$Need help with negative proportions in experiment$

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$Need help with negative proportions in experiment$

Hello! I got referred to here by someone from the econometrics subreddit.

I ran an experiment with a treatment and a control group. Treatment group voted under an electoral rule, where voters could cast a negative vote (with a score of -1) and a positive vote (+1). Control group used the standard First-Past-The-Post rule.

I want to compare the results of extreme parties (I know which those are) and see if the difference is significant. However, these extreme parties obtained a negative result, so a normal test of proportion doesn't work. What do I do?

Statistics

Farmin

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Hey Farmin,

Since your data involves "non-standard" voting scores, you could consider using a "non-parametric" test like the Wilcoxon rank-sum test (also known as the Mann-Whitney U test) to compare the results of the extreme parties between the treatment and control groups. This test doesn't assume a specific distribution and could be suitable for your situation. A traditional test of proportion might not be suitable due to the negative values you got. Just make sure to check the assumptions and conditions for applying this test to your data.

Alternatively, you can transform your negative votes into positive values for the purpose of analysis. You can add a constant value (e.g., the maximum possible negative score) to all the negative votes to make them positive. This will allow you to compare the performance of extreme parties in both groups more easily. Then, you can calculate the difference in the results (after transformation) of extreme parties between the treatment and control groups (subtracting the transformed results in the control group from those in the treatment group). And finally, perform statistical test on these differences to determine whether they are significantly different from zero. Remember, that transforming the data allows you to perform a more standard statistical analysis, but it's important to clearly explain and justify this transformation in your analysis and reporting.

Best,
Kav10

Kav10

2.1K

Farmin

0

Hey Kav10, Thank you very much for your answer. I will look into the first option, but in the meantime, please clarify something for your second suggestion. If I add a constant to the negative votes, should I not add the same constant to all parties? And once I do, what kind of statistical test should I use to determine whether the difference is significantly different from zero?
- Kav10
  
  0
  
  Yes, you should apply the same constant to all parties consistently. This ensures that you're comparing the parties' performance on a common scale. Since you're interested in comparing the differences between two groups (treatment and control), you can use a t-test for paired samples.
Farmin

0

I thought t-tests were only used to compare means. However, I want to compare sums here, not means.
- Kav10
  
  0
  
  That’s right. For comparing sums, you can use the Wilcoxon test I explained above.
Farmin

0

My apologies, but then I don’t understand. So how do I use the t-test after adding a constant?
- Kav10
  
  0
  
  Not the t-test. The Wilcoxon Test.
Farmin

-1

In that case, what is the difference between the two approaches you suggested? I’ll have to use a non-parametric test on both occasions.

$Need help with negative proportions in experiment$

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