Hypothesis tests Single sample Z Zobs Hypothesis tests

Hypothesis tests Single sample Z ( Zobs= ) – (μ ) _________

Hypothesis tests Single sample t ( tobs= ) – (μ ) _________ SX

Hypothesis tests Two samples? tobs= ( ? ) – (? ) _____ (? ) ? = Depends on type of two-sample (t) test Related scores (dependent) Unrelated scores (independent)

Two Sample Tests When do use dependent t test? When scores are related Same person is on both conditions Pre-post design When participation in on condition does not affect performance in other condition When scores are matched on meaningful variable Steroids and weightlifters GPA and SAT scores

Two Sample Tests Advantages of dependent t test Matched scores have less error/variability Unrelated (Observed Value) – (Expected value under H 0) _____________________ Standard error of H 0 distribution (Large) Related (Observed Value) – (Expected value under H 0) _____________________ Standard error of H 0 distribution (Small)

Two Sample Tests Obstacles to using dependent t test • If impossible to participate in both conditions Normal vs. Parkinsons Men vs. Women • If participation in one condition affects other conditions Conjunction fallacy Solving a reasoning problem • If unequal number of participation in two conditions

Two Sample T-test Dependent Means Compute difference scores for all PAIRS of subjects And then use the ordinary one-sample t test D = Difference score = X 2 – X 1 Degrees of freedom = (Number of Pairs)-1

Dependent T-test Outline of hypothesis evaluation I. State null and alternative hypotheses H 0 : Dobs = 0 H 1 : Dobs = 0 II. Collect a sample and compute the observed values of the sample statistic and the test statistic III. Set the criterion for rejecting H IV. Interpret the results

Dependent T-test