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 When there are only two rows

Big picture

Two-way ANOVA can be done with any number of rows in the data table, each representing different levels in one of the grouping variables, but is often done with only two rows. When there are two rows, Prism (starting with version 8) reports the difference between the two row means along with the 95% confidence interval for that difference.

When there is little interaction between the row and column factor, the overall difference between row means (with its confidence interval) may be a useful way to present the data. If there is strong interaction, then the difference between row means varies among columns, so the overall difference between row means may not be useful.

Calculation details

If there are no missing values, the two row means are computed as the mean of the values in all the columns in that row. If there are missing values, the two row means are computed as the mean of the predicted means for all the columns in that row.

The difference between row means is computed as the mean of Row 1 minus the mean of Row 2.

The standard error of the difference is computed. The equation below is used where MSresidual is the mean square of the residuals reported in the ANOVA table, and Na and Nb are the two sample sizes. If row 1 has four columns and entry of data in triplicate with one missing value, Na would equal 11.  When there are missing values, the computation of the SEdifference is more complicated. The margin of error equals SEdifference multiplied by the  critical value of the t distribution, using Na+Nb-2 degrees of freedom.

The confidence interval equals the difference between means plus or minus the margin of error.