Comparing Town A and Town B: What Test to Use?

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Discussion Overview

The discussion revolves around the comparison of red blood cell levels between two towns, Town A and Town B, based on sample data. Participants explore statistical methods for comparing proportions and calculating p-values, addressing the appropriate tests and assumptions necessary for analysis.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asks which statistical test to use for comparing the proportions of individuals with the "right" amount of red blood cells in Town A and Town B, expressing uncertainty about how to begin the analysis.
  • Another participant questions the assumptions regarding the remaining individuals in both towns, suggesting that the analysis may overlook important data about those not described.
  • A suggestion is made to use the Chi-square distribution to assess differences between the two populations, with a promise to provide further details later.
  • A follow-up post outlines a method for calculating the Chi-square statistic, including steps for determining observed and expected frequencies, calculating degrees of freedom, and finding the p-value using a Chi-square distribution table.
  • There is an implication that if the p-value is less than the significance level, it could indicate no difference between the populations, but this is presented as conditional and not definitive.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions necessary for the analysis, particularly regarding the untested individuals in each town. There is no consensus on the appropriate method or the implications of the statistical results.

Contextual Notes

Limitations include assumptions about the populations in Town A and Town B, particularly regarding the individuals not included in the initial sample. The discussion also highlights the need for a clear definition of "right" levels of red blood cells and the significance level for the Chi-square test.

MuhTheKuh
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In Town A in a sample of 3591, 2498 have the "right" amount of red blood cells.
In Town B 856 have been tested and 277 have levels close to the right amount.
What test do I have to use to compare Town A and Town B?
And how do I compute the p-value for this test and what checks have to be done to justify the appropriate test?
I simply have no idea what would be the right thing to even start with...
 
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What about the other people in either town that you have not described? Do the other 1093 people in town A have levels equal to those of the 277 in town B? Do the other 579 people in town B have the "right" amount of red blood cells?
 
For starters, you could use the Chi-square distribution to determine whether there is any difference between the two populations. I'll tell you about that later.
 
I'm back. I am going to assume that the remaining 1093 in town A don't have the "right" amount of red blood cells, and that the remaining 277 in town B do. So, the first step is to calculate the Chi-square statistic. Note: Before you do this, you need to set a level of significance. Anyways, to compute the Chi-square statistic,

1) Take the number of people (say, in town A) that have the "right" amount of red blood cells (the observed frequency)

2) Subtract that from the number of people in town B that have the "right" amount of red blood cells (the expected frequency).

3) Divide that by the expected frequency.

4) Repeat steps 1-3 as necessary.

Next, calculate the degrees of freedom. This step is rather simple. Just take the number of categories you have and subtract that number by one.

Then do a Google search or look in a stats book for a Chi-square distribution table. Using the table, you can compute the p-value. If the p-value is less than your level of significance, you can say that there is no difference between the two populations. If not, you can use a different test to determine which population is different.
 

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