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Chapter 7

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:

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Chapter 7

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  1. Chapter 7 Introduction to the t Test Part 1: One-sample t test Oct. 1, 2013

  2. 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

  3. 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|

  4. One–sample t Test • Must estimate the population variance from the sample scores • Unbiased estimate of the population variance (S2) Sum of squared deviations Use N-1 to make S2 bigger than sample

  5. t Test for a Single Sample • Degrees of freedom • Number of scores that are “free to vary” • Formula for S2 using degrees of freedom Note: S2 indicates we estimated this from a sample ( always indicates population info)

  6. t Test for a Single Sample • Also need to find standard deviation of distribution of means (SM) • The variance of the distribution of means • The standard deviation of the distribution of means

  7. 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 tdistribution

  8. One-sample t Test • State null & research hypotheses • Assuming null is true, compute observed t statistic for your sample mean • Find correct critical t value based on your df • When do we reject the null?

  9. 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…

  10. 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)

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