Psychology 210 Spring, 2007 Lab 6: t-tests for Independent Samples and t-tests for Paired Samples As usual, log on and launch SPSS. The topic of the day is just what we’ve been covering in class most recently – paired and independent samples t-tests. The data file du jour is called fish prices.sav and is located on the class web page, as always: http://people.whitman.edu/~herbrawt/classes/210/psych210.html It contains information about seafood prices at a fish market in 1970 and 1980. Each row represents a particular species of fish or shellfish. There are four variables, each in its own column. The first column is simply the name of the kind of seafood. The second column specifies whether it is a fish or a shellfish. The third and fourth columns specify the price (in cents per pound) in 1970 and 1980, respectively. Paired samples t-tests A paired samples t-test allows you to compare the mean of a variable with the mean of a second variable (rather than comparing the mean of a variable to a static reference point such as 7, like we did last week). If one variable is consistently greater than or less than the other, I can reject the null. Otherwise I can’t. This is nice because sometimes you won’t have an obvious null value. This version lets you derive one from the data. To run a paired groups t-test, select Analyze Æ Compare Means Æ Paired-Samples T Test. This command tells SPSS to test the difference between the means of two variables (columns) against a null difference of 0. In this case, let’s see if there’s a consistent difference in fish prices between 1970 and 1980. Phrased in English, we’re testing the null hypothesis that fish prices don’t change in any consistent manner. If this is true, then the average price in 1970 should be about the same as the average price in 1980. I could also represent it like so: H0: µ1970 = µ1980 H1: µ1970 ≠ µ1980 If I wanted, I might choose to run a one-tailed test based on my knowledge of inflation. If I did, I would be testing the null hypothesis that fish prices didn’t go up from 1970 to 1980 (they either stayed the same or went down). H0: µ1970 ≥ µ1980 H1: µ1970 < µ1980To select variables for your t-test, click on the two you want in succession and they’ll be sent over as a pair, as shown. If you mess up and click the wrong variables, send them back, otherwise you’ll end up running several t-tests and have a cluttered output screen. Click ok, and the results will follow shortly… I’ve circled the important parts of the output above. Notice again that the important values are presented, including t, degrees of freedom, and significance. Just like the t-tests we’ve run in class, I can use these to decide whether to reject or retain the null hypothesis. The calculated t-statistic is -3.702, and is what SPSS gets from the same equation we’ve been using in class: DSDt0μ−= In this case, the appropriate conclusion is to reject the null hypothesis. I can tell this by comparing the significance level with my alpha of .05. For this test, it’s less, so reject the null. I could also reach the same decision by comparing the t statistic to a critical value from a lookup table, like we do in class (but comparing alpha is much easier!).If I were reporting these results in a paper or other scientific communication, I’d write it like so, making reference to the relevant numbers (t, df, and sig) from the output: “Seafood prices in 1980 were reliably different from Seafood prices in 1970, t(13) = -3.702, p < .05”. Incidentally, the probability reported is for a 2-tailed test. If you’re running a one-tailed test, you simply need to divide the given probability (.003) by 2 (yielding .0015). Think about that for a second and see if you can explain why (I think it helps to sketch a quick diagram of the sampling distribution). If you can explain it, then you’ve got a good understanding of the conceptual relationship between one- and two-tailed tests. Note that this demonstrates why it’s important to notice that the upper table reports the group averages. These can be informative, and are critical to check if you’re running a one-tailed t-test, since you need to make sure the difference is in the direction you predicted, not the opposite direction. t-test for Two Independent Groups Now let’s run an independent groups t-test. Select Analyze Æ Compare Means Æ Independent-Samples T Test. The following window will appear, prompting you for a test variable and a grouping variable. These are sometimes called dependent variables and independent variables, respectively. In this case, I want to see whether there was a consistent difference between the prices of fish and shellfish in 1980. Send the test variable (price in 1980) over to the window marked Test Variable. The grouping variable (seafood type) goes to the window marked appropriately. The final step is to indicate how your grouping variable is coded. To do so, click on Define Groups and specify that group 1 (fish) will be designated by the number 1, and group 2 (shellfish) will be designated by the number 2. Note that the number assignments at this step aren’t arbitrary – they’re assigned based on the value labels already defined on the variable view spreadsheet (which I’m pointing out because you weren’t here for that part!). Thus, if you ever forget or just don’t know which numbers are associated withwhich labels, you can check there under value labels. It sure seems like SPSS should be able to figure that out on its own, but apparently it’s not there yet. Maybe the next version… Any time you run an independent samples t-test, the test variable should be a scale variable (interval or ratio), and the grouping variable should be a nominal variable. Otherwise your results will be nonsense. Perhaps even more so than you expected. Click ok and hold onto your hat… The output should look something like this: The first table contains some descriptive statistics that should be familiar – mean, standard deviation and standard error. It’s the second table though, that is the important one. Ignore the first two columns (labeled F and Sig) and the row marked equal variances not assumed for now – we’ll save those for another day. But you should be able to identify the rest. Take a moment to confirm that you know exactly what SPSS is doing here... In