The normal distribution is centered at the mean, μ. What is the consequence in this case? Standard Normal DistributionĬharacteristics of the standard normal distribution Type II error-occurs if Drug B is truly more effective, but we fail to reject the null hypothesis and conclude there is no significant evidence that the two drugs vary in effectiveness. Type I error-occurs if the two drugs are truly equally effective, but we conclude that Drug B is better. Efficacy is measured using a continuous variable, Y, and. Two drugs are to be compared in a clinical trial for use in treatment of disease X. However, in practice we fix α and choose a sample size n large enough to keep β small (that is, keep power large). Ideally, both error types (α and β) are small. Using the p-value also satisfies this criteria. Note that here we compared the test statistic to the critical value.A statement of whether the effect (observed difference) is statistically significant and the significance level (α).The test statistic and degrees of freedom.Note, this should be reported regardless of whether or not it is statistically significant!.a 69.8 unit mean decrease from 1952 to 1962.The magnitude, direction, and units of the effect (observed mean difference).(The mean difference in the previous example) A statement of the null hypothesis and alternative hypothesis in terms of the population parameter of interest.Since the absolute value of our test statistic (6.70) is greater than the critical value (2.093) we reject the null hypothesis and conclude that there is on average a non-zero change in cholesterol from 1952 to 1962. For a significance level of 0.05 and 19 degrees of freedom, the critical value for the t-test is 2.093. The critical value 2.093 can be read from a table for the t-distribution.Ĭholesterol levels decreased, on average, 69.8 units from 1952 to 1962. For this example, the sampling distribution of the test statistic, t, is a student t-distribution with 19 degrees of freedom. The decision rule is constructed from the sampling distribution for the test statistic t. H 1: There is an average non-zero change in cholesterol level from 1952 to 1962ĭecision rule: Reject H 0 at α=0.05 if |t| > 2.093 H 0: There is no change, on average, in cholesterol level from 1952 to 1962 The p-value, the probability of a test result at least as extreme as the one observed if the null hypothesis was true, can also be calculated.Įxample - Paired t-test of change in cholesterol from 1952 to 1962ĭ is the difference in cholesterol for each individual from 1952 to 1962 if the value of the test statistic falls outside the critical region, then there is not enough evidence to reject the null hypothesis at the chosen significance level.if the value of the test statistic falls inside the critical region, then the null hypothesis is rejected at the chosen significance level.This region is chosen such that the probability of the test statistic falling in the critical region when the null hypothesis is correct (Type I error) is equal to the previously chosen level of significance (α). Based on the hypotheses, test statistic, and sampling distribution of the test statistic, we can find the critical region of the test statistic which is the set of values for the statistical test that show evidence in favor of the alternative hypothesis and against the null hypothesis.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |