I'm dealing with a small sample size and my categorical variables tend to be 4 vs 2 or 8 vs 0 in terms of their numerical value. Does this make a Chi Square less powerful or even an inappropriate test to run?
Thank you in advance!
P.S. My suspicion is it does not -- my sample size is 76 and I may just need to address it
Edit: I've attached an image of what I am dealing with -- I don't think Fisher's will work.
Because the Chi- square distribution is asymptotic for this test the usual conditions are np>5 obs per cell. If that is not suitable then exact versions are available for some tables. See chi-square test and Fisher exact test in a good statistics book. These tests are nonparametric. A link is: chi square test - Bing
and Fisher's Exact test: Fisher's exact test - Bing Best
An alternative is Fisher.,'s Exact test if cell frequency is less than 5.
Hello Azeem,
In addition to the advice David Eugene Booth has already given, I will add one point. Yes, the statistical power of any test, exact or asymptotic, will not be very high for this data set because so many of the cells have such low observed (and expected, under the null hypothesis) frequencies.
Unless the effect (here, relationship between yield value and size category) was strong, your current sample size offers little opportunity to detect that the effect is non-zero. That's not your fault; it's just what's there. If you have the luxury of being able to collect far more data, it would be a good idea to do so, if for no other reason than having enough data for negative yield cases to be confident about the relationship.
Good luck with your work.
The standard (asymptotic) chi-square test is susceptible to giving falsely significant results when there are small cell counts. Lack of power is the other half of this problem.
You can use an exact Kruskal test, or an exact Cochran-Armitage Trend test, which will be a little more powerful than the Pearson test because you have ordered categories. I started to do this for you - but you should make your decision about getting more data before you see the results, or that will increase your type-I error rate (unplanned interim testing).
Exact p-values have a problem; they depend on the assumption the data you have is representative of the larger population. With only 6 subjects in the "negative" group, that just isn't reasonable. If it was significant, it would still be inconclusive because the negatives have very poor representation. A not-significant result also isn't meaningful because the power is so low.
Get more data if you can, hopefully enough that you can fairly claim the be representing the population, then do your test.
Thank you all for your responses. Unfortunately, the data collection process is complete. I am in the midst of conducting a retrospective cohort study, comparing the accuracy of a certain diagnostic tool versus the baseline characteristics. In the image attached to my question, the associated numbers are the sizes of certain lesions and the corresponding accuracy of this new tool.
The Chi-square value is a number that puts together all of the variations between the real data and the predicted data if no discrepancy occurs. The chi-square value of the real data and predicted data (unless there is a difference) is 0.
The Chi-square test would not be appropriate here. Chi-square test assumes that the expected frequency count for at least 80% of the cell in a contingency table is at least 5 and should not be less than 1. Read more https://www.reneshbedre.com/blog/chi-square-test.html
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size