July+29th+slides - Quantitative Methods in Psychology July...

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Unformatted text preview: Quantitative Methods in Psychology July 29th, 2009: t-test week Jeff Vietri Corresponding to chapter 11 in the text Today's Agenda • Answer any questions about homework • Introduce paired-samples t-test • Compare t-tests Repeated-sample t-test Repeated-sample • Since human behavior is so variable, Since researchers want to eliminate as many confounds and nuisance variables as possible possible Variability across Ps • There are times when our individuals will be so different on the DV that an independentsamples test lacks sensitivity to pick up differences – Think of an intervention where each sample includes people who are at the extremes on the DV • Harvard grads & HS dropouts in academic achievement • Track stars & couch potatoes in a test of running shoes – Given within-group variability, we are unlikely to detect the differences made by the intervention Example Example • I want to test the effects of sleep on memory want in humans. in • Randomly sample people to be included in my Randomly study study • Randomly assign people to either be in my sleep Randomly deprivation (experimental) condition or control condition condition • I find no significant difference on memory find between the two groups between Example Example • Perhaps, sleep deprivation does not affect Perhaps, memory (H0 is true). (H0 • Perhaps, by chance the people in my sleep Perhaps, deprivation group had better memories to begin with than my control group, and it compensated for the decrease in memory caused by sleep deprivation (H0 is not true, but individual differences masked the effect of treatment). differences • I assumed the groups are the same for all assumed relevant variables at the beginning of the study but that might not be true but Repeated measures Repeated • Subject variables could be confounding Subject experimental variables • A more effective way is to do my study is more to eliminate these subject variables by measuring the same individual both with and without treatment and • Repeated measures (within-subject design) Subjects are compared against design) themselves if data is collected at two different times different • In contrast with independent samples In (between-subject design) (between-subject • A similar method: Matched subject – Each subject in one group matched with a Each subject in the other group (e.g., baseline memory) memory) • This design dramatically reduces error (of This measurement) and increases the power of a study study Repeated measures Repeated • Each individual is compared with him/her self Each (or a matched subject who is similar) to eliminate subject variables as confounds eliminate • We analyze the difference scores. Then, treat We these difference scores as raw scores in onethese sample t-test . t= M D − µD t= sM D Statistic – Parameter Amount of error Null hypothesis states it is 0 sM D = sD n Repeated Samples t-Test Repeated Repeated Samples t-Test Repeated • Do students learn differently Do when texting? when Student 1 2 3 4 5 6 7 No SMS 5 6 8 9 6 7 12 SMS 4 6 7 6 7 6 9 M D − µD t= sM D sM D = sD n = sD 2 n • MD = mean of the difference scores – Add all difference scores and divide by the number of Add difference scores difference • Df = n-1 • Note that this is the number of pairs of difference Note scores! scores! • sMD = estimated standard error of the difference scores scores – Standard deviation of the difference scores (sD) divided by the square root of nD divided – Once you create all the difference scores, you can Once treat them as regular scores and find their SS and s2 and s. SS A researcher obtains t = 2.35 for a repeatedresearcher measures study using a sample of n = 8 measures participants. Based on this t value, what is the correct decision? --- FIRST, α = .05 , THEN α = .01 correct • A sample of n = 16 high school students took the sample SAT before and after a special training course. For each student, the difference between the first score and the second score was measured, and the results showed that their SAT scores averaged MD = results 18 points higher after the course with SS = 6000. On SS the basis of this sample, can you conclude that there was a significant difference after taking the training course? Use a two-tailed test at the .05 level of significance. significance. Repeated Samples t-Test • Advantages – Need less participants since uses participants Need more efficiently more – Good at studying changes over time – Reduces/eliminates individual differences • Assumptions – Independent observations – Distribution of difference scores must be Distribution normal normal Repeated Samples t-Test Repeated • If can control or eliminate other sources of If variability then do it variability • Reducing variability within groups is Reducing important important • Use your brain if you're conducting Use research; are you introducing confounds by your design? by – order/maturity effects • Can you eliminate them somehow? – Counterbalanced designs? Summary Summary If we know the population parameters (µ and σ): Single-sample z-test Single-sample If we know µ, but not σ: but Single-sample t-test Single-sample If we don't know µ/want to compare two unrelated If µ/ samples Independent-samples t-test Independent-samples If we don't know µ/want to compare pairs of scores If µ/ Paired-samples t-test ...
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