Chi-Square Test: What to Report and How to Report Finding
There are a number of Chi-square tests but examples of interpretation are provided for only these four tests:
1. Chi-square test of Goodness of Fit
2. Chi-square of Independence
3. Mann-Whitney U-Test
4. Kruskal-Wallis Test
Generally, when reporting a Chi-Square test the following MUST be included in your write-up.
1. Degrees of freedom (df)
2. Number of observations (N)
3. Observed chi-square value (Χ2)
4. Significant level (p)
5. Effect size (ES [η], varies with test)
Syntax: χ2 (df, N = XX) = observed chi-square value, significant level (p), ES (η)
Format Example: A chi-square test indicated that the relationship between gender and promotion was significant, χ2 (2, N = 112) =13.45, p < .01, η = .29.
1. Goodness of Fit test: A chi-square goodness of fit test was calculated comparing the frequency of occurrence of each value of a die. It was hypothesized that each value would occur an equal number of times. The test showed significant deviation from the hypothesized value χ2 (5, N=85) = 12.24, p < .0005.
2. Chi-square for Independence: A chi-square test for independence was computed comparing the frequency of heart diseases in men and women. A significant interaction was found χ2 (1, N =25) = 23.80, p < .05. Men were more likely to get heart disease (67%) than women (38%). NOTE: if you have a 2x2 table, i.e. each variable has only two categories such as gender (male/Female) and responses such as "Yes" and "No"-use the "Continuity Correlation" (known as 'Yates' Correlation') instead of "Pearson Chi-Square" because Yates' Correlation compensates for the overestimate of the chi-square value when used with a 2 by 2 table.
3. Mann-Whitney U-Test: Report- Observed z or U value (z/U), Significant level (p), Effect size (ES, varies with test), Number of observations (N), Number of observations per group (n), and Mean Rank (M). Syntax example: group-1 (n= XX) was significantly different from Group-2 (n = XX), z [or U] = observed z [or U] value, significant level, ES. NOTE: If one of the sampled groups is lager than 20, use z when reporting and use U when it is smaller than 20.
1. Example: A Mann-Whitney U-test was calculated examining the place that runners with varying levels of experience took in a long-distance race. Runners with medium experience did significantly worse (M place =6.50) than experienced runners (M place = 2.50; U = 0.00, p < .05). OR if the sample group is larger =20 or more you will say: Mann-Whitney U analysis revealed significant differences between volunteers and direct mail members. The sum average ranks that volunteers assigned to the pollution prevention group was significantly higher (M Rank=88.78, n =59) than the sum of the average ranks assigned by direct mail members (M Rank=57.18, n=81) z(140)=14.67, p < .0001.
Kruskal-Wallis Test: in this test report- Degrees of freedom (df), Number of observations (N), Observed test value (H or X2 ), Significant level (p), Effect size (ES, varies with test), Number of observations per group (n), and Mean Ranks. Syntax: H (df, N=XX)=observed H value, significance level, ES. Format Example: The Kruskal-Wallis test indicated a significant effect, H (2, N =25) =12.47, p < .01, n2 = .07. Be sure to report the Mean Rank as well (See Mann-Whitney example).
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