition, for non-academician it might not be as easy to get to gated paper. Sure there is scihub, but then any serious book now is online in pdf posted on some torrent so that is sort of equivalent. For that reason I think we should allow books but require they are technical and perhaps also require more citation like point to page/chapter
Comment: also consider answer to one of my old questions on academia.se https://academia.stackexchange.com/a/140922/41452. The Q agrees with you in regard to writing a paper, but note the 2nd to last paragraphs. Handbooks often have useful info when something needs to be explained from first principles, and thus they are quite useful for entry level q, unless we want to ban them completely. This being said, it is not like this is a hill I would die on, I would rather have your policy than no policy at all I am just a fan of more evolutionary approach in rules than revolution that might overcorrect
Comment: TBH, I can't imagine this coming up much. I've been looking through answers on the site and I haven't really been able to find answers that cite textbooks without also citing peer-reviewed articles. The real issue that that this is solving is to prevent completely uncited answers. (Though, I should continue looking to view a larger sample.) Also, to reduce the burden on everyone, there is something appealing about the simplicity of the rule that only peer-reviewed articles should be allowed.
Comment: In any case, I should mention that this post could be improved by including examples of answers that do and do not satisfy the rules. When the "help page" gets edited, it'd be nice to have some examples of good answers and unsatisfactory answers. Something like what I did here: https://economics.meta.stackexchange.com/a/2098/59 . If you have some examples to help get this going, feel free to share.
Comment: @jmbejara I was considering maybe 3tier system. 1. Peer reviewed article - you are safe. 2. Textbook/handbook - we allow it but if challenged link to primary sources is required (by the way we could apply this to working papers like SSRN which are not peer reviewed as well).  3. No reference - post notice and if correction is not made in 2-3d deletion
Comment: @jmbejara that is actually good point I must concede that, you are right here, although I still think there is the ease of use argument
Comment: @1muflon1 I don't like the 3-tier system because the rule becomes more complicated. I want to keep it simple and easily stated. My preference, the reason why I mentioned the "gray area" in the original post, is that there could be an "unspoken" and "unwritten" 3-tier system. This rule only works if people flag an answer or if a mod happens upon it themselves. Therefore, a unspoken 3-tier system seems like the defacto result even if the written rule is more strict. I prefer writing a strict rule because I know in practice, regardless of how hard we try, it will always be weaker.
Comment: @jmbejara my worry is that if the policy is too strict there will be trolls abusing it, there is already a troll that accused me of not applying post notice fairly (and sometimes trolls are very good at pretending they are reg users). Also as examples, of an answer where books are used and the answer seems to be high quality would be this: https://economics.stackexchange.com/a/9177/15517 (and also some other answers there), or this https://economics.stackexchange.com/a/22643/15517 or this very underated answer of Kitsune https://economics.stackexchange.com/a/43074/15517
Comment: check also this answer that you accepted https://economics.stackexchange.com/a/187/15517 sure it relies on papers but references textbook as well.
Comment: @1muflon1 The idea was to find answers that use textbooks but not articles. All of these answers, except for the soft question, contain article references. They would clear the bar by virtue of references to the articles.
Comment: @jmbejara oh, then maybe we were misunderstanding each other. I understood your proposal as that every substantial claim made not proven mathematically or with data or by code would require its own citation from peer review article to not get post notice, not just that 1 peer review paper would clear the post
Comment: @jmbejara also by the way, would you still be in favor of keeping the current provision [here](https://economics.meta.stackexchange.com/q/2084/15517) about common knowledge in economics? That would for sure make my worry about not supporting textbooks much less relevant
Comment: @1muflon1 Agreed. Thanks. I will. I'll try to do it some time this week or weekend.
Comment: @MichaelGreinecker Hah! So, these soft questions are hard... This is a good example to use to for discussion. Thanks. My best guess is this. I imagine that there might be a Journal of Economic Perspectives article that could be reused for each point. If not, maybe an example from each of the subfields you mention that could illustrate your point? One for psychological game theory, another for evolutionary, and a last one for epistemic.
Comment: @jmbejara I think the issue is that the value one would assign to such an answer will necessarily depend to some degree on how much one trusts the answerer. The value comes not just from the list than in whether one thinks it provides a fair view of a generic game theorist. If we want to attract high level experts to this site, this would probably become worse. Say, Al Roth comes and explains some reasoning behind a design feauture of a kidney exchange program and has the audacity not to add references.
Comment: @MichaelGreinecker This is hard because this question maybe should have been closed as "opinion-based"---it's at least really close to the line. It's literally asking, "what is the opinion of this group of people?"
