Chi squared

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#1
I am measuring if a number of different parameters of two populations changed with time
Male (24 changed, 13 did not change)
Female (32 changed, 5 did not changed)

Is it valid to do a Pearson Chi squared instead of an exact Fischer test to show that more parameters changed in the female than male population
Thanks
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4 years ago
#2
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4 years ago
#3
(Original post by jsmith6131)
I am measuring if a number of different parameters of two populations changed with time
Male (24 changed, 13 did not change)
Female (32 changed, 5 did not changed)

Is it valid to do a Pearson Chi squared instead of an exact Fischer test to show that more parameters changed in the female than male population
Thanks
Chi-Squared is better for large cell sizes, I'm pretty sure you can lose power with Fisher's Exact test.
Some of the varying degrees of what classify as "large" are listed here.
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4 years ago
#4
Hey, I'm doing AS geography and need to know what chi squared is. Can you remind me how it's done and maybe I could help u out with you question????
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#5
(Original post by joostan)
Chi-Squared is better for large cell sizes, I'm pretty sure you can lose power with Fisher's Exact test.
Some of the varying degrees of what classify as "large" are listed here.
So can I not use Pearson Chi?
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4 years ago
#6
(Original post by jsmith6131)
So can I not use Pearson Chi?
Well that depends on how you define a "large sample size" and an "adequate cell size".
The link I posted suggested around 5 or more in each cell is sufficient for a 2x2 table.
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#7
(Original post by joostan)
Well that depends on how you define a "large sample size" and an "adequate cell size".
The link I posted suggested around 5 or more in each cell is sufficient for a 2x2 table.
Ye, I have an expected count of 9.0 as the minimum. THe other expected counts are larger.
So this means it is a valid test then, right?
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4 years ago
#8
(Original post by jsmith6131)
Ye, I have an expected count of 9.0 as the minimum. THe other expected counts are larger.
So this means it is a valid test then, right?
I'd go for it based on what I've read, though I'm not an expert on the matter by any stretch of the imagination.
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4 years ago
#9
(Original post by jsmith6131)
I am measuring if a number of different parameters of two populations changed with time
Male (24 changed, 13 did not change)
Female (32 changed, 5 did not changed)

Is it valid to do a Pearson Chi squared instead of an exact Fischer test to show that more parameters changed in the female than male population
Thanks
The short answer is that it is preferable to do a chi-squared test (with continuity correction) (or the equivalent test-of-proportions). In fact, whichever way you do it, you'll end up with a p-value hovering around the "magic" 0.05 mark - so your conclusion will be that there is only weak evidence to reject the null hypothesis of no difference.

Here's a longer answer. The numbers that you have presented suggest that the experimental design involved selecting 37 men and 37 women from some underlying population and then measuring some fact about them. The question of interest is whether the proportion of men where the fact is true is different from the proportion of women where the fact is true. That is, the experimental design points towards using a test for the difference of proportions. It turns out that the standard test for difference of proportions is equivalent to a chi-squared test (with continuity correction).

If you stick the data in a 2x2 table, you have the situation where the column totals are fixed at 37 for both women and men. This is not the only way in which a 2x2 contingency table can arise. There are experimental designs that lead to 2x2 tables with fixed rows (and not fixed columns), fixed rows and fixed columns, and neither fixed rows nor fixed columns, but fixed overall total. Each of these situations (strictly speaking) has its own statistical test. It just so happens that chi-squared approximates them all pretty well!

The situation in which Fisher's exact test is valid is where both the row totals and the column totals are fixed by experimental design (google the lady tasting tea for the paradigmatic example). In this case, the 2x2 table is exactly specified by the value of a single one of the entries and that distribution is known exactly (it's a hypergeometric distribution) - hence the name of the test. So here, the FET is not really appropriate, although the answers it will give will approximate the chi-squared answer.
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#10
(Original post by Gregorius)
The short answer is that it is preferable to do a chi-squared test (with continuity correction) (or the equivalent test-of-proportions). In fact, whichever way you do it, you'll end up with a p-value hovering around the "magic" 0.05 mark - so your conclusion will be that there is only weak evidence to reject the null hypothesis of no difference.

Here's a longer answer. The numbers that you have presented suggest that the experimental design involved selecting 37 men and 37 women from some underlying population and then measuring some fact about them. The question of interest is whether the proportion of men where the fact is true is different from the proportion of women where the fact is true. That is, the experimental design points towards using a test for the difference of proportions. It turns out that the standard test for difference of proportions is equivalent to a chi-squared test (with continuity correction).

If you stick the data in a 2x2 table, you have the situation where the column totals are fixed at 37 for both women and men. This is not the only way in which a 2x2 contingency table can arise. There are experimental designs that lead to 2x2 tables with fixed rows (and not fixed columns), fixed rows and fixed columns, and neither fixed rows nor fixed columns, but fixed overall total. Each of these situations (strictly speaking) has its own statistical test. It just so happens that chi-squared approximates them all pretty well!

The situation in which Fisher's exact test is valid is where both the row totals and the column totals are fixed by experimental design (google the lady tasting tea for the paradigmatic example). In this case, the 2x2 table is exactly specified by the value of a single one of the entries and that distribution is known exactly (it's a hypergeometric distribution) - hence the name of the test. So here, the FET is not really appropriate, although the answers it will give will approximate the chi-squared answer.
THanks very much for your help
Really appreciate it!!
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