# Interpret all statistics and graphs for Normality Test

Find definitions and interpretation guidance for every statistic and graph that is provided with the normality test.

The Anderson-Darling goodness-of-fit statistic (AD-Value) measures the area between the fitted line (based on the normal distribution) and the empirical distribution function (which is based on the data points). The Anderson-Darling statistic is a squared distance that is weighted more heavily in the tails of the distribution.

### Interpretation

Minitab uses the Anderson-Darling statistic to calculate the p-value. The p-value is a probability that measures the evidence against the null hypothesis. Smaller p-values provide stronger evidence against the null hypothesis. Larger values for the Anderson-Darling statistic indicate that the data do not follow the normal distribution.

## Maximum

The maximum is the largest data value.

In these data, the maximum is 19.

 13 17 18 19 12 10 7 9 14

### Interpretation

Use the maximum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the maximum value is very high, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.

## Mean

The mean describes the sample with a single value that represents the center of the data. The mean is calculated as the average of the data, which is the sum of all the observations divided by the number of observations.

## Minimum

The minimum is the smallest data value.

In these data, the minimum is 7.

 13 17 18 19 12 10 7 9 14

### Interpretation

Use the minimum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the minimum value is very low, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.

## N

The sample size (N) is the total number of observations in the sample.

### Interpretation

The sample size affects the power of the test.

Usually, a larger sample size gives the test more power to detect a difference between your sample data and the normal distribution. That is, when a difference truly exists, you have a greater chance of detecting it with a larger sample size.

## Null hypothesis and alternative hypothesis

The null and alternative hypotheses are two mutually exclusive statements about the distribution of the data. The Anderson-Darling test uses sample data to determine whether to reject the null hypothesis.
Null Hypothesis
The null hypothesis states that the data follow a normal distribution.
Alternative Hypothesis
The alternative hypothesis states that the data do not follow a normal distribution.

## P-value

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

### Interpretation

Use the p-value to determine whether the data do not follow a normal distribution.

To determine whether the data do not follow a normal distribution, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the data do not follow a normal distribution when they actually do follow a normal distribution.
P-value ≤ α: The data do not follow a normal distribution (Reject H0)
If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis and conclude that your data do not follow a normal distribution. If your data do not follow the normal distribution, read the data considerations topic for any other analyses that you want to perform. The data considerations topics indicate one the following:
• The analysis works well with nonnormal data.
• The analysis works well with nonnormal data that were transformed into normal data.
• The analysis does not work well with nonnormal data. The data considerations topics might identify a different analysis that you can use.
P-value > α : Cannot conclude the data do not follow a normal distribution (Fail to reject H0)
If the p-value is larger than the significance level, the decision is to fail to reject the null hypothesis because there is not enough evidence to conclude that your data do not follow a normal distribution. However, you cannot conclude that the data do follow a normal distribution.

## Probability plot

A probability plot creates an estimated cumulative distribution function (CDF) from your sample by plotting the value of each observation against the observation's estimated cumulative probability.

### Interpretation

Use a probability plot to visualize how well your data fit the normal distribution.

To visualize the fit of the normal distribution, examine the probability plot and assess how closely the data points follow the fitted distribution line. If your data are perfectly normal, the data points on the probability plot form a straight line. Skewed data form a curved line.

###### Tip

Hold your pointer over the fitted distribution line to see a chart of percentiles and values. However, be aware that these values are accurate only if the data follow a normal distribution.

## StDev

The standard deviation is the most common measure of dispersion, or how spread out the data are from the mean. A larger sample standard deviation indicates that your data are spread more widely around the mean.

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