Comment: @jmbejara I don't think my answer was that subjective. Its value simply derived from some knowledge that is hard to find in a reference form. Say, somewhat asks why there are many people using linear probability models nowadays even though probabilities cannot be really linear. The correct answer is, no doubt, that this has to do with the popularity of MHE. Citing the arguments there is not enough, one needs to know that it is an extremely influential book. That is is influential is not just subjective opinion, but it is hard to find a reference for.
Comment: @1muflon1 Is there any answer here that could be published in a reputable journal?
Comment: @MichaelGreinecker some of the Alecos or Herr K answers for sure could appear in reputable journal. Also I am not advocating going as far as physicsSE just saying ref requirement is **standard** across science stacks - Econ.SE was *exception* (and in fact even some non science stacks eg skeptics have this requirement). Also let's not throw out baby with the bath water what about provision that this does not apply to soft questions? I mean we have soft question tag for a reason, we can also make better demarcation for that tag so it's not abused
Comment: @1muflon1 My reading of the proposal is that it is not compatible with having soft questions anymore. And [here](https://physics.stackexchange.com/a/618346) is a recent answer from a seemingly highrep user on Physics.SE that has no reference and includes a subjective assessment of what is a good approximation in a certain context. This proposal would mean such answers have to go.
Comment: @MichaelGreinecker yes, but that is precisely point of this discussion we do not need to accept jmbejaras proposal verbatim. But I think the need for doing something is clear. I personally would be in favor of leaving soft questions. I am currently working on some provisional FAQ proposal for this site that would incorporate jmbejaras proposal but also feedback by other users also feel free adding your own proposal
Comment: @MichaelGreinecker We can have soft questions, as long as you back up your answers.
Regarding your [example answer](https://economics.stackexchange.com/questions/30659/what-do-game-theorists-think-of-behavioural-economics/40851#40851), I think you could back this up with references. It might be hard, but that's the point. We're solving an adverse selection problem. The solution is to impose a requirement that is more easily passed by experts than by amateurs. That's where the citations come in.
Comment: @MichaelGreinecker
The idea behind a more mechanical policy is that it is easier to implement and, thus, has a higher chance of success. You need a lot less specialized knowledge to realize when an answer doesn't clear the bar (by design). However, I'm open to a rewrite of the policy if you want to propose some edits to allow for more flexibility on soft questions/answers. I'm just a little uncomfortable saying that we should give out a free pass (in some situations) to reel off opinions without backing them up.
Comment: @HerrK. I agree with you regarding handbooks chapters, AER P&P, etc.  I recognize there is a spectrum here too. I wrote it the way that I did because it was the most straight-forward. See my discussion with 1muflon above about "unwritten" aspects of the policy. Also, I also recognize that we should perhaps put a "reference-request" exception (or something) in the policy. If you have an elegant way to formalize that, please make a suggestion. I'm definitely open to making edits to my proposal. I want to build consensus.
Comment: I tried to combine your answer with the other one into a compromise FAQ consider having a look
Answer: I present here a number of features which I believe a policy on low-quality answers should have (it is not a fully worked-out policy).
1.    The policy should have regard to the needs of all the groups in our strapline "For those who study, teach, research and apply economics and econometrics".
The site does not currently attract enough experts and some degree of change to make it more useful to experts seems sensible.  But change should not be at the price of making the site significantly less useful to others, or significantly devaluing their past efforts.  Compromise between the needs of different groups is required.  Those who would like a radically different kind of site tailored primarily to the needs of experts do have the option of setting up a new site, either within Stack Exchange or elsewhere.
2.    The policy should include explicit guidance on the boundary between what should fall within the scope of the "back it up" principle and what can reasonably be taken to be common knowledge so does not need to be backed up.
This has been well addressed in the answer by 1muflon1.  I would just add that what is common knowledge can be interpreted in two ways.  One is what is common to all or most of the site community.  Another is what is common to the sub-community of those likely to be interested in a particular question.  Favouring the latter interpretation, I suggest that, for an expert question, the scope of what can be taken to be common knowledge is wide (but the quality of back-up for what isn't common knowledge should be high).  For a beginner question, conversely, the scope of common knowledge is narrower (but the quality of back-up for what isn't need not be so high).
3.    Where back-up is required, the type(s) of back-up that is/are appropriate will depend on the question and on the content of the answer.
The following quote is from this post by Monica Cellio on Meta SE:

