Tests of fixed effects table for Fit Mixed Effects Model

Find definitions and interpretation guidance for every statistic in the Tests of fixed effects table.

In This Topic

DF
F-Value
P-Value – Term

DF

The degrees of freedom (DF) are the amount of information in your data. The analysis uses that information for the F tests for testing fixed effect terms. The DF Num displays the numerator degrees of freedom for the F test for a fixed effect term. The value equals the number of parameters for the fixed effect term. The DF Den displays the denominator degrees of freedom for the F test for a fixed effect term.

F-Value

An F-value appears for each fixed effect term in the Tests of Fixed Effects table. The F-value is for the F-test that determines whether the term significantly affects the response.

Interpretation

Minitab uses the F-value to calculate the p-value, which you use to make a decision about the statistical significance of the term. The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

A sufficiently large F-value indicates that the term is significant.

If you want to use the F-value to determine whether to reject the null hypothesis, compare the F-value to your critical value. You can calculate the critical value in Minitab or find the critical value from an F-distribution table in most statistics books. For more information on using Minitab to calculate the critical value, go to Using the inverse cumulative distribution function (ICDF) and click "Use the ICDF to calculate critical values".

P-Value – Term

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

Interpretation

To determine whether a term significantly affects the response, compare the p-value to your 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 an affect exists when there is no actual affect.

The interpretation of each p-value depends on whether it is for the coefficient of a fixed factor term or for a covariate term.

Fixed factor term

For a fixed factor term, the null hypothesis is that the fixed factor term does not significantly affect the response.

P-value ≤ α: The fixed factor term significantly affects the response: If the p-value is less than or equal to the significance level, you can conclude that the fixed factor term does significantly affect the response. The rejection of the null hypothesis means one level effect is significantly different from the other level effects of the term.
P-value > α: The fixed factor term does not significantly affect the response: If the p-value is greater than the significance level, you cannot conclude that the fixed factor term significantly affects the response. You may want to refit the model without the term.

Covariate term

For a covariate term, the null hypothesis is that no association exists between the term and the response.

P-value ≤ α: The association is statistically significant: If the p-value is less than or equal to the significance level, you can conclude that there is a statistically significant association between the response and the covariate term.
P-value > α: The association is not statistically significant: If the p-value is greater than the significance level, you cannot conclude that there is a statistically significant association between the response and the covariate term. You may want to refit the model without the covariate term.