Analysis of variance table for Analyze Taguchi Design

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

In This Topic

DF
Seq SS
Adj SS
Adj MS
F-value
P-Value

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 experiment. 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.

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 lists the sequential sums of squares for the main effects, interactions, and error term.

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 sum of squares and the error sum of squares. It quantifies the total variation in the data.

Interpretation

Minitab does not use the sequential sums of squares to calculate p-values when you analyze a design, but can use the sequential sums of squares when you use Fit Regression Model or Fit General Linear Model. Usually, you interpret the p-values and the R² statistic based on the adjusted sums of squares.

Adj SS

Adjusted sums of squares are measures of variation for different components of the model. The order of the predictors in the model does not affect the calculation of the adjusted sum of squares. In the Analysis of Variance table, Minitab separates the sums of squares into different components that describe the variation due to different sources.

Adj SS Term: The adjusted sum of squares for a term is the decrease in the error sum of squares compared to a model with only the other terms. It quantifies the amount of variation in the response data that is explained by each term in the model.
Adj SS Term: The adjusted sum of squares for a term is the increase in the regression sum of squares compared to a model with only the other terms. It quantifies the amount of variation in the response data that is explained by each term in the model.
Adj 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.
Adj SS Total: The total sum of squares is the sum of the term sum of squares for an orthogonal design and the error sum of squares. It quantifies the total variation in the data.

Interpretation

Minitab uses the adjusted sum 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.

Adj MS

Adjusted mean squares measure how much variation a term or a model explains, assuming that all other terms are in the model, regardless of the order they were entered. Unlike the adjusted sums of squares, the adjusted mean squares consider the degrees of freedom.

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

Interpretation

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

F-value

The Analysis of Variance table lists an F-value for each term. 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. 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

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 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 the coefficient is not 0 when it is. Frequently, a significance level of 0.10 is used for evaluating terms in a model.

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 characteristic and the 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 characteristic and the term. You may want to refit the model without the term.; If there are multiple predictors without a statistically significant association with the response, you can reduce the model by removing terms one at a time. For more information on removing terms from the model, go to Model reduction.