Means/Anova and Means/Anova/Pooled t
The Means/Anova option performs an analysis of variance. If the X factor contains exactly two levels, this option appears as Means/Anova/Pooled t. In addition to the other reports, a t-test report assuming pooled (or equal) variances appears.
 Element Reference Mean diamonds are added to the Oneway plot Reports Note: This report appears only if the Means/Anova/Pooled t option is selected.
 Rsquare Measures the proportion of the variation accounted for by fitting means to each factor level. The remaining variation is attributed to random error. The R2 value is 1 if fitting the group means accounts for all the variation with no error. An R2 of 0 indicates that the fit serves no better as a prediction model than the overall response mean. For more information, see Statistical Details for the Summary of Fit Report. R2 is also called the coefficient of determination. Adj Rsquare Adjusts R2 to make it more comparable over models with different numbers of parameters by using the degrees of freedom in its computation. For more information, see Statistical Details for the Summary of Fit Report. Root Mean Square Error Estimates the standard deviation of the random error. It is the square root of the mean square for Error found in the Analysis of Variance report. Mean of Response Overall mean (arithmetic average) of the response variable. Observations (or Sum Wgts) Number of observations used in estimating the fit. If weights are used, this is the sum of the weights.
Note: This option is applicable only for the Means/Anova/Pooled t option.
 • Equal variances. If you select the Means/Anova/Pooled t option, a t-Test report appears. This t-Test assumes equal variances.
 • Unequal variances. If you select the t-Test option from the red triangle menu, a t-Test report appears. This t-Test assumes unequal variances.
 t Test plot Shows the sampling distribution of the difference in the means, assuming the null hypothesis is true. The vertical red line is the actual difference in the means. The shaded areas correspond to the p-values. Difference Shows the estimated difference between the two X levels. In the plots, the Difference value appears as a red line that compares the two levels. Std Err Dif Shows the standard error of the difference. Upper CL Dif Shows the upper confidence limit for the difference. Lower CL Dif Shows the lower confidence limit for the difference. Confidence Shows the level of confidence (1-alpha). To change the level of confidence, select a new alpha level from the Set α Level command from the platform red triangle menu. t Ratio Value of the t-statistic. DF Prob > |t| The p-value associated with a two-tailed test. Prob > t The p-value associated with a lower-tailed test. Prob < t The p-value associated with an upper-tailed test.
The Analysis of Variance report partitions the total variation of a sample into two components. The ratio of the two mean squares forms the F ratio. If the probability associated with the F ratio is small, then the model is a better fit statistically than the overall response mean.
Note: If you specified a Block column, then the Analysis of Variance report includes the Block variable.
 • The degrees of freedom for C. Total are N - 1, where N is the total number of observations used in the analysis.
 • If the X factor has k levels, then the model has k - 1 degrees of freedom.
The Error degrees of freedom is the difference between the C. Total degrees of freedom and the Model degrees of freedom (in other words, N - k).
 • The total (C. Total) sum of squares of each response from the overall response mean. The C. Total sum of squares is the base model used for comparison with all other models.
 • The sum of squared distances from each point to its respective group mean. This is the remaining unexplained Error (residual) SS after fitting the analysis of variance model.
 • The Model mean square estimates the variance of the error, but only under the hypothesis that the group means are equal.
 • The Error mean square estimates the variance of the error term independently of the model mean square and is unconditioned by any model hypothesis.
Probability of obtaining (by chance alone) an F value greater than the one calculated if, in reality, there is no difference in the population group means. Observed significance probabilities of 0.05 or less are often considered evidence that there are differences in the group means.
 Level Lists the levels of the X variable. Number Lists the number of observations in each group. Mean Lists the mean of each group. Std Error Lists the estimates of the standard deviations for the group means. This standard error is estimated assuming that the variance of the response is the same in each level. It is the root mean square error found in the Summary of Fit report divided by the square root of the number of values used to compute the group mean. Lower 95% and Upper 95% Lists the lower and upper 95% confidence interval for the group means.
If you have specified a Block variable on the launch window, the Means/Anova and Means/Anova/Pooled t commands produce a Block Means report. This report shows the means for each block and the number of observations in each block.
Examples of Mean Diamonds and X-Axis Proportional Options
 • If the X-Axis proportional option is selected, the horizontal extent of each group along the x-axis (the horizontal size of the diamond) is proportional to the sample size for each level of the X variable. Therefore, the narrower diamonds are usually taller, because fewer data points results in a wider confidence interval.
 • The mean line across the middle of each diamond represents the group mean.
 • Overlap marks appear as lines above and below the group mean. For groups with equal sample sizes, overlapping marks indicate that the two group means are not significantly different at the given confidence level. Overlap marks are computed as group mean ± . Overlap marks in one diamond that are closer to the mean of another diamond than that diamond’s overlap marks indicate that those two groups are not different at the given confidence level.
 • The mean diamonds automatically appear when you select the Means/Anova/Pooled t or Means/Anova option from the platform menu. However, you can show or hide them at any time by selecting Display Options > Mean Diamonds from the red triangle menu.
Show mean lines by selecting Display Options > Mean Lines. Mean lines indicate the mean of the response for each level of the X variable.
Mean error bars and standard deviation lines appear when you select the Means and Std Dev option from the red triangle menu. See Mean Lines, Mean Error Bars, and Std Dev Lines. To turn each option on or off singly, select Display Options > Mean Error Bars or Std Dev Lines.
Mean Lines, Mean Error Bars, and Std Dev Lines