Normality Test in Minitab: Minitab with Statistics

Normality is a key notion in statistics that is employed in a variety of statistical procedures. The normality test determines whether or not data follows a normal distribution. A normal distribution is a symmetric bell−shaped curve around its mean. Because approaching normality occurs spontaneously in many physical, biological, and social measuring circumstances, the normal distribution is the most frequent statistical distribution. Many statistical studies demand data from regularly distributed populations.

Minitab may be used to run a normality test. Minitab has statistical tools that make it simple to do statistical computations. Let's look at how to do a normalcy test in Minitab.

What Exactly is a Normality Test?

Also known as the Anderson−Darling Test, a normality test is a statistical test that assesses whether or not a data set is regularly distributed. A normal distribution is often known as a "Bell Curve." Which tests or functions can be used with a given data set are determined by whether the distribution is normal.

How to Perform a Normality Test on Minitab?

Before beginning any statistical analysis of the provided data, it is critical to determine if it follows a normal distribution. If the presented information has a normal distribution, you may utilize parametric tests (test of means) to do additional statistical analysis. If the submitted data does not have a normal distribution, you must perform non−parametric testing (test of medians). Parametric tests are more powerful than non−parametric tests. Checking the normalcy of the presented data becomes much more critical as a result.

  • Make a hypothesis − A smart technique to begin any statistical study is to write the hypothesis. The null hypothesis for the normality test is "Data follows a normal distribution," whereas the alternative view.

  • Select the information − Copy the data from the spreadsheet on which you wish to run the normalcy test.

  • Copy and paste the data into the Minitab spreadsheet − Open Minitab and copy and paste the data into the Minitab spreadsheet.

  • In the menu bar of Minitab, Click Stat.

  • Click Basic Statistics.

  • Click Normality Test

  • Select data − A little window titled "Normality Test" will appear on the screen. Click inside the white box on a practical choice, then click "Select."

  • Be careful that the name of the selected data will appear on the "Variable" tab.

  • Also, remember that "Anderson−Darling" is already checked under "Tests for Normalcy." The most often used Normality test is the Anderson Darling. As a result, the default selection of Tests for Normality in Minitab is "Anderson−Darling."

  • Click "Ok".

  • Recognize the p−value shown in the Normal Probability Plot − A normal probability plot will emerge on the screen.

    Please check if the p−value indicated in the normal probability plot is more than or less than 0.05.

  • Assume the outcomes − If we fail to reject the null hypothesis, as indicated in the drafting phase, the inference will be "Data follows a normal distribution." If the null hypothesis is rejected, the conclusion will be "Data does not follow a normal distribution." Let us now connect the p−value to the written thesis.

  • Do not reject the null hypothesis if the p−value is larger than 0.05 − The null hypothesis is not rejected if the p−value found in the normal probability plot is more than 0.05. As a result, the conclusion is "Data follows a normal distribution.

    If the p−value is less than 0.05, reject the null hypothesis− We leave the null hypothesis if the p−value in the normal probability plot is less than 0.05. As a result, the conclusion is "Data does not follow a normal distribution."

Graphical Methods

A histogram of the sample data can be compared against a normal probability curve as an informal method of assessing normality. The data's empirical distribution (the histogram) should be bell−shaped and similar to the normal distribution. If the sample size is tiny, this may not be easy to observe. In this scenario, regressing the data against the quantiles of a normal distribution with the same mean and variance as the sample could be appropriate. A lack of fit to the regression line indicates a deviation from normalcy (see Anderson Darling coefficient and Minitab).

The normal probability plot, a quantile−quantile plot (QQ plot) of the standardized data versus the standard normal distribution, is a graphical tool for testing normality. The correlation between the sample data and normal quantiles (a measure of goodness of fit), in this case, indicates how well a normal distribution describes the data. The dots depicted in the QQ plot for normal data should fall roughly on a straight line, suggesting a high positive correlation. These charts are simple to read and have the added benefit of highlighting outliers.

Back-of-the-envelope Test

The 68−95−99.7 rule states that a normal distribution will underestimate the maximum magnitude of deviation if it contains a three event (properly, a 3s event) and substantially fewer than 300 samples or a 4s event, especially rarer than 15,000 samples. A simple back−of−the−envelope test uses the sample maximum and minimum to compute its z−score, or more appropriately, t−statistic.

A Normality Test Example

A processed food manufacturer's scientist attempts to determine how much fat is included in the company's bottled sauce. 15% is the stated percentage. In 20 random samples, the scientist calculates the proportion of fat.

Before conducting a hypothesis test, the scientist wishes to confirm the validity of the assumption of normalcy.

Describe the Findings

The fitted normal distribution line and the data points are rather close. The p−value is higher than the 0.05 threshold of significance. As a result, the scientist cannot prove that the data do not follow a normal distribution.

Updated on: 08-Dec-2022


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