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I have Two related questions:

1) I have raw counts for voting vs. non-voting for the years 2018 and 2020.

2018 -> 11,000 voters and 3,000 non-voters

2020 -> 10,000 voters and 3,500 non-voters

How can I calculate that the decrease in voters from 2018 to 2020 is significant or not? What test would I use?

2) I also have the voter turnout rate which is 67% in 2018 and 66% in 2020. How can I check whether this 1% drop in voter turnout rate is significant?

what tests could I use in each case?

Thank you in advance!

anonxyz
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  • I should add that--I have the total voting population number as well (if that is helpful) – anonxyz Feb 06 '22 at 02:21
  • [Significantly *what* kind of change](https://stats.stackexchange.com/a/125538/44269)? – Alexis Feb 06 '22 at 02:30
  • If that is what actually happened in the election, then any change is significant in the sense that you can be sure that there was a change. If this is based on random sampling of individuals from a much larger population and asking them whether they were voters or non-voters or something else (e.g. children or non-citizens) then you can apply usual techniques – Henry Feb 06 '22 at 02:43
  • It sounds like the total population for 2018 is 14,000 people. Is this true? If so, there's probably no need to conduct a hypothesis test (like a chi-squared test), since you have data on the whole population. If this is not true, wouldn't you be able to get the data for the total potential voters in the election and the total number of actual voters? – Sal Mangiafico Feb 06 '22 at 16:03
  • @SalMangiafico Thanks for the question. No, the total population is a bit bigger because it includes those who are not allowed to vote (I do have the total population size as well). But my problem is that I wanted to know whether the year-to-year change is significant. The total population size and sample sizes across both years are slightly different in size. – anonxyz Feb 06 '22 at 18:48
  • My point is that if you are looking at the whole voting population, there's no point in conducting a hypothesis test. You know how many people voted. There's nothing to estimate. It's like if I have 10 dollars in my wallet yesterday and 12 dollars in my wallet today, there's no place for a statistical test. There's some discussion on the topic here: [stats.stackexchange.com/questions/70296/how-to-report-data-for-an-entire-population/](https://stats.stackexchange.com/questions/70296/how-to-report-data-for-an-entire-population/). – Sal Mangiafico Feb 07 '22 at 10:45

1 Answers1

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(1) In 2018, you have 11,000 voters out of 14,000 potentially available, and in 2020, you have 10,000 voters out of 13,500.

In R, assuming randomness in willingness and ability to vote, you could compare the two proportions of voters using prop.test as follows (declining continuity correction with parameter cor=F on account of large sample sizes):

prop.test(c(11000,10000), c(14000,13500), cor=F)

        2-sample test for equality 
        of proportions without 
        continuity correction

data:  c(11000, 10000) out of c(14000, 13500)
X-squared = 77.015, df = 1, p-value < 2.2e-16
alternative hypothesis: two.sided
 95 percent confidence interval:
  0.03493139 0.05501570
 sample estimates:
    prop 1    prop 2 
 0.7857143 0.7407407

The proportions $.786$ and $.741$ are significantly different on account of the P-value near $0.$

Alternatively, you could do a chi-squared test on a $2\times 2$ table:

TBL = rbind(c(11000, 10000), c(3000, 3500)); TBL
      [,1]  [,2]
[1,] 11000 10000
[2,]  3000  3500

chisq.test(TBL, cor=F)

        Pearson's Chi-squared test

data:  TBL
X-squared = 77.015, df = 1, p-value < 2.2e-16

Except for the input syntax, the two tests are essentially equivalent.

(2) You need to use counts (as above) instead of percentages.

BruceET
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