PSYCH 240 1st Edition Lecture 19Section 11: Independent-Samples T-Test cont.Example-In an experiment, people read a series of jokes and rated each on a scale from 0 (not funny) to 100(hilarious). 30 participants were told that the jokes were written by a man, and a separate 30 were told that they were written by a woman. The “man” group had a mean rating of 48 with a standarddeviation of 16. The “woman” group had a mean rating of 41 with a standard deviation of 12. Withalpha = .01, does this sample provide evidence that the reported gender of the author affects humor ratings? oStep 1-Null Hypothesis: The humor ratings for the "man" group and the "woman" group comefrom populations with the same mean-Alternative Hypothesis: The humor ratings for the "man" group and the "woman" group come from populations with different meansoStep 2-oStep 3-Two-tailed-Alpha=.01-dfTOT=58-Tcv=-2.661,2.661If the alternative hypothesis is directional, you have to figure out whether you are looking for a positive or negative difference between meansIn this test you get to decide which condition is considered sample 1 and which is considered sample 2For a directional test always make sample 1 the condition that is hypothesized tohave a higher mean (which is not necessarily the one with a higher sample mean)If you do this then you will always need to use a positive critical value for a directional testThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.This is you subtract the one that should have a lower mean from the one that should have a higher mean, so the difference should be positiveoStep 4-Step 4 will have multiple steps this time-First you need to get the pooled variance estimate. If you are given standard deviations in the problem remember to square them to get variances-Next you need to estimate the standard deviation of the distribution of differences between means using the pooled variance estimate-Finally, compute toStep 5--2.661<1.92<2.661-Non-significant-The test failed to produce evidence that gender affects humor ratings. Independent T Assumptions-Normality: the test assumed that the original scores follow normal distributions-Equal Variance: the test assumes that the populations for both groups have the same variability-Violating these assumptions usually isn't a problem if you have equal sample sizes, but can invalidate the test if you don't Which Test To Use?-You'll need to figure this out in two contexts:oOn the final you might see hypothesis problems for any type of t test, and you have to figure out which one to useoYou will be given a general description of a study and the research question, and you have tofigure out which test to use-If the problem gives you two sample means (M) and to sample standard deviations (S), then you need to do an independent-samples t test-If the problem only gives you one sample mean (M) and one sample standard deviation (S), then you either need to do a single-sample t test or a dependent-samples t testoIf the problem says something about difference scored then it’s a dependent-samples t testoIf not, then it’s a single-sample t test-If you just get a general research description then you need to pull a little more through it-If the researched want to test the hypothesis that a population mean is a particular value, then it's a single-sample t test-Single-sample t test example:oThe state government offered a funding bonus to any school district if the teachers averaged higher than 3 hours of volunteer work per week. An official for one school district decided tosave herself some work. Before collecting data from all of the hundreds of teachers in the district, she took a random sample of 45 teachers. Based on this sample, she conducted a test to see if the sample provided evidence that the mean for all of the teachers in the district was higher than 3 hours per week. -If the researchers want to see if they have evidence for a difference between two conditions or samples, then it is either a dependent- or independent-samples t test-Comparing two conditions:oIts an independent t test if scores in one sample are completely unrelated to scores in the otheroIt’s a dependent t test if there is any potential link between the scores across the two samples-Ex. The same person, same married couple, same family, etc. provides scores in both samples-Independent-samples t test example:oResearchers want to know if stress affects short- term memory. They see how many digits people can repeat immediately after they hear them. 20 participants are randomly assigned to do this after they had to give an impromptu public speech (high stress condition), and 20 participants do the task without giving a speech (low stress condition). They conduct a test to see if this sample provides evidence that short-term memory capacity is different in high-stress versus low-stress situations.-Dependent-samples t test example:oParticipants saw lists of 12 words, and they had to recall as many words as they could after each list. For some of the lists, they had to try to recall the words in the same order as they were presented (order-recall condition). For the other lists, they could recall the words in any order they wanted (free-recall condition). Each participant completed 30 order- recall lists and 30 free-recall lists, and there were a total of 36 participants. The researchers conducted a test to see if their sample provided evidence that the number of words recalled was higher with free recall than order recall. Within v. Between-When we say "subject" we usually mean a person, but it really can be any unit that provides a score on a variable-For our example, the "subjects" are teams in the NBA-We are interested in whether or not NBA teams have home-court advantageoNull Hypothesis: The winning % across all MBA teams is equal for home and away gamesoAlternative Hypothesis: The winning % across all NBA teams is higher for home games than away gamesoBetween-subjects design:-Sample size=10. So we'll take a random sample of 10teams and look at their home winning %, then we'll take an independent random sample of another 10 teams and look at their away winning %---If we wanted to do an independent-sample t test, we would get a mean from each sample of 10 scores and take the difference between the means (home minus away)-We would compare this to a