For a one-way ANOVA,

a. identify one purpose of one-way ANOVA tables.

b. construct a generic one-way ANOVA table.

The statistical approach of analysis of variance, or ANOVA, divides observed variance data into multiple components for use in additional tests. For three or more groups of data, a one-way ANOVA is used to learn more about the relationship between the dependent and independent variables.

The error mean square is the variance within the sample means. That is, the $(n-k)$divides the error sum squares.

MSE is calculated using the following formula:

$MSE=\frac{SSE}{n-k}$

The squared difference between the measured dependent variable and its mean is S S T (Sum of Squares Total).

The sum of the discrepancies between the predicted value and the dependent variable's mean is called S S R (Sum of Squares due to Regression).

The discrepancy between the actual and anticipated values is called S S E (Sum of Squares Error).

The F-statistic is the ratio of deviation between sample means and variation within the sample. That is, the Error Mean square is divided by the Treatment Mean square.

F-statistic is calculated using the formula:-

$F=\frac{MSTR}{MSE}$

Two mean squares are formed, one for treatments and the other for an error, using the sums of squares S S T R and S S E previously computed for the one-way ANOVA. M S T R and M S E are the abbreviations for these mean squares. An ANOVA table is a common format for displaying these results. The statistics used to test hypotheses about population means are also shown in the ANOVA table.

The statistical approach of analysis of variance, or ANOVA, divides observed variance data into multiple components for use in additional tests. For three or more groups of data, a one-way ANOVA is used to learn more about the relationship between the dependent and independent variables.

The ANOVA table demonstrates how the sum of squares, and thus the mean sum of squares, is distributed per source of variation.

The general form of the table is

$\begin{array}{|lllll|}\hline \text{Source}& \mathrm{df}& \mathrm{SS}& \text{MS=SS/df}& \text{F-statistic}\\ \text{Treatment}& \mathrm{k}-1& \text{SSTR}& \begin{array}{l}\text{MSTR=}\\ \frac{\text{SSTR}}{k-1}\end{array}& F=\frac{MSTR}{MSE}\\ \text{Error}& \mathrm{n}-\mathrm{k}& \text{SSE}& MSE=\frac{SSE}{n-k}& \\ \text{Total}& \mathrm{n}-1& \text{SST}& & \\ \hline\end{array}$