# Comparison of dispersion measures of different samples with different subsamples

Context: I have data on movie ratings and I want to find what factors affect the rating the most. I have $$k$$ features $$F_1, F_2,\ldots,F_k$$ characterizing a movie - for example, director, lead actor, genre, etc.

Now for each feature value, I need to get a representative rating. For example, I'll fix the "value for director feature" (say $$F_1$$) as Steven Spielberg and calculate the median of the ratings of all movies by Spielberg (avoiding mean due to potential outlier ratings). This will give me a representative rating of a movie directed by Spielberg. I can do the same thing for other directors, getting representative ratings for movies directed by each.

Notationally, let the values of $$F_1$$ be $$F_1^1,F_1^2,\ldots,F_1^{n_1}$$ (different directors). More generally, the different values of feature $$F_i$$ are $$F_i^1,F_i^2,\ldots,F_i^{n_i}$$. For each feature value, we calculate the medians of all movies having that feature value: $$M_i^1,M_i^2,\ldots,M_i^{n_i}$$. Next, I calculate the coefficient of variation of these medians for each feature. e.g. for $$F_1$$, I'll calculate CV of $$M_1^1,\ldots,M_1^{n_1}$$.

If the CV of medians for $$F_1$$ is high, that means the representative rating varies substantially as we change the directors, which in turn means that director is probably an important factor in deciding movie rating. On the other hand, if $$F_r$$ feature corresponds to the distributor, and if the CV of medians $$M_r^1,\ldots,M_r^{n_r}$$ is low, that means even if we vary the distributor, it doesn't impact the representative rating that much, and hence distributor is probably not an important factor for rating.

Question 1: Some features may have several possible values (e.g. director) - in that case I'll have enough representative values, and I'm comfortable taking the CV because I have a good enough "sample of medians". But what about features with very few values? e.g. broad genre category may only have $$5$$ or $$6$$ or $$7$$ values. I may even have a feature like "International / Domestic" that only has $$2$$ values. Any suggestions on how to deal with such cases?

Question 2: What other caveats should I be looking out for? Any problems or major fail conditions with the overall approach? Again, would appreciate any tips/suggestions or modifications to the approach.