Analysis of variance table for Stability Study

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

In This Topic

DF
Seq SS
Seq MS
F-value
P-Value – Fixed Factor Model Selection
P-value – Random Factor Model selection

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.

For a stability study with fixed factors, the ANOVA table includes the following degrees of freedom: Time, Batch, Time*Batch.

Seq SS

Sequential sums of squares 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 Analysis of Variance table, Minitab separates the sequential sums of squares into different components that describe the variation due to different sources.

Seq SS Term: The sequential sum of squares for a term is the unique portion of the variation explained by a term that is not explained by the previously entered terms. It quantifies the amount of variation in the response data that is explained by each term as it is sequentially added to the model.
Seq SS Error: The error sum of squares is the sum of the squared residuals. It quantifies the variation in the data that the predictors do not explain.
Seq SS Total: The total sum of squares is the sum of the term sums of squares and the error sum of squares. It quantifies the total variation in the data.

Interpretation

In the Model Selection table, Minitab uses the sequential sums of squares to calculate the p-value for a term. Usually, you interpret the p-values instead of the sums of squares.

Seq MS

Sequential mean squares measure how much variation a term or a model explains. The sequential mean squares depend on the order the terms are entered into the model. Unlike sequential sums of squares, sequential mean squares consider the degrees of freedom.

The sequential mean square error (also called MSE or s²) is the variance around the fitted values.

Interpretation

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

F-value

An F-value appears for each term in the Analysis of Variance table. The F-value is the test statistic used to determine whether the term 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 terms and 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 term or 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 – Fixed Factor Model Selection

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 no association exists between the term and the response. For a stability study, these are the specific null hypotheses for each term:

Time: The product does not degrade over time.
Batch: The batches all have the same mean response before they start to degrade.
Time*Batch interaction: The batches all degrade at the same rate.

For a stability study, Minitab removes any terms that do not have p-values less than your significance level. The default significance level is 0.25. A significance level of 0.25 indicates a 25% 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. Minitab retains the term in the model.
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. Minitab removes the term from the model.

P-value – Random Factor Model selection

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 one model fits the data better than another one, compare the p-value for the model to the significance level to assess the null hypothesis. The null hypothesis is that the additional coefficient in the larger model is zero. The alternative hypothesis is that the additional coefficient in the larger model is different from zero. For a stability study, the default significance level is 0.25. A significance level of 0.25 indicates a 25% risk of concluding that the models are the same when one model fits the data better.

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 the difference between the models is statistically significant. Minitab retains the more complex model for more analysis.
P-value > α: The association is not statistically significant: If the p-value is greater than the significance level, you cannot conclude that the difference between the models is statistically significant. Minitab retains the simpler model for more analysis.