 from that population∗ Want to talk about the larger population fromwhich the subjects are drawn, not theparticular subjects!
What Do We Test ?∗ Effect or Difference we are interested in∗ Difference in Means or Proportions∗ Odds Ratio (OR)∗ Relative Risk (RR)∗ Correlation Coefficient∗ Clinically important difference∗ Smallest difference considered biologicallyor clinically relevant
Hypothesis TestingGoal: Make statement(s) regarding unknown populationparameter values based on sample data∗Elements of a hypothesis test:∗ Null hypothesis - Statement regarding the value(s) ofunknown parameter(s). Typically will imply no associationbetween explanatory and response variables in ourapplications (will always contain an equality)∗ Alternative hypothesis - Statement contradictory to the nullhypothesis (will always contain an inequality)
Null Hypothesis∗ Usually that there is no effect∗ Mean = 0∗ OR = 1∗ RR = 1∗ Correlation Coefficient = 0
Alternative Hypothesis∗ Contradicts the null∗ There is an effect∗ What you want to prove ?
Null Hypothesis expresses no differenceExample:H0: µ = 0Often said“H naught” Or any numberLater…….H0: µ1 = µ2
Alternative HypothesisH0: µ = 0; Null HypothesisHA: µ = 0; Alternative HypothesisResearcher’s predictions should bea priori, i.e. before looking at the data
Estimation: From the Sample∗ Point estimation∗ Mean∗ Median∗ Change in mean/median∗ Interval estimation∗ 95% Confidence interval∗ Variation
Parameters andReference DistributionsContinuous outcome data∗ Normal distribution: N( μ, σ2)∗ t distribution: tω (ω = degrees of freedom)∗Mean = (sample mean)∗Variance = s2(sample variance)Binary outcome data∗ Binomial distribution: B (n, p)X
Hypothesis TestingGoal: Make statement(s) regarding unknown populationparameter values based on sample dataElements of a hypothesis test:∗ Test statistic - Quantity based on sample data and nullhypothesis used to test between null and alternativehypotheses.∗ The test statistic is found by converting the sample statistic(proportion, mean or standard deviation) to a score (z, tz, t or xx22))
∗ Critical region (Rejection region): Values of the teststatistic for which we reject the null in favor of thealternative hypothesisCritical Region, Significant level,Critical value and p-value
∗ Significant level (α ): the probability that the teststatistic will fall in the critical region when the nullhypothesis is actually true.Critical Region, Significant level,Critical value and p-value
∗ Critical value: is any value that separates the criticalregion from the values of the test statistic that do notlead to rejection of the null hypothesis .Critical Region, Significant level,Critical value and p-value
∗ Two tailed: the critical region is in the two extremeregions (tails) under the curveTwo-Tailed, Left Tailed, Right Tailed
∗ Left tailed: the critical region is in the extreme leftregion (tails) under the curveTwo-Tailed, Left Tailed, Right Tailed
∗ Right tailed: the critical region is in the extreme rightregion (tails) under the curveTwo-Tailed, Left Tailed, Right Tailed
∗ P-value (p-value or probability value: is theprobability of getting a value of the test statistic thatis at least as extreme as the one representing thesample data assuming the null hypothesis is true.∗ The null hypothesis is rejected if the p-value is verysmall such as 0.05 or less.Critical Region, Significant level,Critical value and p-value
Reject the null hypothesis (or other)Fail to reject the null hypothesisProve the null hypothesis to be trueAccept the null hypothesisSupport the null hypothesisStatisticallycorrectOk but misleading
∗ Traditional Method: Rejection of the null hypothesisif the statistic falls within the critical region Fail to reject the null hypothesis if the test statistic doesnot fall within the critical region∗ P – value methodP – value method: rejection H0 if p-value < α (where αis the significant level such as 0.05)Decision Criterion
∗ Another option:Another option: Instead of using a significant levelsuch as α = 0.05, simply identify the P value and leavethe decision to the reader∗ Con