Backing up an answer includes citing sources, making a logical argument, and sharing relevant personal experience.

With the caveat that personal experience will rarely be relevant on Economics SE, this is I suggest a good summary of the variety of forms which back-up may take.  But not all forms of back-up are appropriate in all circumstances.  A few examples:
a)  Empirical claims (unless common knowledge) require citing sources.  They could require logical argument as well (eg to draw a conclusion where a cited source just provides data).
b)  Theoretical claims (unless common knowledge) require logical argument, but that could be by presenting an argument, or by citing a source containing an argument (though in the latter case it would be good practice to give a brief summary rather than a bare citation).
c)  Textbooks and online teaching sites can usefully be cited in answers to elementary questions (and may well be more useful to questioners than peer-reviewed papers which for many can be difficult to access or understand).  They will rarely be appropriate in answering expert questions (not so much because of doubts about reliability but because their contents, to experts, will probably be common knowledge).
d)  Newspapers and online news sites will rarely be appropriate sources for citation (because they tend to misinterpret or sensationalize scientific findings), but could be useful in answering questions on specific events too recent to have been considered in other sources.
e)  Occasionally, questions specifically ask for a particular type of back up.  Such requests should be respected.
4.    Where back-up is by logical argument, the policy should not privilege mathematics over other recognised forms of reasoning, eg verbal or diagram-based.
This is not in the least to criticise the use of mathematical reasoning in economics.  I am merely asserting that each of these forms of reasoning can be used well or used not so well, and that different forms of reasoning may be appropriate to different questions or to different questioners (ie where their level of knowledge and understanding can be inferred from the wording of the question).
Answers which merely use verbal reasoning to draw conclusions from common knowledge assumptions (and therefore contain neither citations nor mathematical formulae) should be judged on their merits and not automatically assessed as low-quality.  By judging on their merits, I mean assessing whether the assumptions really are common knowledge and whether there has been a reasonable attempt to present a logical argument rather than just make assertions.
5.    Compliance with the policy should be encouraged and enforced primarily by the community, rather than by use of moderator powers.
I understand the attraction of using moderator powers to deal with a case such as recently arose in which a low-quality answer to this question received a large number of votes giving it more prominence than several other very good answers.  Such an answer does not give a good impression of the site, and for a case such as that, I think deletion using moderator powers is appropriate (see 6 below).
However, the maxim "hard cases make bad law" is relevant here.  Although low-quality answers are quite common, most of them do not gain such prominence.  For many such answers, the voting system works well in ensuring that they are listed below better answers.  I have two suggestions to try to make it work better still.  One is to positively encourage downvoting of low-quality answers.  I don't share the view occasionally expressed that it is rude to downvote without giving the reason in a comment.  Giving a reason would be helpful to a new user, but I don't think it should be considered essential if a regular participant posts an answer that is clearly in breach of published policy.  Those of us with a decent amount of rep shouldn't be concerned by the small loss of rep (-1) that downvoting an answer entails.
My second suggestion starts from the likelihood that, when low-quality answers receive a lot of votes, some of those votes are by people who are not regular users of Economics SE but have seen a question on Hot Network Questions.  We might explore (I think it would have to be raised with Stack Exchange management) the possibility of excluding our site from HNQs.  This has already been done for several other sites (see here).  The grounds for requesting exclusion would be that some economic questions are liable to attract attention from those with more interest in some social, political or other agenda than in economic science and that their votes can be harmful to the site.
