Jaymie Ticknor Quantitative Methods 2317 Sect 001 26 and 28 February 2014 Lecture 7 Introduction to t tests Single Sample and Dependent Means Chapter 7 Hypothesis Testing knowing population mean and variance is rare in psychological research T test for a Single Sample used when we have a sample of individuals and we want to compare our sample to a population in which we know the mean but not the variance use t test Need 2 new things need to estimate population variance because it is not given to us when have to estimate the population variance shape of comparison distribution isn t quite normal so we need to use a different table in the back of our book cut off scores will be different as well Use formula to find estimated population variance S2 X M 2 N 1 N 1 degrees of freedom df M S2 N M S2 N S2 SM S2 Step 2 Estimating population variance distribution is close to normal but not quite because there is more room for error slightly more extreme means than exact normal curve larger the sample size closer to normal Different type of table to get cut off value need a slightly more extreme value to reject the null hypothesis than when you use a z test t M M SM T test for Dependent Means used when you have two scores for each person in your sample repeated measures design study same person multiple times called dependent means because the two means are dependent on each other because they come from the same person or similar people relational desirable and power increases Use difference scores for each person subtract one score from the other also called change scores Test the null hypothesis that there is no difference between the two groups of scores no difference mean of the population of difference scores is zero Measure participants levels of happiness before AND after Assumptions of the T test most statistical tests have assumptions requirements that are necessary for the test to work correctly One assumption of the t test and most of the tests we will learn about is that the sampling distribution is normally distributed population is normally distributed remember that the sampling distribution approaches normality when sample sizes are large even if the population is not normal Effect Size for T test for Dependent Means d 1 2 S Repeated Measures Design Dependent Measures Test Advantages larger effect sizes than other designs higher power standard deviation of difference scores is low Disadvantages alternative explanations for change