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For many people, when they think of statistics, they think of inferential statistics, and not always fondly. Of course, there is much more to statistics and data analysis than the calculation of probability values, and this should be evident by the amount of time we spent so far on graphics and descriptive statistics. However, the ability to go beyond the data at hand and make inferences about a larger group of people--hence the name inferential statistics--is one of the great beauties of analysis. In this set of movies, I want to start with the simplest kinds of inferential statistics, those for one variable at a time.
There are few different procedures that we'll cover, such as confidence intervals and hypothesis tests, for scale variables and proportions, as well as the distribution of a single categorical variable. But let's start with what is probably the simplest and most familiar, the confidence interval and hypothesis test for a single proportion. For this example, I'm going to be using the GSS.sav data set. That stands for General Social Survey. And it has one variable on the end here that I think is interesting. If I scroll to the end, I have a variable here that's called ReadBook, and what it means is whether the person says that they've read a novel, a poem, or a play in last year.
We might be interested in the percentage of people who say that they have read one, whether that is significantly higher then, for example 50% and what the confidence interval for that might be, like you would get from a political poll where they say 73% of respondents plus or minus 3% who are in favor of a particular candidate. To do this, I'm going to many use one of SPSS's more interesting features. It's called nonparametric tests, and I get to it by going to the Analyze menu, down to Nonparametric Tests.
It's called nonparametric because we're not using parameters like means and standard deviations. Then I come over to One Sample. And here it will do a lot of things automatically, but I'm going to be a little bit selective and customize it to actually make things simpler for right now. The first thing I'm going to do is I'm going to come here to Fields, and that really means variables. And right now it's putting in nearly every variable. It would test for equality of distribution on categorical variables, and it would also test for scale variables, whether they are normally distributed like a bell curve.
I don't want to do all of that, so what I'm going to do is I'm going to take all of these variables, I'm going to put them back into the original field. The only test variable that I want is this one: Read Novel, Poem, or Play. So I'll double-click to move that over. Then I go to the Settings tab to choose exactly what test it is that I want to do. Now I'm going to do Customized tests here, and I'm going to choose Compare the observed binary probability--binary means two answers: yes or no--to the hypothesized value with what's called the binomial tests.
And click on Options, and what it's going to do is it's going to do a hypothesis test to see if the proportion of people who say they've read a novel, poem, or play in the last year is statistically significantly different from a hypothesized proportion, which right now I'll leave at 50%. I can also get what's called the confidence interval. That's like the plus or minus 3% in a political poll. Now sometimes you can use conventional statistics, but right here SPSS is doing a very nice thing and it's letting me use what's called an exact statistic. In this case, it's called the Clopper- Pearson for the confidence interval.
We don't need to go into any details except to say this would be a good choice. So I'm just going to click on that and I'm going to come down and press OK, and then I'm going to press Run. Now the output for this looks little different from what we've had so far, because it's a table with colors and shading in it. Also, it's not showing me everything right now. This is actually what's called a model viewer. Now right now, all it's telling me is that the proportion of people who say they've read a novel, poem, or play in the last year is significantly different from 50%. It's not telling me what's the actual proportion was or how far away it is, but I can get that through going onto the Model Viewer.
I'll double-click here and it brings up the Model Viewer. I'll maximize that window. And what I have here is the output that I saw on the other page. It tells me that the proportion of people who say they've read one of these is not 50%. It's significantly different from 50%. In fact, what I can do is I can come over here and the hypothesized, that 50%, is this blue bar right here. But what I really have is an observed 71% of the people say that they've read a novel, poem, or play in the last year. That's out of 349 people, and this tells me that that is significantly different from 0.
To get the confidence interval, I need to do one other thing. I come back over to this left pane and I go down to where it says View. Right now we're looking at the Hypothesis Summary. If I click on that, I can get the Confidence Interval Summary. It's a slightly different table here, and it tells me how it calculated the confidence interval by using the Clopper-Pearson. It tells me what the Parameter was, the probability that a person read a novel, a poem, or play in the last year. It tells me that the proportion of people who said yes, because they put ones instead of zeroed, is 71%. That corresponds to what I have over here.
The yes is the 71%. The confidence interval at the 95% confidence interval, which is the most common, is from 66% to 76%. And what this means is that while in my sample of 349 people 71% may have said they've read these, in the population of those 349 people came from, the true value could be somewhere between 66% and 76%. This is like the plus or minus 5% that you would get from a political poll. So the new nonparametric tests in SPSS is actually a very flexible procedure that can perform an entire range of tests all on its own.
It's also the easiest way to get confidence intervals and hypothesis tests for a single proportion. We'll come back to this procedure in another movie on testing nominal variables with multiple categories, but for now this should give you a good start on dealing with inferential statistics for dichotomous variables in SPSS. In the next movie, we'll look at common tests for scale variables.
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