Using Chi Square Test to check the effect of a variable?

#1
So I am a quite beginner in statistics and I am trying to see whether I am using a statistical method in a correct way or not.
I am trying to see the effect of income level towards fraud behavior. So in the so-called population, I have counts for each of the bad/good/new users:
BAD: 260
GOOD: 480
NEW:50

I also have a group of high-income users with these counts:
BAD: 50
GOOD: 95
NEW: 8

I am trying to see whether high income affects user fraudulent behavior. Can I use Chi-Square Goodness of Fit test in this problem? By using Chi-Square Goodness of Fit test, I am trying to see if the distribution of bad/good/new user with high income level differs significantly from the expected.
When I do this, my chi-square-stat does not exceed critical value and have high p-value (0.88) and thus I don't reject the null hypothesis (ie. there is not effect of income level towards user fraudulent behavior)
I would like to see if this is the correct way in applying the Chi-Square test.
 

Miner

TS Contributor
#2
Yes, you can use the chi-square test for this. The only caution I would give is that if your sample size gets too large, it can give false positive results.
 
#3
Thanks for that!

Why large data can give false positive results? I am actually asking this in other forum as well and people are saying my data are actually still very small.
 

obh

Active Member
#4
I assume this is relevant to every statistical test.

If there is a very small unimportant difference between the two groups it will be still statistical significant with a large enough sample size.
Also, if one group is very small and the other is very big, part of the difference may be only a technical difference related to the fact that the count is discrete.

The solution is also to look at the effect size, not only on the p-value.