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In the last few movies, we have looked at procedures that can compare the average score of two or more groups on a single variable. However, there may been times when you are more interested in comparing the same group on two variables, either the same idea measured at two point in time or on two related variables that are on the same scale. In that case, you will want to use something called a paired t-test also known as a within subjects t-test or repeated measures t-test. The nice thing about this test is that each person serves as their own little comparison or control group which makes it much more precise.
In fact, what's really going on with this test is that you are getting the difference between each variable for each person and you're looking at that change between the two and then doing simply a one sample t-test on those different scores, just like we did in an earlier section. For this example, I am going to be using a new dataset that's called Success.sav. This is from a survey of adults in the Midwest on how much money they felt a person needed to earn annually to be considered successful as the first variable, and then also how much money they felt a person needed to earn annually in order to be happy and we are looking at whether there's a difference in the means between these two groups.
To do this, we come up to Analyze, to Compare Means, to the Paired Samples T-test, and what you need to do is select two variables at a time. This is easy because we only have two variables. So I select the both of them over here, I am Shift+clicking, and then you move them over to the right as a paired variable. Now let's take a quick look at the Options. You get a Confidence Interval of the difference as 95% by default. You can change it to 90 or something if you have a really small sample. Also, you can talk about how you exclude cases either by analysis-by-analysis or list wise but since we are only making one comparison, these will be the same.
So I am just going to press Continue and then here I will press OK. We get a few tables of output from these procedures. The first one gives the Descriptive Statistics for the two variables. So for instance, we see that for this particular sample, the average amount of money that people felt a person needed to make annually to be considered successful was $64,000. That had a standard deviation of about $35,000. On the other hand, the amount of money that people thought a person needed in order to be happy was lower at about $42,000 a year, with a standard deviation of about $33,000.
That table also has the standard error of the mean at the end. That simply goes into calculating the inferential statistics and we don't need to deal with it directly. The second table is the Paired Samples Correlation, because these are the scores for the same group of people each person answered the both of them, you can calculate a correlation and we see here that we have a statistically significant positive correlation. What that means is people who put a high answer for one question, for instance, how much he needed to be successful, are also more likely to put a high answer for how much you needed to be happy and vice versa.
People who put a low answer would generally put a lower answer for the both of them. But the important question about whether people put different answers for the two of these is answered in the next one. We see that if we take each person's response to the question how much money you need to be successful, and subtract the amount of money you need to be happy, the difference between those is about $22,000 a year with a standard deviation of $30,602. The standard error for that difference is next, but we can ignore that and then we have a Confidence Interval for the difference and this lets us know that while the difference in this particular sample was about $22,000 a year.
In the larger population the difference between the amount of money you need to be successful and to be happy could be anywhere between $16,700 and $27,600. The next column that says T. That's the actual inferential test. That's the one sample t-test. We have a value of 8.079. The next column, the decrease of freedom is related to how many people there are in the sample. The last one here of interest and that is the significance level, the probability value for the hypothesis test. In this case, it says 000 and that means it is actually less than 001.
It's a very small probability value and this means that this is a statistically significant difference. On the other hand, looking up at the top table where the first mean was $64,000 and the second mean was $42,000, we can see there is a big difference of $22,000 between what people believe you need to make to be successful and what you need to be happy. So this example shows another variation on the procedure that SPSS gives you to compare means, only this time it compares means on two different variables for a single group of people.
I should mention it's also possible to look at changes in several points in time or differences in the evaluations of several different products and variables but those procedures become rather complicated and we won't address them in this course. We will, however, start looking at ways to explore the relationships of three or more variables at a time, starting with the next movie.
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