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PSYC*2040 Lecture #2.docx

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PSYC 2040
David Stanley

[email protected] t-test Outline 1. Independent-Groups t-test 2. Repeated-Measures t-test • Two populations (Guelph and Waterloo) • Do they like Bueller's to the same extent? • Random sample of 50 from Guelph, and 50 from Waterloo • Rate the movie on a hundred point scale • Want to know whether the populations like the movie to the same extent • Interested in EVERYONE in both schools, so we're making our best guess from our sample • Target product for the first half of the lecture • Ending result • You're writing to a general audience that may not know everything the instructor/TA knows!!! o Do NOT write it for the TA or for the professor!!! • Tested an assumption, it was violated, I took the required action • There's two versions of the independent t test: one when the assumption is true, one when the assumption is not true • Reported both means and SE of both groups, reported there was a difference, "significant", t-value, went as far as reporting the direction of the effect (one group enjoyed the movie more than the other one) • Need to say which group was different, the direction, don't just say they were different, say how they were different • The last bit, the wrap up, the take home message, so in case someone misunderstands it on the way, you use repetition to hammer home the most important part of your findings 1. Determine Required Analysis • Are you comparing a sample mean to a hypothesized population mean? • How many dependent variables? Are they continuous or categorical? • How many independent variables are used? Are they continuous or categorical? • Did University influence movie ratings? (one independent variables) • Did University and gender influence movie ratings? (two independent variables) • Repeated measures - was it the same people twice? Remember • How well did my sample mean estimate the population? • In this example, the University of Waterloo sample mean may overestimate or underestimate the University of Waterloo population mean due to random sampling • Similarly, the University of Guelph sample mean may overestimate or underestimate the University of Guelph population mean due to random sampling • Consequently, the different between the sample means may overestimate or underestimate the difference between the population means • There 's a real number that represents the Waterloo and Guelph population mean, there is a true difference. But we're not looking at that; we're looking at the difference between the sample means. Is that going to be the same between the sample means?? Null Hypothesis: H0: µguelph = µwaterloo • Population means identical if null is true, but you might see a difference between your sample means, but that difference is just due to random sampling • With the null hypothesis you assume that the mean enjoyment of the movie in the University of Guelph population is the same as the mean enjoyment of the movie in the University of Waterloo population (i.e., that the population means are the same). Therefore, a difference between the sample means is simply due to random sampling error Alternative Hypothesis: H1: µguelph ≠ µwaterloo • Population means are different, and we also see that reflected in the sample means being different • In both cases, there's different sample means: due to random sampling (null), or is it because the populations are different (alternative) • If you reject the null hypothesis, you conclude that the alternative hypothesis is correct. Specifically, you conclude that the sample means from the University of Guelph and University of Waterloo populations are so different that random sampling is not sufficient to explain the difference. Therefore, we conclude the mean enjoyment of the movie is different in University of Guelph and University of Waterloo populations Rejecting the Null Hypothesis • SPSS provides p-values (labelled Sig.). This value indicate the probability of obtaining the difference of your data due to random sampling/assignment if the Null Hypothesis is true. • If the null is true, how likely is it that I would get this result? • If the p-value is less than .05 we reject the Null Hypothesis can conclude the Alternate Hypothesis is correct • Then the population means probably aren't the same if they're less than that 5%, so it's the Alternative Hypothesis that is correct • One row per person • Independent and dependent variable, have a column for each of those • Red arrow • Need to click the Define Groups button • Put a dialogue box up, value for group 1: 1, value for group 2: 2 (because we used ones and twos to define the universities/our groups •Shows both of the universities, and their mean and standard errors •Why do we need to report standard error and not standard deviation? o Because SE is what most people want to know o Want to know how accurate that mean is o On average, how close is your sample mean to the population mean? o SD just says how spread people are, doesn't really matter Test Assumptions •Not yet doing the t-test 1. Random sampling from two clearly defined populations 1. Population values (e.g., movie ratings) are normally distributed a. No way to test it, in general we just assume that's true a. We can test number 3 1. Variances of the two populations are the same a. All our conclusions are about population variances, estimate! Based on sample • First two columns are regarded separately from the rest of the outcome • They test the assumption (F, Sig) • Two rows: equal variance is as
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