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SPSS makes it very easy for you to go beyond your sample data and make inferences about the population that those data came from, that is, you can calculate inferential statistics. In the last movie, we looked at how to work with proportions for a single dichotomous variable-- that's a yes/no, 0/1 variable-- to get a hypothesis test and a confidence interval. In this movie, we will do the same procedure for a scale variable, something that could be measured in set units, like time to complete a project or bids from vendors. I am going to use the same data set for this one, the GSS, or General Social Survey.sav, data set, and this time I'll be looking at the one variable here that's called FamilyIncome that measures the total family income in dollars.
Now I should point out that these are actually the midpoints for categories, which is why they seem to be very precise amounts, and you will see them repeated, like here's 115,841, and here's the same number again. Nevertheless, these are scale variables because the dollars move in set amounts. So I am going to be doing a hypothesis test and a confidence interval for the family income for the 349 people in this particular sample. Now there's two ways to do this, and both of them go in the Analyze menu.
For the first one, I am going to come up to Analyze and I am going to go Compare Means and I am going to use what's called the One-Sample T-Test. And all I need to do here is I need to pick the variable that I want. In that case, it's FamilyIncome. So I just double-click on that and it moves it over. Let's look at some of the options. I can get a confidence interval, and I can change it from 95% to some other values, sometimes 90% or 80% is appropriate, but 95% is the most common. So I am going to leave it right there.
So I'll click Continue. I'm going to ignore the bootstrap, because that's there because of an extra add-in that's installed in this version of SPSS that normally you have to pay for. Below the test variables box, I have another box that says test value, and this is the value that SPSS is going to compare the mean family income to, to find out if it's significantly different from it. Now I can guarantee you that the mean family income is not going to be 0, so I am going to pick another number to put there. Let's say, for instance, I want to compare it to $45,000 for family income.
This is how I can do it to find out whether this average value is higher or lower than that significantly. So now I click OK, and what I have is one sample of statistics. It tells me that I have 349 people, that the mean family income is $32,781 with a standard deviation of 29,000. The last one, the standard error, is used in calculating the hypothesis test and the confidence intervals. Below that I have what's called a One- Sample Test where SPSS is taking the average value, the mean of 32,781, and comparing it to a hypothesized value of $45,000.
The first column has what's called the t statistics, and that's an inferential statistic, and it doesn't necessarily mean a lot on its own. The second one is the degrees of freedom, which has to do with the sample size. It's the third one in particular that we want to look at. It says Sig. (2-tailed). That's the significant value, or the probability value for the hypothesis test. And in this case that number is 000. Now it's not literally 0. it's just it's less than 001, so it shows up truncated here. What this tells me is that the observed average value of $32,781 per year for a family is significantly different from my hypothesized value of 45,000.
I was optimistic in my hypothesis. Now these last two columns have what's called confidence interval for the difference from the mean. You see that the mean difference that's in the third column from the end is -12,000. That's because the observed value is about $12,000 less than my hypothesized value. These last two columns give me the confidence interval for that difference. Now an interesting thing here is had the hypothesized value been 0, these would have been an actual conference interval for the mean, but because I felt that having 0 would be a silly test value, I put something else in. The confidence interval is for the difference.
Now if I want a regular confidence interval, a better way to get that, instead of from the T-Test, is to go back to a procedure we looked at in the last set of the videos, the Explore command. I just go back up to Analyze > Descriptive Statistics > Explore. I take the one variable that I want out of this list, which is FamilyIncome, and I put it into the Dependent List, that means outcome variables, or the ones we are trying to chart. All I want here is a list of statistics. I am going to come down to Display and click on Statistics and press OK.
I'm going to get a big table here, but the only one I really want to look at is this one that says 95% confidence interval for the mean, with the lower bound and the upper bound. There's actually several ways of interpreting a confidence interval, but one sort of colloquial way is to say that the population value is between 29,692 and 35,871, so between 30,000 and 36,000. There is about 95% chance that the true population mean is between those two values. Anyhow, SPSS makes it simple to perform two of the most basic and two of the most useful inferential statistics for a single scale variable: the One-Sample T-Test and the simple confidence interval.
In the next movie, we will look at something slightly more complicated as we look at the distribution of cases across a nominal variable with several groups.
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