One-Way ANOVA Analysis Results

When accessed from a one-way ANOVA folio, the Analysis Summary window will contain detailed information about analysis results, including information that describes how the factor levels affect the response.

If the current response data has been analyzed, you can open the window by clicking the View Analysis Summary icon on the control panel.

If the current response data has not been analyzed, the icon will still be available so you can view the folio's analysis history.

Select an item in the Available Report Items panel to display it on the spreadsheet. Each item is described next.

Analysis Results

The following table provides general information about the effects of the factor levels on the selected response.

The Analysis of Variance (ANOVA) table includes the following columns:

Source of Variation is the source that caused the difference in the observed output values. This can be a factor, factorial interaction, curvature, block, error, etc. If your design includes more than one factor and you have selected to use grouped terms in the analysis (specified on the Analysis Settings page of the control panel), the effects will be grouped by order (i.e., main effects, two-way interactions, etc.). Sources displayed in red are considered to be significant.
The number of Degrees of Freedom for the Model is the number of regression coefficients for the effects included in the analysis (e.g., two coefficients might be included in the regression table for a given main effect). The number of degrees of freedom for the Residual is the total number of observations minus the number of parameters being estimated.
Sum of Squares is the amount of difference in observed output values caused by this source of variation.
Mean Squares is the average amount of difference caused by this source of variation. This is equal to Sum of Squares/Degrees of Freedom.
F Ratio is the ratio of Mean Squares of this source of variation and Mean Squares of pure error. A large value in this column indicates that the difference in the output caused by this source of variation is greater than the difference caused by noise (i.e., this source affects the output).
P Value (alpha error or type I error) is the probability that an equal amount of variation in the output would be observed in the case that this source does not affect the output. This value is compared to the risk level (alpha) that you specify on the Analysis Settings page of the control panel. If the p value is less than alpha, this source of variation is considered to have a significant effect on the output. In this case, the term and its p value will be displayed in red.
The following values are shown underneath the ANOVA table, and they indicate how well the model fits the data:

S is the standard error of the noise. It represents the magnitude of the response variation that is caused by noise. Lower values indicate better fit.
R-sq is the percentage of total difference that is attributable to the factors under consideration. It is equal to Sum of Squares(factor)/Total Sum of Squares. Higher values usually indicate better fit.
R-sq(adj) is an R-sq value that is adjusted for the number of parameters in the model. Higher values indicate better fit.

The following table gives the mean and standard deviation of the output at each level of the factor.

This table includes the following columns:

Factor Level is the name of the qualitative level.
Number in Level is the number of data points obtained at the factor level.
Estimated Mean is the average of the data points obtained at the level.
Standard Deviation is the standard deviation of the data points obtained at the level.

The following table provides information on comparisons between levels of the factor.

This table includes the following columns:

Contrast gives the paired comparison of any two levels. Level 1 - Level 2 means the difference between Level 1 and Level 2. Contrasts displayed in red are considered to be significant.
Mean Difference is the mean value of the difference in output between the two levels.
Pooled Standard Error is the standard error of the mean difference in output between the two levels.
Low Confidence and High Confidence ares the confidence bounds on the mean difference.
T Value is the normalized difference, which is equal to Mean Difference/Pooled Standard Error.
P Value is the probability that an equal amount of variation in the output would be observed in the case that there is no significant difference between the levels. This value is compared to the risk level (alpha) that you specify on the Analysis Settings page of the control panel. If the p value is less than alpha, there is considered to be a significant difference between the levels. In this case, the contrast and its p value will be displayed in red.

This information is presented using multiple tables.

The Response table displays the response that the regression equation applies to and the units of measurement that were entered for the response (if any).
The Additional Settings table shows the transformation and risk level you entered for the response.

	Related Topics and Links:
	One-Way ANOVA Folio