# what statistical test should be used for testing number/proportion of people who agreed in 2 different years

I want to measure if the number of people who agreed on a likert scale (1 strongly disagree - 5 strongly agree), so responded with a 4 or 5 had a statistically significant increase from the previous year.

2 different groups were surveyed and they have different sample sizes but they were the same questions so I'm thinking 2 sample t-test, but I'm not sure if i should just run a t-test since I'm only concerned about people who disagreed or were neutral.

• As you have formulated it, this appears to be a (simple, textbook) Binomial test of proportions. With a sufficient number of both 4/5 responses and 1-3 responses in both years, a t-test would be an adequate approximation. Is there some aspect of your data or objectives that would suggest otherwise?
– whuber
Commented Jun 17, 2022 at 17:21
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– Sycorax
Commented Jun 17, 2022 at 22:17

Comment: Suppose that Gp 1 had 345 agreements (Likert 4 or 5) out of 1000 subjects and Gp 2 had 551 agreements out of 1500 subjects. Then as @whuber suggests prop.test seems appropriate. However, in R this test would not--even nearly--find a significant difference at the 5% level between proportions $$0.345$$ and $$0.367$$ "in favor." [Even if Gp 2 had a much larger proportion of Likert 5's.]

prop.test(c(345, 551), c(1000, 1500), cor=F)

2-sample test for equality of proportions
without continuity correction

data:  c(345, 551) out of c(1000, 1500)
X-squared = 1.3014, df = 1, p-value = 0.2539
alternative hypothesis: two.sided
95 percent confidence interval:
-0.06058569  0.01591902
sample estimates:
prop 1    prop 2
0.3450000 0.3673333


If you need a discussion using a t test, then please give an example of Likert-5 sample distributions for Groups 1 and 2. (There are several reasons why a two-sample Wilcoxon test might not work well.)