Distributional analysis

Distributional analysis.

Well, you are probably familiar with the terms normal distribution, binomial distribution, hypergeometric distribution, and poison distribution. They are known as probability distribution functions, and they yield a list of all the possible outcomes of a random variable. The world of statistics includes dozens of them. You might ask why they are essential in statistical analysis. They help to model a random phenomenon. One such probability distribution that is commonly used is the normal distribution. It’s important that before you conduct any analysis, the data should be normally distributed. How can we know that the data has a normal distribution? There are various ways that we can deduce if the data has a normal distribution, which is explained in this article.

Methods of testing for normality.

We can broadly classify the tests for normality into two.

  1. Visualization methods
  2. Statistical tests

Visualization methods.

When it comes to testing for normality, you won’t run out of options. Even the simplest graphs that you can think of can be an asset in these cases. There are various plots that can be used in  tests for normality. These graphs try to form the normal distribution curve.


Through plotting a histogram, we can know if a dataset that we are using is normally distributed or not. First, let’s start by noting down the shape that you would expect of a normally distributed data set. A normal dataset can be bell-shaped, right-skewed, and left-skewed.

A histogram plots the values of a dataset whereby each bar represents the frequency of the data. The highest value displays the highest rate. Conversely, the lowest bar represents the lowest frequency.

A simple clue for normality is if the tallest bars of the histogram are clustered at the center, it’s normally distributed. The data is said to be right-skewed or left skewed if the tall bars are clustered to the right or left, respectively.

Scatter plots.

Scatter plots can be used to check the normality of a dataset. Here we check where the data points are clustered. If they are grouped in the middle, right, or left, we can conclude that the dataset has a normal distribution.

Normal probability plots

They are plots that are used to approximate if the data sets have normal distribution. In these plots, the datasets are plotted against a theoretical normal distribution. Thus, if the data has a normal distribution, the curve should show a straight line.

Statistical tests for normality

Statistical tests for normality are considered more accurate than the visualization methods. Let’s take a look at some of them.

The Shapiro Wilk test.

Every statistical software has Shapiro Wilk test function. This is a hypothesis test where the null hypothesis asserts the normality of the dataset. In such a case, we are interested in the p-values. If the p-value is less than the 0.05 (significant value for the 95% confidence interval), we do not accept the null hypothesis but take the alternative hypothesis. If it’s larger than 0.05, we go with the null hypothesis.

Kolmogorov-smirnov test.

This another statistical test for normality. It’s more like the Shapiro-Wilk test, but its better suited for large samples of data.

Which is the best method to use?

The Shapiro-Wilk is the most commonly used statistical test for normality. However, if you are using it, it’s best if you start with the visualization methods before you can proceed to the Shapiro-Wilk test.

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