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I have a dataframe in R that contains the the total number of girls and boys at a school, along with the total number of girls and boys who did not complete their summer reading list. I would like to do a proportions test to see if the fraction of boys who do not complete their reading is significantly higher than the fraction of girls;

head(tmp)

       TOTAL  INCOMPLETE
BOYS   1345     534
GIRLS  798      308

Using R, I run the proportion test;

prop.test(x=c(534,308),n=c(1345,798),alternative='less',correct=F)

2-sample test for equality of proportions without continuity correction

data:  c(534, 308) out of c(1345, 798)
X-squared = 0.2569, df = 1, p-value = 0.6939
alternative hypothesis: less
95 percent confidence interval:
 -1.00000000  0.04690901
sample estimates:
   prop 1    prop 2 
0.3970260 0.3859649

I am not sure how to interpret the output. Is the fraction of boys that don't read significantly higher than girls?

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  • $\begingroup$ Is the issue that you don't know how to interpret the p-value? We have numerous answers on site about doing that. Or is it that you don't know how p-values come into it at all? Please add the self-study tag, read its tag-wiki and modify your question to follow the guidelines on asking such questions. In particular, you'll need to clearly identify what you've done to solve the problem yourself, and indicate the specific help you need at the point you struck difficulty. $\endgroup$
    – Glen_b
    Sep 3, 2015 at 1:48
  • $\begingroup$ Also, additionally to what @Glen_b mentioned, by specifying alternative = 'less' you're investigating if the first proportion (boys) is statistically significantly less than the second proportion (girls). I don't know if you designed an experiment for that, but it makes more sense to use alternative = 'greater', as the observed proportion for the boys is larger than the girls. $\endgroup$
    – AntoniosK
    Sep 3, 2015 at 7:59
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    $\begingroup$ @AntoniosK the alternative should not be chosen by examining the data but by prior considerations relevant to the question of interest and subject-area knowledge. If it is chosen with reference to the data, p-values no longer mean what they should (typically, p-values are artificially small). $\endgroup$
    – Glen_b
    Sep 3, 2015 at 9:14
  • $\begingroup$ Totally agree @Glen_b. That's why I mentioned the experiment design, but maybe I wasn't clear. No one should chose the test (especially one-tailed) after observing the results. What I meant was that if his experiment design focused on spotting whether the boys % is stat sign less than girls %, then by just observing the data (39.7% > 38.6%) he didn't have to bother running the prop test. $\endgroup$
    – AntoniosK
    Sep 3, 2015 at 9:23
  • $\begingroup$ @AntoniosK That makes sense. $\endgroup$
    – Glen_b
    Sep 3, 2015 at 10:33

1 Answer 1

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Statistical tests and their interpretation makes sense only when you have previously defined your objective and designed your experiment in order to capture statistically significant differences based on your objective (see my comments above for the reason behind it).

In many cases, however, someone was given a dataset and needs to compare percentages. In that case you interpret the p-value as a metric which classifies your difference as significant or not. You don't know how confident you are about that classification (this is what the statistical power of test exists for).

In your case prop.test(x=c(534,308),n=c(1345,798),alternative='less',correct=F) is not useful as the % of boys is observed to be higher than the girls. So, there's no point in investigating if it is smaller.

You can either:

a) Use prop.test(x=c(534,308),n=c(1345,798),alternative='greater',correct=F) if you have strong evidence that the boys % is generally expected to be larger than the girls, or

b)Use prop.test(x=c(534,308),n=c(1345,798),correct=F) if you don't have any idea which proportion is expected to be higher generally. This is the most common way to investigate differences in %.

All 3 tests will tell you that there's no statistically significant difference, based on what you observed on this dataset.

It will be useful to search about : p value interpretation, statistical power, efficient sample size, designing experiments, designing AB tests.

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