Normality Test

From Grapheme wiki


Many statistical procedures, including correlations and t-tests, rely on the assumptions that the analysed data set is normally distributed. To determine how likely it is for a random variable underlying the data set to follow a normal distribution, a normality test is usually performed. Types of normality tests include:

  • Anderson–Darling test
  • Shapiro–Wilk test
  • Kolmogorov–Smirnov test

Any Hypothesis test in statistics requires the definition of a null hypothesis and an alternate hypothesis. The goal of the test is to aid the analyst in deciding which one of the two hypothesis is true. The table below shows a common set of choices for the null and alternate hypothesis for a normality test:

Null hypothesis Alternate hypothesis
Data follow a normal distribution Data do not follow a normal distribution

Before running a statistical test, the analyst must choose a significance level, or the probability of rejecting the null hypothesis given that it were true (i.e. the probability of making a wrong decision). An alpha value of 0.05 (5%) is usually adopted but a different value may be used depending on the field of the study. If the p-value obtained at the end of the test is less than the selected significance level, the Null Hypothesis should be rejected in favour of the Alternate Hypothesis.

More details on Normality testing can be found here:

Practical Example

Suppose an engineer for a manufacturing company wants to verify whether the steel shafts produced by a certain manufacturing process have a mean diameter of 55 mm. He has measured the diameter of 40 random samples and he wants to assess whether the selected diameters follow a normal distribution before performing an hypothesis test on the mean.

A normality test performed on the sample produces a p-value, for the Anderson-Darling test, of 0.89. Being the p-value greater than the adopted significance level of 0.05, the engineer fails to reject the hypothesis that the data follow a normal distribution (i.e. the engineer does not have enough evidence to conclude that the data do not follow a normal distribution).

Within Grapheme

To perform a Normality Test in Grapheme, click on Create New Analysis from the toolbar of the Statistical Analysis View. Assign a name to the panel and select “Normality Test” from the list. Click on Next.

In the Sources tab, select the Source Table from the ones available in the Tables view, select the view of the table and the column you want to analyse. Click on Next.

In the Configuration tab, select one or more test methods and Click on Finish.

Grapheme: Normality Test Panel

  • All the data available in the panel are updated on the fly, so that any change in the table values, is immediately reflected by the panel tables and charts. Automatic update can be temporary suspended, by clicking on the lock button in the main panel toolbar.
  • All the data contained in each table, can be copied to the clipboard for further reporting by clicking on the button available in the toolbar.
  • Each chart can be exported as Image by clicking on the “Save as Image” button available in the toolbar

See also