Foundations of Statistics - Tutorial Week 8 The Paired Samples t-test Learning Objectives V Be able to produce a paired samples t-test in SPSS v Be able to write a report based on the paired samples t-test v Be able to distinguish between independent and paired samples Producing the Paired samples t-test using SPSS Paired samples t-test report writing Researchers predicted that tea would have an effect on cognitive function. A random sample of English adults took part in a study to test this claim. During a period of one week no tea was to be drunk - they then undertook a cognitive function test [0 - 80 with higher scores indicating higher cognitive function]. For the following week the participants were allowed two cups of tea per day. At the end of the week their cognitive function was then tested [using a different test - but of similar standard]. Use the Tea_Makes_You_Brainy.sav data file to test the prediction. Instructions for producing the Paired samples t-test are included in this handout. Before we conduct the paired samples t-test, we should check the assumptions 1. Independence of observation - we check for random selection. In this study, the English adults were randomly selected, so we assume this assumption has been met 2. Normality - the distribution of different scores in the population should be normally distributed Check the distribution of the sample difference scores if they come from a normally distributed population, if so, it is reasonable to assume the population of difference scores is normally distributed Difference = Tea - No_Tea (assume Tea is higher than No_Tea) Transform -> Compute Variables -> Create new variable called 'Difference' Page 1 of 6 Foundations of Statistics -
To check if this is normally distributed, we use the Analyze -> Descriptive Statistics -> Explore -> Ask for Histogram Histogram Mean = . 70 Std. Dev. = 8.207 N = 716 60 40 Frequency 20 0 -20.00 -10.00 .00 10.00 20.00 Difference 221 Difference 638 335 270 10583 -30.00 -20.00 -10.00 .00 10.00 20.00 30.00 The distribution of the difference scores in the sample appears to be normally distributed, which suggests that the population difference scores are normally distributed. Foundations of Statistics - Page 2 of 6
Our assumptions have been met, so we can do the paired samples t-test. To run the t-test we Analyze -> Compare Means and Proportions -> Paired Samples t-test Paired Samples Statistics Mean N 51.36 716 Std. Deviation 12.832 Pair 1 Cognitive Function Score (Max = 80) / With 2 cups Tea Cognitive Function Score (Max = 80) / No Tea 50.65 716 9.436 Std. Error Mean .480 .353 On average, cognitive function score is higher after 2 cups of tea than after no tea. Paired Samples Test Paired Differences 95% Confidence Std. Interval of the Std. Error Difference Mean Deviation Mean Lower Upper t df 8.207 .307 .102 1.306 Significance One- Sided Two- Sided p p Pai Cognitive .704 r 1 715 .011 .022 Function Score (Max