Introduction to the t statistic

Steps to calculate the denominator for the t-test 1. Calculate variance or SD s 2 = SS/n-1 2. Calculate the standard error

T-test Procedure Set the hypotheses (null and alternative) Set the decision criteria (by selecting the alpha level, directionality, and critical values). Compute the test-statistic (t) Compare obtained t-statistic to critical value(s) Make a statistical decision Concluding statement

Conducting a t-test It’s not a normal distribution, and you don’t use the unit normal table Using the t- distribution (William Sealy Gosset, 1908) instead

T-distribution Bell-shaped and symmetrical A ‘family’ of distributions - depends on the degrees of freedom The mean of the t-distribution is zero

T-distribution table When the df is NOT listed in the table provided in Appendix B, you should look up the critical t for both of the surrounding df values listed and use the LARGER value for t

Measuring Effect Size with the t Statistic (cont.) Estimated Cohen’s d

Measuring Effect Size with the t Statistic (cont.) percentage of variance accounted for = r 2 (aka  2 )

Assumptions for a One-sample t- Test 1. Independent observations 2. The sample data come from a normal population distribution

Example 1 The legal highway limit near populated areas in many parts of the US is 55 mph. To determine whether people exceed the 55mph, suppose a state monitored the speeds of 25 cars at selected highway locations. Can we conclude that the average speed is higher than the 55 mph limit?

Example 1 - Data Find the following: Mean SS s 2 s