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Chapter 7 Introduction to the t Test Part 1: One-sample t test Oct. 1, 2013 t Test for a Single Sample • Z test requires that you know from pop • Use a t-test when you don’t know the population standard deviation. • One sample t-test: – Compare a sample mean to a population with a known mean but an unknown variance Hypothesis testing procedure for t-test • Same general procedure: – Assume null hypothesis is true, relative to an alternate (research hypothesis) – Compute observed t statistic from sample data based on sampling distribution of the mean – Determine cutoff point (now a critical t) in comparison distribution based on – Reject the null hypothesis if your observed t value falls in critical region • |t observed| > |t critical| One–sample t Test • Must estimate the population variance from the sample scores – Unbiased estimate of the population variance (S2) S 2 (X M ) Use N-1 to make S2 bigger than sample N 1 2 SS N 1 Sum of squared deviations t Test for a Single Sample • Degrees of freedom df N 1 – Number of scores that are “free to vary” – Formula for S2 using degrees of freedom S 2 2 ( X M ) df SS df Note: S2 indicates we estimated this from a sample ( always indicates population info) t Test for a Single Sample • Also need to find standard deviation of distribution of means (SM) • The variance of the distribution of means S 2 SM N 2 • The standard deviation of the distribution of means 2 SM SM t Test for a Single Sample • For t-tests, relevant comparison distribution is t distribution (not the normal curve used before in z test) • The t distribution One-sample t Test • State null & research hypotheses • Assuming null is true, compute observed t statistic for your sample mean M t SM • Find correct critical t value based on your df • When do we reject the null? Note on t-table • When > 30 df, critical values only given for 35, 40, 45 df, etc. • If your df are in between these groups, be more conservative and use the lower df • Do example in class… One Sample t-test in SPSS • Use menus for: Analyze Compare Means One sample t Gives pop-up menu…need 2 things: – select variable to be tested/compared to population mean (use “self-esteem”) – Notice “test value” window at bottom. Enter the population/comparison mean here (use x.xx from past semester) – Hit OK, get output and find sample mean, observed t, df, significance value (if < .05, reject null)