Скачать или смотреть video 14.1. non-parametric statistics

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So far in this class, we have talked about a bunch of different inferential statistical tests, and all of them have been a type of statistical test called "parametric." So, they have all been parametric statistical tests. Parametric statistical tests assume various things about the population.

Remember, a long time ago, when we talked about descriptive statistics, we talked about parameters being descriptive statistics for populations, like mu and sigma, as the population mean the standard deviation, and like sample statistics, which is your sample mean and standard deviation. Well, population parameters are assumed by all the tests that we have talked about so far.

So, these parametric statistical tests, they assume things about populations. We are going to go through some of these. These assumptions can be violated sometimes, so you end up with problems, potentially anyway. So we will just talk through that a little bit, and then what we will do is we will talk about non-parametric tests, which are alternative tests that are available that don't make these same kinds of assumptions.

The first assumption of all these parametric tests we have talked about is that the dependent variable is scale. So that means interval or ratio scale of measure. So, if we are looking at this example, I put up an independent-samples t-test here for us to talk about, we are saying men and women are the same, that is with the null hypothesis says. For example, maybe this is height. In that case the scale of measure for the dependent variable would be ratio, because height is a ratio variable. In practice, though, you can run into problems if your dependent variable is not ratio or interval. It is actually common in psychology because we use Likert scales a lot, and those are scales where, for example, you might say, on a 1 - 5 scale, are you happy or sad. So, somebody would say, "Oh I am right in the middle today. I am a three." So people treat these, psychologists treat these measures as interval, assuming this distance is the same as this distance, but really, if push comes to shove, these are ranks. Two is higher than one, five is higher than four, but we don't know that those distances are the same. This is an example where there is a mismatch between the assumptions of our test, and what we actually end up doing. Generally, psychologists think that' i not too big of a problem, but sometimes the reviewers of our manuscripts that we submit for journal articles sometimes those reviewers disagree, and then we will do the nonparametric test that is okay with rank order data.

Another assumption of these parametric tests is that the population distribution, one or more, is distributed normally. These are normal distributions. So here there is a men's and a women's distribution, and they are perfectly overlapping, and they are both normal distributions. In practice, it is pretty common that you might get data that suggests that, (observed data that) suggests that the population is actually not perfectly normally distributed. It might be skewed. In fact, if there is like an absolute limit on the top or the bottom you kind of expect it to be skewed. Generally, that is not a huge problem if you have a large enough sample size, because, recall, that the central limit theorem tells us that, even if the population isn't normally distributed, if your sample size is large enough, say 30 or more, then the distribution of sample means will be normally distributed anyways, or nearly so, or maybe a t-distribution or something, but it will be close to normal. So skew is usually not a big problem. Outliers would be individuals that we observe them, like if this is everybody in our sample, except for there is one person way over here, or even two ... outliers are a bigger problem for these parametric tests, because they really influence sum of squares, which are actually involved in all these tests. So these outliers are more of a problem. In that case, you might even want to use one of the nonparametric tests that we will talk about.
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