# WARNING: public use of this package can lead to social media abuse. library("tidyverse") poll <- tribble( ~Title, ~votes, "Irregularly Tyre-annical", 2, "Tyre Repair", 7, "Small things done great", 0, "Where the rubber meets the road", 6 ) ggplot(data = poll, aes(x=reorder(Title, votes), y = votes)) + geom_col() + theme_minimal() + coord_flip() + labs(y = "Title", x = "Votes")
Boo. My personal contribution scored 0. Although the winner is “Tyre Repair”1, the sample size is small, and I couldn’t help wondering if there was a statistically significant difference between that and “Where the rubber meets the road”2. This is a blog partly about statistics after all.
library("EMT") mt <- multinomial.test(poll$votes, prob = rep(1/4, 4))
## ## Exact Multinomial Test, distance measure: p ## ## Events pObs p.value ## 816 2e-04 0.0171
But that’s not a terribly interesting hypothesis – it says that my voters care what title I use. What I really want to know is if there is any that beats all the others. I discovered a post-hoc test for for the Exact GOF, essentially testing each category against the sum of the others, and using Bonferroni corrections. So I’ll have 4 comparisons, and thus my p value should be less than 0.05/4 = 0.0125.
pvals <- tribble( ~Comparison, ~p, "Irregularly Tyre-annical vs. others", multinomial.test(c(2,13), prob = c(0.25, 0.75))$p.value, "Tyre Repair vs. others", multinomial.test(c(7,8), prob = c(0.25, 0.75))$p.value, "Small things done great vs. others", multinomial.test(c(0,15), prob = c(0.25, 0.75))$p.value, "Where the rubber meets the road vs. others", multinomial.test(c(6,9), prob = c(0.25, 0.75))$p.value )
I had to hide the results of that code chunk because package EMT isn’t very nice about output.
|Irregularly Tyre-annical vs. others||0.3845|
|Tyre Repair vs. others||0.0700|
|Small things done great vs. others||0.0307|
|Where the rubber meets the road vs. others||0.2285|
So, basically none of the individual titles can be ruled out! Hmmm. Maybe I have the wrong hypotheses here.
Well, there was also a great write-in candidate “Entyrely Optional”3, and protests to re-open the polls erupted. So I think I will try again with the top two from the first round plus the new candidate.