How do I calculate effect size for percentages of totals? I apologize if this questions is poorly worded or has a very simple answer but I work in a field very different than statistics. I am looking at diction (word use) in books from two different artistic movements  over time. I want to compare words that were first used in each century by each set of authors. For example both sets use words from the 18th century at a rate of 15.5 and 15.2 percent of their total word use. How do I find out if this .3 percent means anything? Would I be looking at effect size? And, if so, what measure should I use?
 A: Look up Cohen's $h$. First, you calculate $h$, which is pretty straightforward:
$$h = 2\times\arcsin\left(\sqrt{p_1}\right) - 2\times\arcsin\left(\sqrt{p_2}\right)$$
Where $p_1$ and $p_2$ are the two proportions.
Then, you have to decide on a cutoff. The "rule of thumb" cutoff is that if $h \ge 0.2$, then you have something interesting. Though in your particular science, a different cutoff might be more appropriate.
A: You can test whether two proportions are equal using a test like the one described here.
This is implemented in R in the prop.test function. For example, your data might look like this:
# count of target words for author 1 and author 2
word_counts <- c(27, 46) 

# total words for author 1 and author 2
total_words <- c(173, 302)


# here are the proportions for the two authors:
> word_counts/total_words
[1] 0.1560694 0.1523179

This tests the null hypothesis that the rate in both groups is the same:
> prop.test(x=word_counts, n=total_words)

    2-sample test for equality of proportions with continuity correction

data:  word_counts out of total_words
X-squared = 2.2201e-30, df = 1, p-value = 1
alternative hypothesis: two.sided
95 percent confidence interval:
 -0.06757982  0.07508279
sample estimates:
   prop 1    prop 2 
0.1560694 0.1523179 

Note that if the sample size is large enough, even this small difference in proportions can be significant:
# count of target words for author 1 and author 2
word_counts <- c(27000, 46000) 

# total words for author 1 and author 2
total_words <- c(173000, 302000)

> prop.test(x=word_counts, n=total_words)

    2-sample test for equality of proportions with continuity correction

data:  word_counts out of total_words
X-squared = 11.873, df = 1, p-value = 0.0005696
alternative hypothesis: two.sided
95 percent confidence interval:
 0.001609876 0.005893091
sample estimates:
   prop 1    prop 2 
0.1560694 0.1523179

A: There are a few ways to do this, but I think that the way to go there is making a contingency table with the counting and applying a chi-square test to check if counting of the sets differed on the centuries.
