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This might be a bit of a dunce's question, but I was wondering about the difference between a sample and a population.

Obviously, if you have data relating to 200,000 people but you only look at 200 people, then that is a sample. But what if you are comparing one year to another but using all data?

For example, if you make a change to remuneration and staff turnover drops from 12% to 10%, what is the process you'd go through to work out if that change is significant? Look at turnover for each year?

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    $\begingroup$ If you have a notion of “significant” then you are treating your observations as a sample from some larger population. $\endgroup$
    – Dave
    Apr 14, 2021 at 10:48

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If you want to know if there is a significant difference in the "before" and "after", then you probably should do a Paired t-test. These tests are done when the same individuals are measured twice.

When you perform the Paired t-test, you choose the significance level that you want and then you check the p-value obtained from the test. If the p-value is lower than the significance level you choose, then you can reject the null hypothesis that the "before" remuneration and "after" remuneration values are the same, i.e, there is a significant difference. However, I don't understand what is your question regarding the sample.

Edit: If you want to test a "group" vs another different "group" then you can just do a regular unpaired t-test. It handles unequal sample sizes, however, you have to check if the assumptions for the test hold. If you are also concerned about unequal variance (or standard deviation), then you should use a slightly modified version of the unpaired t-test called the Welch test.

Do you have the pay for each one in the 300 employees group and the pay for each of the 400 employees group? Or do you only know the total (30k and 32k)? If you only have the total, I don't think you can do much.

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  • $\begingroup$ Rather than looking at the different between the same individuals, what if the samples are of different individuals and the samples of different sizes? Eg mean pay for 300 employees is £30k in one year but £32k in the next year when there are 400 employeess What is the best test to use then? $\endgroup$
    – StatisticsPersonInTraining
    Apr 15, 2021 at 6:43
  • $\begingroup$ If you want to test a "group" vs another different "group" then you can just do a regular unpaired t-test. It handles unequal sample sizes, however, you have to check if the assumptions for the test hold. If you are also concerned about unequal variance (or standard deviation), then you should use a slightly modified version of the unpaired t-test called the Welch test. $\endgroup$
    – Numbermind
    Apr 15, 2021 at 9:44
  • $\begingroup$ Do you have the pay for each one in the 300 employees group and the pay for each of the 400 employees group? Or do you only know the total (30k and 32k). If you only have the total, I don't think you can do much.. $\endgroup$
    – Numbermind
    Apr 15, 2021 at 9:46
  • $\begingroup$ I do have the data for each. They are two different group since they are from two different years, but there is a big overlap. Many of the employees are the same. $\endgroup$
    – StatisticsPersonInTraining
    Apr 15, 2021 at 10:31
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    $\begingroup$ Just do a regular t-test to test if group A (group with 300 persons) is statistically different than group B (group with 400 persons). $\endgroup$
    – Numbermind
    Apr 16, 2021 at 13:13

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