Sequential analysis of variance table for Fitted Line Plot

Find definitions and interpretations for every statistic in the Sequential Analysis of Variance table.

In This Topic

DF
SS
F-value
P-Value – Term

DF

The total degrees of freedom (DF) are the amount of information in your data. The analysis uses that information to estimate the values of unknown population parameters. The total DF is determined by the number of observations in your sample. The DF for a term show how much information that term uses. Increasing your sample size provides more information about the population, which increases the total DF. Increasing the number of terms in your model uses more information, which decreases the DF available to estimate the variability of the parameter estimates.

If two conditions are met, then Minitab partitions the DF for error. The first condition is that there must be terms you can fit with the data that are not included in the current model. For example, if you have a continuous predictor with 3 or more distinct values, you can estimate a quadratic term for that predictor. If the model does not include the quadratic term, then a term that the data can fit is not included in the model and this condition is met.

The second condition is that the data contain replicates. Replicates are observations where each predictor has the same value. For example, if you have 3 observations where pressure is 5 and temperature is 25, then those 3 observations are replicates.

If the two conditions are met, then the two parts of the DF for error are lack-of-fit and pure error. The DF for lack-of-fit allow a test of whether the model form is adequate. The lack-of-fit test uses the degrees of freedom for lack-of-fit. The more DF for pure error, the greater the power of the lack-of-fit test.

SS

Sequential sums of squares (SS) are measures of variation for different components of the model. Unlike the adjusted sums of squares, the sequential sums of squares depend on the order the terms are entered into the model. In the sequential analysis of variance table, Minitab separates the sequential sums of squares by the polynomial terms (i.e. linear, quadratic, and cubic) in the model.

SS: The sequential sums of squares for each polynomial term is the unique portion of the variation explained by that term that is not explained by the lower order terms already entered into the model. It quantifies the amount of variation in the response data that is explained by each polynomial term as it is sequentially added to the model.
Seq SS Total: The total sum of squares is the sum of the term sum of squares and the error sum of squares. It quantifies the total variation in the data.

Interpretation

Minitab uses the sequential sums of squares to calculate the p-value for a term. Minitab also uses the sums of squares to calculate the R² statistic. Usually, you interpret the p-values and the R² statistic instead of the sums of squares.

F-value

The F-value is the test statistic used to determine whether the model is associated with 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 model. 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 model 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 the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that the term's coefficient is equal to zero, which indicates that there is no association between the term and the response. 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 association exists when there is no actual association.

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 variable and the term. If you fit a quadratic model or a cubic model and the quadratic or cubic terms are significant, you can conclude that the data contain curvature.
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 variable and the term. If you fit a quadratic model or a cubic model and the quadratic or cubic terms are not statistically significant, you may want to select a different model.