Randomized trials can be used for many purposes. They can be used for evaluating new drugs and other treatments of disease, including tests of new health and medical care technology. Such trials can be used to assess new programs for screening and early detection, or new ways of organizing and delivering health services.
A planned trial was described by the Scottish surgeon James Lind in 1747. Lind became interested in scurvy, which killed thousands of British seamen each year. He was intrigued by the story of a sailor who had developed scurvy and had been put ashore on an isolated island where he subsisted on a diet of grasses and then recovered from the scurvy. Lind conducted an experiment which he described as follows: I took 12 patients in the scurvy on board the Salisbury at sea. The cases were as similar as I could have them … they lay together in one place and had one diet common to them all. Two of these were ordered a quart of cider per day.… Two others took 25 gutts of elixir vitriol.… Two others took two spoonfuls of vinegar.… Two were put under a course of sea water.… Two others had two oranges and one lemon given them each day.… Two others took the bigness of nutmeg. The most sudden and visible good effects were perceived from the use of oranges and lemons, one of those who had taken them being at the end of 6 days fit for duty.… The other … was appointed nurse to the rest of the sick. Interestingly, the idea of a dietary cause of scurvy proved unacceptable in Lind's day. Only 47 years later did the British Admiralty permit him to repeat his experiment-this time on an entire fleet of ships. The results were so dramatic that, in 1795, the Admiralty made lemon juice a required part of the standard diet of British seamen and later changed this to lime juice. Scurvy essentially disappeared from British sailors, who, even today, are referred to as "limeys."
When we carry out a study we are only looking at the sample of subjects in our study, such as a sample of patients with a certain illness who are being treated with treatment A or with treatment B. From the study results, we want to draw a conclusion that goes beyond the study population-is treatment A more effective than treatment B in the total universe of all patients with this disease who might be treated with treatment A or treatment B?
Under the assumption that the binomial distribution will approximate the normal distribution The probability of at least 52 of 100 attempts 0.3821 (high probability to be due to chance)
In probability and statistics, Student’s t-distribution (or simply the t-distribution) is a continuous probability distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. It plays a role in a number of widely-used statistical analyses, including the Student’s t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. The Student’s t-distribution also arises in the Bayesian analysis of data from a normal family. The t-distribution is symmetric and bell-shaped, like the normal distribution, but has heavier tails, meaning that it is more prone to producing values that fall far from its mean. This makes it useful for understanding the statistical behavior of certain types of ratios of random quantities, in which variation in the denominator is amplified and may produce outlying values when the denominator of the ratio falls close to zero. The Student’s t-distribution is a special case of the generalized hyperbolic distribution.
Binomial Experiment A binomial experiment (also known as a Bernoulli trial) is a statistical experiment that has the following properties: ■ The experiment consists of n repeated trials. ■ Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure. ■ The probability of success, denoted 