Spss which test for normality

There are a number of different ways to test this requirement. Frisbee Throwing Distance in Metres highlighted is the dependent variable, and we need to know whether it is normally distributed before deciding which statistical test to use to determine if dog ownership is related to the ability to throw a frisbee. You can either drag and drop, or use the blue arrow in the middle.

The Factor List box allows you to split your dependent variable on the basis of the different levels of your independent variable s. In our example, Dog Owner, our independent variable, has two levels — owner and non-owner — so we could add Dog Owner to the Factor List box, and look at our dependent variable split on that basis. So say I've a population of 1,, people.

I think their reaction times on some task are perfectly normally distributed. I sample of these people and measure their reaction times. Now the observed frequency distribution of these will probably differ a bit -but not too much- from a normal distribution.

So I run a histogram over observed reaction times and superimpose a normal distribution with the same mean and standard deviation. The result is shown below. The frequency distribution of my scores doesn't entirely overlap with my normal curve. Now, I could calculate the percentage of cases that deviate from the normal curve -the percentage of red areas in the chart. This percentage is a test statistic: it expresses in a single number how much my data differ from my null hypothesis.

So it indicates to what extent the observed scores deviate from a normal distribution. Now, if my null hypothesis is true, then this deviation percentage should probably be quite small. That is, a small deviation has a high probability value or p-value. Reversely, a huge deviation percentage is very unlikely and suggests that my reaction times don't follow a normal distribution in the entire population. So a large deviation has a low p-value.

So that's the easiest way to understand how the Kolmogorov-Smirnov normality test works. Computationally, however, it works differently: it compares the observed versus the expected cumulative relative frequencies as shown below. The Kolmogorov-Smirnov test uses the maximal absolute difference between these curves as its test statistic denoted by D.

In this chart, the maximal absolute difference D is 0. We'll demonstrate both methods using speedtasks. Our main research question is which of the reaction time variables is likely to be normally distributed in our population? But given these data, we'll believe it. For now anyway. The Shapiro-Wilk and Kolmogorov-Smirnov test both examine if a variable is normally distributed in some population.

But why even bother? Well, that's because many statistical tests -including ANOVA , t-tests and regression - require the normality assumption : variables must be normally distributed in the population. For larger sample sizes, the sampling distribution of the mean is always normal, regardless how values are distributed in the population.

This phenomenon is known as the central limit theorem. And the consequence is that many test results are unaffected by even severe violations of normality. So if sample sizes are reasonable, normality tests are often pointless. Sadly, few statistics instructors seem to be aware of this and still bother students with such tests. And that's why I wrote this tutorial anyway.

Well, in that case, many tests do require normally distributed variables. However, normality tests typically have low power in small sample sizes. As a consequence, even substantial deviations from normality may not be statistically significant. So when you really need normality, normality tests are unlikely to detect that it's actually violated.

Which renders them pretty useless. Hi Ruben, I definitely didn't look at it close enough, haha. Sorry about that. I'd also like to thank you for this tutorial. I've been struggling with using SPSS and was unable to find an easy and accessible explanation for certain concepts. Your tutorial has helped me greatly! Thank you so much once again. Tell us what you think! Your comment will show up after approval from a moderator.