ANOVA tables are also used in regression and DOE analyses.
Source  indicates the source of variation, either from the factor, the interaction, or the error. The total is a sum of all the sources.
SS  sum of squares between groups (factor) and the sum of squares within groups (error)
MS  mean squares are found by dividing the sum of squares by the degrees of freedom.
F  calculate by dividing the factor MS by the error MS; you can compare this ratio against a critical F found in a table or you can use the pvalue to determine whether a factor is significant.
P  use to determine whether a factor is significant; typically compare against an alpha value of 0.05. If the pvalue is lower than 0.05, then the factor is significant.
The pvalue of 0.000 indicates that the factor of color is significant.
For a twoway ANOVA, you will have two factors and an interaction term. For DOE and regression applications you can have several factors, or sources of variation.
Lackoffit tests
Used in regression and DOE, lackoffit tests assess the fit of your model. If the pvalue is less than your selected level, evidence exists that your model does not accurately fit the data. You may need to add terms or transform your data to more accurately model the data. Minitab calculates two types of lackoffit tests:
Pure error lack of fit test: Use if your data contain replicates (multiple observations with identical xvalues) and you are reducing your model. Replicates represent "pure error" because only random variation can cause differences between the observed response values. If you are reducing your model and the resulting pvalue for lackoffit is less than your selected level, then you should retain the term you removed from the model.
Data subsetting lack of fit test: Use if your data do not contain replicates and you want to determine if you are accurately modeling the curvature. This method identifies curvature in the data and interactions among predictors that may affect the model fit. Whenever the Data Subsetting pvalue is less than the level, Minitab displays the message "Possible curvature in variable X (PValue = 0.006 )." Evidence exists that this curvature is not adequately modeled. After examining the raw data in a scatterplot, you might try including a higherorder term to model the curvature.
Residual Plot Choices
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Minitab generates residual plots that you can use to examine the goodness of model fit. You can choose the following residual plots:
Histogram of residuals . An exploratory tool to show general characteristics of the data, including:
Typical values, spread or variation, and shape
Unusual values in the data
Long tails in the plot may indicate skewness in the data. If one or two bars are far from the others, those points may be outliers. Because the appearance of the histogram changes depending on the number of intervals used to group the data, use the normal probability plot and goodnessoffit tests to assess the normality of the residuals.
Normal probability plot of residuals. The points in this plot should generally form a straight line if the residuals are normally distributed. If the points on the plot depart from a straight line, the normality assumption may be invalid. If your data have fewer than 50 observations, the plot may display curvature in the tails even if the residuals are normally distributed. As the number of observations decreases, the probability plot may show substantial variation and nonlinearity even if the residuals are normally distributed. Use the probability plot and goodnessoffit tests, such as the AndersonDarling statistic , to assess whether the residuals are normally distributed.
You can display the AndersonDarling statistic (AD) on the plot, which can indicate whether the data are normal. If the pvalue is lower than the chosen alevel , the data do not follow a normal distribution. To display the AndersonDarling statistic, choose Tools > Options > Individual Graphs > Residual Plots. For additional tests of normality, see Stat > Basic Statistics > Normality Test.
Residuals versus fits . This plot should show a random pattern of residuals on both sides of 0. If a point lies far from the majority of points, it may be an outlier . Also, there should not be any recognizable patterns in the residual plot. The following may indicate error that is not random:
a series of increasing or decreasing points
a predominance of positive residuals, or a predominance of negative residuals
patterns, such as increasing residuals with increasing fits
Residuals versus order. This is a plot of all residuals in the order that the data was collected and can be used to find nonrandom error, especially of timerelated effects. A positive correlation is indicated by a clustering of residuals with the same sign. A negative correlation is indicated by rapid changes in the signs of consecutive residuals.
Four in one. Select this option to produce a normal plot of residuals, a histogram of residuals, a plot of residuals versus fits, and a plot of residuals versus order in one graph window.
Residuals versus other variables. This is a plot of all residuals versus another variable. Plot the residuals against:
Each predictor to look for curvature or differences in the magnitude of the residuals
Important variables left out of the model to see if they have critical additional effects on the response.
If certain residual values are of concern, you can brush your graph to identify them. See graph brushing.
Residual
The difference between an observed value (y) and its corresponding fitted value (ŷ). For example, the scatterplot below plots men's weight against their height; the regression line plots the fitted values of weight for each observed value of height. Suppose a man is 6 feet tall and the fitted value of his weight is 190 lbs. If his actual weight is 200, the residual is 10. If his actual weight is 175, the residual is 5.
weight



height

Residual values are especially useful in regression and ANOVA procedures because they indicate the extent to which a model accounts for the variation in the observed data.