Normality test Simply Explained

In this video, show you how to test your data for normal distribution. First of all, why do you need normal distribution? Let's say you've collected data and you want to analyze this data with an appropriate hypothesis test. For example, test or an analysis of variance. One of the most common requirements for hypothesis testing is that the data used must be normally distributed. Data are normally distributed if the frequency distribution of the data has this bell curve. Now, of course, the big question is how do you know if your data is normally distributed or not or how can you test that? There are two ways. Either you can check the normal distribution analytically or graphically. We now look at both in detail. Let's start with the analytical test for normal distribution. In order to test your data analytically for normal distribution, there are several test procedures. The best known are the cologn test, the Shapiro Wilk Anderson Darling test. With all these tests, you test the null hypothesis that the data are normally distributed. So the null hypothesis is that the frequency distribution of your data fits the normal distribution. In order to reject or not reject the null hypothesis, you get value out of all these tests. Now the big question is whether this value is greater or less than 0.05. 05. If the value is less than 0.05, this is interpreted as significant deviation from the normal distribution and you can assume that your data are not normally distributed. If the value is greater than 0.05 05 and you want to be statistically clean, you cannot necessarily say that the frequency distribution corresponds to the normal distribution, you just cannot disprove the null hypothesis. In practice, however, values greater than 0.05 are assumed to be normally distributed. To be on the safe side, you should always take look at the graphical solution which we will talk about in moment. So in summary, all these tests give you value. If this value is less than 0.05, you assume no normal distribution. If it is greater than 0.05, you assume normal distribution. For your information, with the colmoger of Smearov test and with the Anderson Darling test, you can also test distributions other than the normal distribution. Now, unfortunately, there is big disadvantage of the analytical methods, which is why more and more people are switching to using the graphical methods. The problem is that the calculated value is influenced by the size of the sample. Therefore, if you have very small sample, your value may be much larger than 0.05. But if you have very large sample, your value may be smaller than 0.05. Let's assume the distribution in your population deviates very slightly from the normal distribution. Then if you take very small sample, you will get very large value and thus you will assume that it is normally distributed data. However, if you take larger sample, then value becomes smaller and smaller even though the samples come from the same population with the same distribution. Therefore, if you have minimal deviation from the normal distribution, which isn't actually relevant, the larger your sample, the smaller the value becomes. With very large sample, you may even get value smaller than 0.05 and thus reject the null hypothesis that it is normal distribution. To get around this problem, graphical methods are being used more and more. We'll come to that now. If the normal distribution is checked graphically, you either look at the histogram or even better at the QQ plot. If you use the histogram, you plot the normal distribution in the histogram of your data and then you can see whether the curve of the normal distribution roughly corresponds to that of the normal distribution curve. However, it is better if you use the so-called quantile quantile plot or QQ plot for short. Here the theoretical quantiles that the data should have if they are perfectly normally distributed and the quantiles of the measured values are compared. If the data is perfectly normally distributed, all points would lie on the line. The more the data deviates from the line, the less it is normally distributed. In addition, data dep plots the 95% confidence interval. If all or almost all of your data lies within this interval, it is very strong indication that your data is normally distributed. Your data would not be normally distributed if, for example, they form an arc and lie far away from the line in some areas. If you use data in order to test for normal distribution, you get the following evaluation. First, you get the analytical test procedures clearly arranged in table. Then come the graphical test procedures. How you can test your data with data tab for normal distribution? will show you now. Just copy your data into this table. Click on descriptive statistics and then select the variable you want to test for normal distribution for example age. After that you can simply click on test for normal distribution here and you will get the results down here. know that test procedures are not actually descriptive methods, but if you want to get an overview of your data, it's usually also relevant to look at the distribution of your data. Furthermore, if you calculate hypothesis test, for example, whether gender has an influence on the salary of person, then you can check the preconditions for each hypothesis test. And you will also get the test for normal distribution. If the brie is not met, you would click on this and non-parametric test, the Man Whitney test would be calculated. The Man Whitney test does not need normally distributed data. Thanks for watching and hope you enjoyed the video.