# Probability distribution for political partys

If you make an opinion poll over which party people will vote on in a country with seven partys, you get different percentages for the different partys, based on a sample. Say one party has, according to the poll, increased its voters from 5 to 10 percentage points. You want to test if this is statistical significant. What kind of distribution are you using then? It cannot be the normal, can it? Maybe the multinomial, as in septimonial? Or is it the binomial? Which one is it and why is it that one?

Hope someone knows and can explain a little bit! You can use the normal distribution, performing a difference of means test between a sample of voters before the apparent increase and a sample of voters afterwards.

But how do I know it's a normal distribution here? What's the argument one should use?

I know that when doing repeated measurements of for instance the length of 20-year old girls in a population, I will get a normal distribution. But now we don't have a continuous variable (length), but instead a discrete variable with seven possible values (the seven different partys). Doesn't that make any difference?

CRGreathouse
Homework Helper
I would model it as a binomial distribution: the number of voters for the party in question vs,. the number of voters not for that party.

Ah, okey. That seems reasonable. I think I understand now. Thank you! Although the number of observed votes for a party is technically binomially distributed, for a large enough sample size in comparison to both p and 1-p (where p is the probability of a vote for the party), it is approximately normal. Approximating it with a normal distribution is traditional and makes analysis simpler.

CRGreathouse