6.    Deletion by use of moderator powers should be limited to answers which are a) clearly offensive, or b) amount to non-answers, or c) contain contentious empirical claims that are BOTH not adequately backed up AND of a kind liable to attract attention from those with more interest in a social, political or other agenda than with economic science.
Category (c) is deliberately quite narrow.  The fact that a claim is a matter of academic dispute does not in itself qualify.  For example, Richard Carson and Jerry Hausman have published opposing views on the reliability of contingent valuation as a method of valuing environmental assets (see here).  A post taking one side or other in that dispute in itself would I think be unlikely to attract the wrong sort  of attention.  But if someone were also to make a claim about the value of a particular well-known environmental asset (New York's Central Park, say) then it might be judged likely to do so, and deletion (in the absence of adequate back-up) would I think be appropriate.
It is I suggest fairly straightforward to identify topics that might be liable to attract the wrong sort of attention.  An initial list might be any economic questions involving reference to race, gender, environment and climate change, and international disputes.
Category (b) is helpfully explained in Herr K's answer here.
7.    Deletion of an answer, whether by use of moderator powers or by the community via the low quality review queue, should normally be based on careful judgment.  Only in the most blatant cases should it be an instant decision.
I am not persuaded by the argument that a policy should be simple.  A simple policy will almost inevitably have unfortunate results in some cases.  It is true that if many answers are to be deleted by use of moderator powers, a simple policy will place less burden on moderators than a more complex one, and I recognise that the burden on moderators, who act voluntarily for no tangible reward, is an important consideration.  My proposal in 6 above, limiting the scope of deletion by use of moderator powers, would address that.
8.    Any application of a new policy to old answers should be preceded by a substantial grace period, allowing time for people to consider editing their answers to comply with the policy.
Many people have put a lot of effort into answers over the years, in many cases trying hard to comply with policies applying at the time and to tailor answers to the particular needs of questioners.  Some would probably be inclined to react strongly if deletion of many of their answers were to result, either suddenly or progressively over time, in significant loss of rep.
Comment: I think you make some good points about use of diagrams and other techniques that we should incorporate but I also have some criticism on some points.  On point 1. Originally the Economics.SE site had subtitle "For professional and academic economists and analysts" implying much narrower scope - this was changed by meta discussion, no reason why now it could not be changed back. If back then those people who wanted wider scope were not told to set up their own new site why should now the people who would narrow the scope down do so?
Comment: on the point 5 - 6 note that moderators not just community is quite heavily involved in deleting answers that do not follow some community standards on sci stacks. On physics even nonmainstream answers get deleted by mods (to make it clear I would oppose such policy on economics.se as I think heterodox answers/questions have their place here), so this would really not be huge expansion of power. In fact currently we are allowed to do so we just choose to self regulate ourselves. The policies above state objective criteria that can be followed I think by most people if they are just willing
Comment: In fact on the codidact I had some exchanges with monica on these topics  for proposed site for economics there (see [here](https://meta.codidact.com/posts/277995#answer-278491)) and she seems to agree that in order to create community the site should primarily be set up to attract experts - as Jmbejara often mentions experts attract wider audience not the other way around. 8 I fully agree with you, this is why I made provision for my proposal to apply the new policy to past answers only on case by case bases (meaning only to very bad answers, I would definetly not want to target excellent
Comment: @1muflon1 I think there are some nice things in this answer, but I don't like the part of this that puts limits on the ability of moderators to delete answers. It would be nice if the community could do all of policing, but the site doesn't have a critical mass to make this happen. I feel like this requirement would make it very, very difficult to enforce the new policy. I don't think we need to worry about moderator abuse. There are already other checks in place.
