# Probability distribution for political partys

• Mårten
In summary, the conversation discusses the use of different distributions to test for statistical significance in an opinion poll. The normal distribution can be used for a difference of means test, while the binomial distribution is suitable for a discrete variable with multiple possible values. However, for a large enough sample size, the binomial distribution can be approximated with a normal distribution. This is due to the central limit theorem, which allows for simpler analysis.

#### Mårten

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?

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.

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.

## 1. What is a probability distribution for political parties?

A probability distribution for political parties is a mathematical representation of the likelihood of each party winning in an election. It takes into account various factors such as past voting patterns, demographics, and current events to predict the probability of each party's success.

## 2. How is a probability distribution calculated for political parties?

A probability distribution for political parties is calculated using statistical methods and data analysis. Different models and techniques may be used, such as regression analysis or machine learning algorithms, to determine the probabilities of each party's success in an election.

## 3. Why is a probability distribution important for political parties?

A probability distribution provides valuable insights for political parties to make strategic decisions and allocate resources effectively. It can help parties understand their chances of winning an election and identify key areas to focus on to improve their chances of success.

## 4. Can a probability distribution accurately predict election outcomes?

While a probability distribution can provide a good estimate of the likelihood of each party winning an election, it is not a guarantee of the actual outcome. Many other factors, such as unforeseen events or changes in public opinion, can influence the final result.

## 5. How can a probability distribution be used to analyze political trends?

A probability distribution can be used to analyze political trends by tracking changes in party probabilities over time. This can help identify shifts in public opinion and predict potential outcomes in future elections. It can also highlight the impact of certain events or policies on party probabilities.