The purpose of an Analysis of Variance (ANOVA) is to test for significant differences between means of three or more groups. However, to use this statistical technique, certain assumptions must hold true.
One of these assumptions is that each cell is an independent sample of interval or ratio scores. This means that each group tested is independent from the other groups, and the data collected are measured on an interval or ratio scale.
The second assumption required is that the populations represented are normally distributed. This indicates that the sample data from each group forms a bell curve or normal distribution when plotted on a graph.
The third assumption necessary is that the variances of all the represented populations are homogeneous. This, in essence, means that the variability or spread of scores within each group is approximately equal.
However, the statement that "the means of all the populations represented are equal" is not an assumption for conducting a two-way, between-subjects ANOVA. It's actually the null hypothesis which the ANOVA seeks to test. The goal of the two-way, between-subjects ANOVA is to determine whether there are significant differences among the group means. Stating beforehand that all the group means are equal runs contrary to the purpose of the test itself.
Therefore, the incorrect assumption for conducting a two-way, between-subjects ANOVA among the provided options is D: "the means of all the populations represented are equal".