In the Oneway platform, use the Means/Anova option to perform an analysis of variance. If the X variable has only two levels, this option appears as Means/Anova/Pooled t. The report contains tables for the summary of fit, an analysis of variance (ANOVA), and summary statistics for each group. The report includes a Pooled t test table if the X variable has only two levels. The report includes a Block Means table if you have specified a Block variable in the launch window and there are equal counts in each combination of block and level of the X variable. Other blocking configurations result in a Oneway Anova with Blocking report.
In the Oneway platform, the Summary of Fit table contains the following statistics:
Rsquare
The proportion of the variation that is explained by the model. The remaining variation is attributed to random error. The RSquare is 1 if the model fits perfectly. See Statistical Details for the Summary of Fit Report. R2 is also called the coefficient of determination.
Note: A low RSquare value suggests that there might be variables not in the model that account for the unexplained variation. However, if your data are subject to a large amount of inherent variation, even a useful ANOVA model can have a low RSquare value. Read the literature in your research area to learn about typical RSquare values.
Adj Rsquare
The RSquare statistic adjusted for the number of parameters in the model. The adjusted R2 statistic enables you to make comparisons among models that contain different numbers of parameters. See Statistical Details for the Summary of Fit Report.
Root Mean Square Error
The estimate of the standard deviation of the random error. This quantity is the square root of the mean square for Error in the Analysis of Variance report.
Mean of Response
The overall mean (arithmetic average) of the Y variable.
Observations (or Sum Wgts)
Number of observations used in estimating the fit. If weights are used, this is the sum of the weights. See Statistical Details for the Summary of Fit Report.
In the Oneway platform, the Pooled t Test table summarizes the results of a t test to compare two group means assuming equal variances across groups. This table is available only when the X variable has exactly two levels. See t Test Report.
In the Oneway platform, the Analysis of Variance table summarizes the results of the ANOVA analysis. An ANOVA partitions the total variation into components.
Note: If you specified a Block column, then the Analysis of Variance report includes the Block variable.
Source
The sources of variation. These sources are the model source, Error, and C. Total (corrected total).
DF
The degrees of freedom (DF for short) for each source of variation:
– The degrees of freedom for C. Total are N - 1, where N is the total number of observations used in the analysis.
– The degrees of freedom for the model is k - 1, where k is the number of levels of the X variable.
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).
Sum of Squares
The sum of squares (SS for short) for each source of variation:
– 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 total SS minus the error SS gives the sum of squares attributed to the model. This tells you how much of the total variation is explained by the model.
Mean Square
The sum of squares divided by its associated degrees of freedom:
– 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.
F Ratio
The model mean square divided by the error mean square. If the hypothesis that the group means are equal (there is no real difference between them) is true, then both the mean square for error and the mean square for model estimate the error variance. Their ratio has an F distribution. If the analysis of variance model results in a significant reduction of variation from the total, the F ratio is higher than expected.
Prob>F
Probability of obtaining an F value greater than the one calculated if 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.
In the Oneway platform, the Means for Oneway Anova table summarizes response information for each level of the nominal or ordinal factor.
Level
The levels of the X variable.
Number
The number of observations in each group.
Mean
The mean of each group.
Std Error
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%, Upper 95%
The lower and upper 95% confidence interval for the group means based on a pooled estimate of the error variance and pooled degrees of freedom.
In the Oneway platform, the Block Means report appears only if you have specified a Block variable in the launch window and there are equal counts in each combination of block and level of the X variable.