a linear contrast is a linear combination of variables (parameters or statistics) whose coefficients add up to zero. This is used to compare different levels of a factor in analysis of variance (ANOVA), for example. The coefficients are chosen based on the specific comparisons of interest and they usually sum to zero. This is to ensure that the contrast is not influenced by the overall mean. But the weighted average is most often computed to equalize the frequency of the values in a data set. What then does the weighted average do in a linear contrast? I know that the weights in a linear contrast are used to emphasize or de-emphasize different variables in the combination. But how does it do this and what is the procedure or process for how they are determined?

a linear contrast is a linear combination of variables (parameters or statistics) whose coefficients add up to zero. This is used to compare different levels of a factor in analysis of variance (ANOVA), for example. The coefficients are chosen based on the specific comparisons of interest and they usually sum to zero. This is to ensure that the contrast is not influenced by the overall mean. But the weighted average is most often computed to equalize the frequency of the values in a data set. What then does the weighted average do in a linear contrast? I know that the weights in a linear contrast are used to emphasize or de-emphasize different variables in the combination. But how does it do this and what is the procedure or process for how they are determined?