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.
The total DF depends on the number of observations. In a mixture design, the total DF is the number of observations number minus 1. The DF for a term is the number of coefficients estimated for that term. The residual error DF is whatever is left over after accounting for all model terms.
Sequential sums of squares are measures of variation for the different sources that are listed for the model. Unlike the adjusted sums of squares, the sequential sums of squares depend on the order that the terms are in the model. In the Analysis of Variance table, Minitab separates the sequential sums of squares into different sources as listed below.
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 R^{2} statistic based on the adjusted sums of squares.
Adjusted sums of squares are measures of variation for the different sources that are listed for the model. The order of the predictors in the model does not affect the calculation of the adjusted sums of squares. In the Analysis of Variance table, Minitab separates the adjusted sums of squares into different sources as listed below.
Minitab uses the adjusted sums of squares to calculate the p-values in the ANOVA table. Minitab also uses the sums of squares to calculate the R^{2} statistic. Usually, you interpret the p-values and the R^{2} statistic instead of the sums of squares.
Adjusted mean squares measure how much variation a term or a model explains, assuming that all other terms are in the model, regardless of their order in the model. 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 s^{2}) is the variance around the fitted values.
Minitab uses the adjusted mean squares to calculate the p-values in the ANOVA table. Minitab also uses the adjusted mean squares to calculate the adjusted R^{2} statistic. Usually, you interpret the p-values and the adjusted R^{2} statistic instead of the adjusted mean squares.
An F-value appears for each test in the analysis of variance table.
Minitab uses the F-value to calculate the p-value, which you use to make a decision about the statistical significance of the test. 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 statistical significance.
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".
The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
If the p-value is greater than the significance level, you cannot conclude that the model explains variation in the response. You may want to fit a new model.
The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
Minitab does not display p-values for main effects in models for mixtures experiments because of the dependence between the components. Specifically, because the component proportions must sum to a fixed amount or proportion, changing a single component forces a change in the others. Additionally, the model for a mixtures experiment does not have an intercept term because the individual component terms behave like intercept terms.
The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis. Minitab automatically performs the pure error lack-of-fit test when your data contain replicates, which are multiple observations with identical x-values. Replicates represent "pure error" because only random variation can cause differences between the observed response values.
If the p-value is larger than the significance level, the test does not detect any lack-of-fit.