# Comparison of item frequencies

I have 3 set of items:

sample1 -> #trump: 25, #hilary: 0, #hillarycrooked: 2, ...
sample2 -> #hilary: 1, #notmypresident: 15, #trump: 0, ...
sample3 -> #obama: 5, #tcot: 10, #hilary: 0, ...


I wanted to use the chi-square test to see how my sample2 and sample3 are similar to my sample1. So I wanted to compare the result of the chi-squared(sample1,sample2) opposed to chi-squared(sample1, sample3) where sample1 would have been my expected values.

The problem is that the expected value may sometime be equal to 0 (so not applicable with the chi square test). What other statistical tool can I use to reach my purpose knowing that my expected and observed data may be <= 0

• @NickCox All my sample are group of twitter users. I count how many times they use some hashtags. For example the sample1 us 25 the hashtag "#trump" but 0 times the hashtag #hilary. – mel Apr 19 '17 at 17:27

Note, instead of a similarity you can also go for a distance function and transform the resulting distance $d$ into a similarity score $s \in [0 ; 1]$, for example through: $$s = \frac{1}{1 + d}, \;\textrm{or: }\; s = \frac{1}{\textrm{exp}\{d\}}$$
I recommend my favorite distance function, the Manhatten distance M$(\cdot)$: $$d = \textrm{M}(X,Y) = \sum^{n}_{i = 1} |x_i - y_i|$$
Here, $X$ and $Y$ refer to sample1 and sample 2, respectively.