Comment: @1muflon1 Right. Your policy is different from Adam's. Your answer allows it to happen after 3 days.
Comment: 1. but also in the past it seems meta was frequented by more users. All past meta posts got more upvotes then recent ones, last y and this y  almost no post got more than 10 upvotes. 2. Note this proposal here does not change the scope of a site, my point 1 was just rebuttal to your point 1, but having a stricter policy on citation does not mean; a) we would disallow non-expert questions - this proposal is just for answers. B) disallow non-professionals from participation. It just follows the practices of other sci stacks and weeds out opinion answers that are discouraged on SE network anyway.
Comment: On the Monica Chello quote "Backing up an answer includes citing sources, making a logical argument, and sharing relevant personal experience." Monica is/was excellent mod but she used to mod sites where personal experience is more useful like Judaism or workplace etc. I dare to say that in science stacks like Physics.SE, Biology.se, Economics.SE personal experiences are not very helpful and scientifically not valid form of evidence. I can see them be  helpful in soft-questions where the back it up policy could have exemption as I proposed
Comment: or not just excellent but even good past contributions)
Comment: PS: I edited my original proposal. Now graphs are also included, and I removed the provision that would allow mods to delete very bad answers sooner than after 3 days (of having post notice), I think that this should be sufficient check on any potential moderator abuse - a)  it is enough to add sources for the user if the answer is based on some legitimate arguments b) 3 days is enough for an answer for any regular to see it, and thus see if post notice was appropriate or not and then complain on meta for cases where it was misapplied
Comment: @jmbejara I dont think it would be hard to enforce. It would not be perfect but I am personally not opposed to have some constraints. I think that anyone who would ever review my mod decisions would find that I always erred on the side of caution and acting too little rather than too much, but not all mods share this view, and even if I plan to mod for long time I wont be able to do that forever so I can see Adams concerns
Comment: Also, IMO, graphical argumentation that appears in economics really is a form of mathematical argumentation. I don't think it needs to be spelled out. @1muflon1 I think your answer before the last edit (some 14 minutes ago) was great.
Comment: @jmbejara thank you, I will consider rewriting it, you are right that graphical argumentation is a part of mathematical argumentation, but at the same time Adam (judging by most of his answers) is good economist but he somehow missed that as well I think some other people might miss it too so maybe just reminding users that it is part of mathematical argumentation is not so bad
Comment: @1muflon1 I don't think it would work at all. Take the example of gender inequality question. From my reading, under this "community only" policy, you would not be able to delete any of those answers. The community member with high enough reputation can only delete an answer if it has a score of -1 or lower. Because of all the laypeople voting, there is no way that answer would get to -1, even if we had dozens of new experts on our site.
Comment: @jmbejara no I disagree. 1. We would be able to delete the answer that was deleted by Kitsune (after 3 days - just not immidately) as that answer was just basked by opinion peace not directly by research. 2. next there are also couple of other answers that are not backed at all that could be deleted some already have post notices those would not pass this new policy as well. 3. Some things would probably fall through the cracks but no policy will be perfect there could always be abuse
Comment: @1 muflon1  In response to your first comment.  The change now proposed is significantly different from that in 2016.  I could point to the fact that [the 2016 proposal](https://economics.meta.stackexchange.com/questions/1646/its-identity-crisis-time/1647#1647) received more net upvotes (15) than have any of the current proposals - though there is time for that to change.  More importantly, the site itself did not significantly change in 2016; rather, the subtitle was changed to reflect what the site at that time had already become.
Comment: @jmbejara  Re your comment on the gender equality question, my point 6(c) would have allowed deletion of the low-quality answer by a moderator regardless of the number of votes it had received and without having to wait 3 days.


