Interpret all statistics for a histogram with a lognormal distribution

Find definitions and interpretation guidance for every statistic that is provided with a histogram with a fitted lognormal distribution.

N

The sample size (N) is the number of nonmissing observations for a Y variable or a group.

Location and scale

A lognormal distribution is defined by two parameters: the location and the scale. When you fit a lognormal distribution, Minitab estimates these parameters from your sample. Generally, the location parameter describes how large the data values are and the scale parameter describes how spread out the data values are.

The following graphs show lognormal distributions with location parameters of 1 and 10. Each graph shows distributions with scale parameters of 0.1, 0.2, and 0.4. For a given location parameter, the larger scale parameters result in data values (X values) that are less peaked and more spread out. The larger location parameter results in generally larger data values.

Location = 1
Location = 10

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

One of the simplest ways to assess the spread of your data is to compare the minimum and maximum.

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

One of the simplest ways to assess the spread of your data is to compare the minimum and maximum.

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 lognormal distribution.
Alternative Hypothesis
The alternative hypothesis states that the data do not follow a lognormal distribution.

AD-value

The Anderson-Darling goodness-of-fit statistic (AD-Value) measures the area between the fitted line (which is based on a lognormal 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 a lognormal distribution.

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.

Interpretation

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

To determine whether the data do not follow a lognormal 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 lognormal distribution when they actually do follow a lognormal distribution.
P-value ≤ α: The data do not follow a lognormal 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 lognormal distribution.
P-value > α : Cannot conclude the data do not follow a lognormal 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 lognormal distribution. However, you cannot conclude that the data do follow a lognormal distribution.
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