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In the last movie we looked at the general purpose means procedure, which is a recent addition to SPSS's bag of the analytic tricks. That procedure allowed us to compare for example, the means of two groups on scale variables. However, SPSS also has a specialized procedure for this comparison that's been around since version 1.0 as mainframe and punch card days. That is the Independent Groups T-Test. It's called the Independent Groups because it's comparing the means of two different groups as opposed to for example, the means of the same group on two different variables or two different points in time which we will cover later.
Because this procedure gives a few more pieces of information than the means procedure does, we will take a close look at it too. For this example, I am going to use the same GSS data set and the same variables that I did in the last one, when we look at the means procedure, so you can compare the results of the two of them directly. To compare the means with the Independent Means T-Test I go to Analyze, come down to Compare Means, and I go to the third choice which is the Independent Samples T-Test. From there, I need to pick the Test Variable, those are the ones that I am looking at for outcomes.
In this particular case, I am going to look at Family Income. You can see, however, that I can do a lot more at once. Then I have the Grouping Variable, sometimes called the independent variable or the predictive variable. It's the groups with the different means. In this case, I am going to use the Dance Performance question. So I can click that and I move it into Grouping Variable. However, with this procedure, I need to explicitly tell SPSS what the codes are for the two different groups. So I click on Define Groups and I tell it that I am using a 0 and a 1.
Now the interesting thing about this is that it means that if you have more than two groups, you could select two at a time to compare them here. Also, if you are using a scale variable as your predictor, you can select a cut point. For instance, people above 7 on a 0 to 10 scale. But I am just going to put in that this is a 01 indicator variable and I will Continue. Under Options, it asks me what Confidence Interval Percentage I want to use. 95% is the default and it's used when you have at least reasonably large samples.
It may be if you have a small sample, that you would want to use a smaller number like 90% or maybe even 80% but generally we stay with 95%. Also there's a question about whether I want to Exclude cases, analysis by analysis, that's if I had several variables I was looking for Group Differences on and that means that if they were missing it on, for instance, the first variable, they wouldn't be included there but they would be included by other ones, or whether I want to exclude cases list wise, which means if they're missing the score on any of the variables, they get left out entirely.
That gives you consistent sample size across tests. Now I'm only doing one outcome variable. So it would give the exact same thing anyhow. I am just going to leave it as default. I will press Continue, then I will press OK. And what I have here are a couple of tables. The first one is the Group Statistics. Now this is the same as what we saw in the Means procedure. This tells means that 76 people said they saw a dance performance in the last year and that their average income, their Mean, was about $47,000 with a Standard Deviation of 36,000.
On the other hand, we have a new column here down it's called the Standard error of the mean and that actually is the standard deviation divided by the square root of the sample size. But it's something that's used as part of the inferential procedure. So we usually don't need to deal with that one directly. The second table, it says Independent Samples Test and this is where we have the inferential procedure. What's interesting though about doing this command in SPSS is that it actually gives us two procedures. The first one, in the Columns it says, Levene's Test for Equality of Variances.
This is a specific test for an assumption for a valid t-test and the idea here is that their groups shouldn't be too different from each other in how spread out their scores are. And what we see here in the top table is that the one group had a standard deviation of 36,000 and the other group had a standard deviation of about 26,000. And what the Levene's test tells us is that these two groups do not have equal variances, which are related to the standard deviation. As such I really shouldn't use a standard t-test, which is the one across the top; and instead I should use one that has something called Fraction of Degrees of Freedom and that's the one on the second row.
One the other hand, they give functionally the same output. Let's look at this test. It says T-test for quality of means, and we have three members. We have the T that's the actual value of the test statistic, then we have the Degrees of Freedom which is used in calculating the probability value. The third one, Sig (2-tailed), is the actually probability value and the result of the inferential test. In both cases, it comes out as 000. Again it's not literally zero. It's just is less than 001.
So, regardless of which test we use, we find that there is a highly significant difference in the means between these two groups. And if I scroll over to the right a little bit, I can see the rest of this table and what it does is it's giving me a 95% confidence interval of the difference between the two groups. And you could see, it's slightly different for these two verses of the T-Test but in either case, we have a large difference in the means. It's about $18,000 and the confidence intervals are somewhere between $9,000 and $27,000, difference between those who say they have seen the dance performance last year and those who haven't.
So the specialized procedure for comparing the means of the two different groups, the independent samples t-test, it's a convenient test. It provides a few extra options over the general purpose means procedure and if you have more than two groups you may want to look at another specialized procedure called the one-way analysis of variance, which we will turn to next.
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