Introduction to the t Test Part 1: One-sample t test Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014

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) Sum of squared deviations Use N-1 to make S2 bigger than sample

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)

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

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 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)