Which of the following statements is true if a study measures two groups on each of 27 variables,and the experimenter carries out a t test for independent means for each variable (that is,27 t tests)using the .05 significance level?
A)If any of the t tests are significant,there is clearly a difference between groups on all variables at the overall .05 level.
B)It is not proper to carry out any t tests in this situation.
C)The chance of a Type II error is high.
D)The chance of at least one t test being significant is greater than 5%.

Question

Quizplus · Accepted Answer

The chance of making a Type I error (false positive) for each t test is .05. Therefore, the probability of at least one t test being significant is greater than .05, which means that the chance of at least one false positive is greater than 5%. However, this does not mean that there is a difference between groups on all variables. The probability of making a Type II error (false negative) depends on the effect size, sample size, and variability of each variable, and cannot be determined solely based on the information given. Conducting multiple t tests increases the chance of making a Type I error, and adjustments such as Bonferroni correction or controlling the false discovery rate should be considered to reduce the overall Type I error rate.

Which of the Following Statements Is True If a Study