Access Denied even if permission is given

Question: I have this module, as admin users I can access this module normally. But when I add permission to other roles (and it saved), other users who have the permimssion couldn't access it. Please help me.
This is the code.
include_once(drupal_get_path('module', 'tb') .'/tb.menu.inc');
include_once(drupal_get_path('module', 'tb') .'/tb.inc');

function tb_perm() {
  global $user;
  return array('trial_balance');
}

function tb_menu() {
  global $user;
  $items = array();

  $items['akuntansi/tb'] = array(
    'title' => 'Trial Balance',
  'type' => MENU_NORMAL_ITEM,
    'page callback' => 'tb_neracapage',
    'file' => 'tb.inc',
    'access arguments' => array('akuntansi'),
    'access callback' => TRUE,
    //'type' => MENU_CALLBACK,
  );

  $items['akuntansi/tb/pdf'] = array(
    'page callback' => 'tb_neracapage_pdf',
    'file' => 'tb.inc',
    'access arguments' => array('akuntansi'),
    'type' => MENU_CALLBACK,
  );
$items['akuntansi/tb/xls'] = array(
    'page callback' => 'tb_neracapage_xls',
    'file' => 'tb.inc',
    'access arguments' => array('akuntansi'),
    'type' => MENU_CALLBACK,
  );

  return $items;
}

?>

Answer: Your implementation of hook_perm() (which is not valid for Drupal 7), only defines the trial_balance permission, not the akuntansi permission your code is trying to use.
The fact the user #1 has the permission to see those pages is just because the user #1 by-passes all the permissions; in fact, user_access() returns TRUE for that user.
  // User #1 has all privileges:
  if ($account->uid == 1) {
    return TRUE;
  }

To make it clear, without explicitly setting an access callback, the access arguments are expected to be an array with the user permission string, which in your case would be trial_balance.
If the module is for Drupal 7, then hook_perm() is not even used; instead, Drupal 7 uses hook_permission(), which is not a simple renaming of the previous hook. It is expected to return a differently structured array; using the same array as Drupal 6, will cause it to not properly work.


Null hypothesis is the opposite of study hypothesis or the one which states no difference

Question: My study hypothesis is that drug A will be at least 10% better than drug B. The most appropriate null hypothesis for this should be 1 or 2?

Drug A is not at least 10% better than drug B (i.e., the opposite of the study hypothesis)
Drug A and drug B are not different (0% difference)

I believe that option 1 is correct. Am I right?
Comment: I feel we need more information about the data for which you want to run your test and the type of test. But typically, the null hypothesis states that there is no effect (drug A equals drug B in your case) and the alternative hypothesis states that the population value is different from the null hypothesis. So, the test will determine whether you can reject the null hypothesis in favor of the alternative hypothesis.

Your first option seems to me challenging to develop because you are making assumptions on the effect size... which is strongly linked to the nature of your data.
Comment: I used this effect size to calculate the sample size. Hence, I assumed that the null hypothesis should be relevant to this effect size alone. In truth, I am just trying to prove that drug A is better than drug B.
Comment: null hypothesis would be that Drug A<=DrugB, is 10% the confidence interval?
Answer: The null hypothesis should be stated in a way that it
implies a specific probability distribution (called the 'null' distribution), which is used to compute the P-value.
In general, the alternative might be one-sided or two-sided.
Two-sided: $H_0: \mu_A = \mu_B$ against $H_a: \mu_A \ne \mu_B.$
Right-sided: $H_0: \mu_A \le \mu_B$ (or $H_0: \mu_A = \mu_B);$
against alternative $H_a: \mu_A > \mu_B.$
Left-sided: $H_0: \mu_A \ge \mu_B$ (or $H_0: \mu_A = \mu_B);$
against alternative $H_a: \mu_A < \mu_B.$
Based on the information provided, you need the left-sided alternative. Notice that the null hypothesis contains an $=$-sign
in all of the formulations---whether as $=, \ge,$ of $\le.$
[Different authors have various preferences about this.]
In any case, you should choose Answer (2).
The effect size (10% or whatever)
can be determined after you have data. If you want to be reasonably sure
to detect an effect of a particular size, then you need to do a 'power and sample size' procedure to see how many subjects should be used in the study.
I agree with @Pitouille that specifying the desired effect as "10%" better may lead to confusion. Ten percent of what? (More increase in red blood cells? decrease in blood sugar level? decrease in patient complaints of pain? increase in patient 'recovery"?
What will you do if the data from the study show a clear indication of "8%" better?
Abandon Drug A as useless? do a new study a double the dosage?
What will you do if Drug A shows slightly better results, but
not by quite enough to be statistically significant at the desired level?  These are important considerations that should influence the design of the study, but usually not for inclusion in the statement of $H_0.$
Comment: "do a new study a double the dosage"? Yes. Drugs do not give all or none effects and so statistical analyses that give all or none ('significant' or not) are not particularly helpful without thoughtful consideration. The habit of assuming that a singular statistical analysis (or a singular experiment) can reveal a truth is dangerous.
Comment: For the sample size calculation, I had assumed that the response rate with drug A will be at least 10% higher than drug B (absolute difference). That is why I had assumed that the null hypothesis would mean that the response rate with drug A is not at least 10% higher than drug B. If my study fails to reject this null hypothesis, the response rate of drug A can be: (1) better than drug B by a value <10%, (2) can be equal to drug B, (3) can be worse than drug B.

