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Suppose we have test scores on a set of individuals at various time points and wish to assess if more than would be expected are increasing or decreasing over the course of these time points. We are specifically interested in strict monotonicity in a specified direction. e.g. for three time points t1 < t2 < t3 or t1 > t2 > t3. We do not allow for ties because this would water down the hypotheses of interest to further include no change between all groups or between subsets of groups as well as increasing or decreasing scores. We can test the ''observed number'' of individuals showing a strictly increasing or decreasing set of scores to the ''expected number'' we would obtain by chance using a chi-square test. This calculation is performmed in this [attachment: spreadsheet.] |
Testing for an increasing or decreasing trend across categories
Suppose we have test scores on a set of individuals at various time points and wish to assess if more than would be expected are increasing or decreasing over the course of these time points. We are specifically interested in strict monotonicity in a specified direction. e.g. for three time points t1 < t2 < t3 or t1 > t2 > t3.
We do not allow for ties because this would water down the hypotheses of interest to further include no change between all groups or between subsets of groups as well as increasing or decreasing scores.
We can test the observed number of individuals showing a strictly increasing or decreasing set of scores to the expected number we would obtain by chance using a chi-square test. This calculation is performmed in this [attachment: spreadsheet.]