I want to test the association between the ethnicities of the respondents (6 groups) with study sites (2 study sites), to see whether the distribution of the ethnicities varies across the study sites.
I intend to use chi-square or fisher exact test, but the SPSS automatically convert it into 2x2 contingency table. May I know is there any test that could test the association between two categorical variables with 6x2 contingency table (and some of the groups are zero in frequency)?
You can do the chi-squre test for contingency tables online:
http://www.physics.csbsju.edu/stats/contingency_NROW_NCOLUMN_form.html
For example 2 rows, 6 columns:
A B C D E F 1 35 30 25 15 5 0 2 15 20 25 35 45 50
Yields:
chi-square = 84.7 degrees of freedom = 5 probability = 0.000
If some of the rows in your 6x2 contingency table are empty (zero row totals) you cannot do a chi-square test on the full table. It would be like testing a hypothesis that 0 = 1. The Chi-square test uses the expected frequencies (row total x column total / grand total) and empty row totals will yield zero expected frequencies; in calculating the chi-square statistic each term is divided by the expected frequency, which cannot happen if some of the expected frequencies are zero.
Francois E Steffens , thank you for your answer. May I know what is your suggestion if some of the rows in the table are empty? Any other statistical test that could be used?
Francois is saying you cannot run a chi-square test when a row total is empty, not when a row cell is empty. Thee Fisher exact chi-square test can be used in your case. Most (if not all) statistical software packages include such a test, provided the contingency table is not too complex (e.g., an 12 x 12 table).
https://www.researchgate.net/post/How_does_one_do_chi_square_test_in_SPSS_for_a_3_x2_contingency_table_and_cells_with_a_count_less_than_5
I am afraid you cannot create something out of nothing. Without any responses you can report on their response rate, not on the details of their response. At best you can report that four of the groups did not respond, which is in itself a finding. You may try to interview members of the non-responding groups to find out why they did not respond, which would also be worth reporting, and then do your best to attract some responses from those groups.
Samuel if you have zero in some categories, you have to use "maximum likelihood" method instead of Pearson's with chi-square. Maximum lilkelihood is more robust (it has more power) against small sample sizes. For 2-way tables, small sizes are considered when having scores with less than in any of the frequencies.
Jos Feys
Francois E Steffens
Rafael Sanchez-Marquez
Thank you for the detail explanations. I still wondering whether Fisher exact or maximum likelihood better suited for my case.
I agree with you in using Fisher's exact test for this case, but because the sample size is very small (C=0 for some categories). The reason is not the word 'exact'. In the context of confidence interval estimation and hypothesis testing, 'exact' does not mean 'better' or 'precise', it means that the method uses the exact (discrete) distribution of the statistic that represent the counts instead of an approximation or an asymptotic method. The result, in terms of actual coverage, is more conservative, so greater than the nominal coverage chosen for the test (1-alpha). Conclusion: Yes, you can use Fisher's 'exact' test for this case, but is not always the 'best' method. It depends on the case and the objective.
Some researchers have worked on this topic: 'exact' methods vs approximate. See:
- Agresti, A., & Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician, 52(2), 119-126.
- Barker LA. A comparison of nine confidence intervals for a poisson parameter when the expected number of events is ≤5. Am Stat 2002;56(May (2)):85–9.
- Sanchez-Marquez, R., Guillem, J. A., Vicens-Salort, E., & Vivas, J. J. (2018). A statistical system management method to tackle data uncertainty when using key performance indicators of the balanced scorecard. Journal of Manufacturing Systems, 48, 166-179.
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