Inferences about Means of Dependent Samples Chapter 12 Homework: 1-4, 7 Problems 3, 4, & 7: skip parts i and l, do not calculate U in part n

Exam 3: Wednesday, May 3

Dependent Samples n Subjects are statistically related l 2 measurements of same individual l individuals that are related u IQ, GPA, married, etc n Order of data in each sample important n Not independent l must modify hypothesis testing ~

Dependent Samples: Examples n Pretest-posttest design u also called repeated measures l measure each individual twice l pretest ---> treatment ---> posttest l compare scores n Matched pairs l match individuals on important characteristic l assign to different levels of IV ~

Difference Score n D i = X i 1 - X i 2 l subject’s score in group 1 minus related score in group 2 l Requires same number of scores in each group n Mean difference score is sample statistic

Evaluating Hypotheses: Dependent Samples n Treat difference scores as if a single sample l same test just substitute difference score n Null hypothesis text: H 0 :  D = 0 (nondirectional) H 0 :  D 0 (directional) ~

Test Statistic n t test for 2 dependent samples l n = number of pairs of scores [df = n - 1] u standard error of the mean of differences ~

Test Statistic n Standard deviation of differences l same as for single sample 2 dependent samplesSingle sample

Example n Does drinking 3 oz of alcohol affect performance on an object recognition task? l n 1 = 6, n 1 = 6 l pretest-posttest l count number of errors 1. State Hypotheses H 0 :  D = 0 H 1 :  D  0 ~

Example 2. Set criterion for rejecting H 0,  =.05 l directionality? l df = l t CV =

Example

n compute s D

Example n compute test statistic [df = n - 1]

Example 4. Interpret results l Is t obs beyond t CV ? l decision: l practical significance u effect size index