Chapter 9 Introduction to the t Test t

Chapter 9 Introduction to the t Test

t Test for a Single Sample § Compare a sample mean to a population with a known mean but an unknown variance

t Test for a Single Sample § Estimating the population variance from the sample scores – Biased estimate of the population variance – Unbiased estimate of the population variance (S 2)

t Test for a Single Sample § Degrees of freedom – Number of scores that are “free to vary” – Formula for S 2 using degrees of freedom

t Test for a Single Sample § The variance of the distribution of means § The standard deviation of the distribution of means

t Test for a Single Sample § The t distribution – Varies in shape according to the degrees of freedom

t Test for a Single Sample § Cutoff sample score for rejecting the null hypothesis – t table § Sample mean’s score on the comparison distribution – t score

t Test for Dependent Means § Unknown population mean and variance § Two scores for each person – Repeated measures design § Same procedure as t test for single sample, except – Use difference scores – Assume that the population mean is 0

t Test for Dependent Means § Difference scores – For each person, subtract one score from the other – Carry out hypothesis testing with the difference scores § Population of difference scores with a mean of 0 – Population 2 has a mean of 0

Assumptions § Normal population distribution – t tests are robust to moderate violations of this assumption

Effect Size for t Test for Dependent Means § small d =. 2 § medium d =. 5 § large d =. 8

Approximate Power for t Test for Dependent Means (. 05 significance level)

Approximate Sample Size Needed for 80% Power (. 05 significance level)

Controversies and Limitations § Repeated measures designs – Have high power • Standard deviation of difference scores usually low – Weak research design without a control group

t Tests in Research Articles § t(24) = 2. 80, p <. 05