1. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Chapter 8 Introduction to the t Test

2. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall t Test for a Single Sample Used to compare the mean of a sample with a population for which the mean is known but the variance is unknown Unlike previous methods, one must now estimate the population variance from the scores in the sample

3. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall t Test for a Single Sample Estimating population variance from sample scores –Variance in sample generally slightly smaller than population Sample is a biased estimate of population So, divide by N-1 rather than N to correct for bias –N-1 is known as the “degrees of freedom,” the number of scores that are free to vary

4. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall t Test for a Single Sample Because variance is estimated, comparison distribution is not a normal curve –t distribution –Like a normal curve Bell-shaped Unimodal Symmetrical –But has more scores at the extremes (i.e., heavier tails) and varies somewhat according to degrees of freedom Sample mean thus has to be slightly more extreme to be significant with a t distribution than with a normal curve

5. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall t Test for a Single Sample Comparison distribution is the distribution of means –Figuring variance of the distribution of means –Figuring standard deviation of the distribution of means

6. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall t Test for a Single Sample Determine cutoff sample score for rejecting the null hypothesis (using t table) Figure sample mean’s score on the t distribution (t score)

7. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall t Test for Dependent Means Used to compare two sets of scores where there are two scores for each person –Repeated-measures –Within-subjects –Paired Compares mean difference score across pairs of scores against a difference of 0 under the null hypothesis. In other respects, t test for dependent means is just like a single sample t test with a population mean of 0

8. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Assumptions Assume that the population of individuals from which the sample was taken is normally distributed In practice, one seldom knows if a population is normally distributed –OK because many distributions in nature do approximate a normal curve –The t test is often still fairly accurate even when this assumption is violated

9. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Effect size conventions –Small =.20 –Medium =.50 –Large =.80 Effect Size Effect size for the t test for dependent means is –the mean of the difference scores –divided by the estimated SD of the population of individual difference scores Studies using the t test for dependent means typically have larger effect sizes and more power than do studies with participants divided into two groups