From the responses here, I believe that some of my assumptions may have been incorrect.
Comment: I understand now. Thanks!
Comment: Do you have a huge problem with the $10\%$ better part of the question? The way I see it, it seems straightforward, at first, to take $10\%$ of the value (I guess the mean) of drug B, but we know we didn't get exactly the population value of drug B's mean. Then the sample statistics make it into the null hypothesis. (I suppose the percentage difference could make sense if we are dealing with proportion data. $A=0.7$ and $B=0.65$ isn't good enough, because $A$ only beats $B$ by $0.05$ instead of the desired $10\%=0.10$.)
Comment: It is useful to distinguish between errors of Type I and II.  Type I error is to reject $H_0$ when it is true, and Type II is failing to reject $H_0$ when it $H_a$ is true. Significance level $\alpha$ is P(Type I) and power is 1 - PIType II). // State null and alternative first (where alternative includes 'research' hypothesis). Then determine rejection region for desired significance level. Finally, approx sample size req'd for reasonable power. Following this sequence helps to clarify null, alt hyp, sig level, power, and sample size. They are related, but you're entangling them needlessly.
Comment: Thanks for your clarifying comments along the way.


Characteristic Curves of $\frac{\partial{u}}{\partial{t}}+(a+b u)\frac{\partial{u}}{\partial{x}}=0$

Question: I reach to a problem in engineering, and I really appreciate if some body can help me. what is the characteristic curves of following quasi_linear equation:
$\frac{\partial{u}}{\partial{t}}+(a+b u)\frac{\partial{u}}{\partial{x}}=0$ which $a$ and $b$ are constant.
Comment: You want "the method of characteristics": https://en.wikipedia.org/wiki/Method_of_characteristics
Answer: $$\frac{\partial{u}}{\partial{t}}+(a+b u)\frac{\partial{u}}{\partial{x}}=0$$
The set of characteristic equations is :
$$\frac{dt}{1}=\frac{dx}{a+bu}=\frac{du}{0}$$
Necessarily $du=0 \quad\to\quad u=c_1 \quad$ which is the equation of a first characteristic curve.
A second characteristic curve comes from $\frac{dt}{1}=\frac{dx}{a+bc_1} \quad\to\quad (a+bc_1)t-x=c_2$
The equation of the second characteristic curve is : $\quad (a+bu)t-x=c_2$
The general solution od the PDE expressed on the form of an implicit equation is :
$$\Phi\left(u\:,\:(a+bu)t-x \right)=0$$
where $\Phi$ is any differentiable function of two variables.
Solving this implicit equation for the first variable leads to an equivalent form of the general solution :
$$u=f\left((a+bu)t-x \right)$$
where $f$ is any differentiable function.
Since $u$ appears in both terms of the equation, in the general case $u(x,t)$ cannot be expressed on explicit form insofar the boundary conditions are missing in the wording of the question. Without specified boundary condition, it isn't possible to go further and see if a particular solution can be explicitly derived.