Probability distribution for political partys

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Discussion Overview

The discussion centers on the appropriate probability distribution to use when analyzing opinion poll data for political parties in a country with seven parties. Participants explore the statistical significance of changes in voter percentages and debate the suitability of various distributions, including binomial and normal distributions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions which distribution to use for testing statistical significance when a party's voter percentage increases, suggesting multinomial or binomial distributions.
  • Another participant proposes using the normal distribution for a difference of means test between pre- and post-increase samples.
  • A participant expresses uncertainty about the normal distribution's applicability, noting the discrete nature of the voting data compared to continuous variables.
  • One participant suggests modeling the situation as a binomial distribution, comparing voters for the party against those not voting for it.
  • Another participant agrees with the binomial model but notes that with a large enough sample size, the binomial distribution can be approximated by a normal distribution, referencing traditional practices in statistical analysis.
  • A later reply reiterates the approximation of the binomial distribution to a normal distribution under certain conditions, invoking the central limit theorem.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate distribution to use, with some advocating for the binomial model and others supporting the normal approximation. The discussion remains unresolved regarding which distribution is definitively the best choice for this scenario.

Contextual Notes

Participants highlight the dependence on sample size and the nature of the data (discrete vs. continuous) as factors influencing the choice of distribution. There is also mention of the central limit theorem as a justification for using the normal approximation.

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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! :smile:
 
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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?
 
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! :smile:
 
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.
 
mXSCNT said:
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.

Ah, central limit theorem, how we love thee.
 
Okey, I see.
 

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