I have an independent variable is a manipulation/predictor which is applied in increasing degrees of strength across groups. The independent variable alters the amount of variation in the dependent variable.
Because we are looking at variance, I cannot use Spearman's Rho to calculate correlation without a weird hack (detailed below).
What is the best way to measure the correlation of variance?
In non-mathematical terms, I am testing if increasing the use of a metaphor/mental model unifies responses. If the mental model alters the way people think about a problem, then increasing the "reminders" of this mental model should unify the responses.
There are 5 independent groups, 0-4, ranked according to the number of "reminders" in each one. As the reminders are qualitatively different, I must use ranks.
If one examines the SD of each group according to rank, they line up almost perfectly:
SD - group
- .639 - drop down menu
- .604 - vertical
- .484 - horizontal
- .4504 - colored
That's a difference of ~15% and ~8%, albeit a very rough and indirect way of measuring change in variance. However, Bartlett and Levene's tests confirm a statistically significant difference in the variance between the groups.
However, neither Spearman nor Kendall look at variance directly, so a difference of -1 and +1 will negate each other using these measures. If I combine the two extreme scores (0-1-2 -> 0-1) then I get a Spearman's of .142 with a sig <.001.
While I think this is a defensible hack, it doesn't seem to match up with my ad-hoc analysis above.