How to Find Differences Between Three or More Groups or Conditions Preparatio
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Jf_wseek4DixussionAutosaved.docx1 Finding the Difference between Three Groups Statistics for the Health Sciences
Jennifer Franks
Capella University MPH5509 Principles of Biostatistics Dr. Fatma Shebl October 30, 2025
A one-way ANOVA revealed that Verbal IQ (VIQ) scores differed significantly among individuals with inflammatory bowel disease (IBD), irritable bowel syndrome (IBS), and a control group. The control group had a notably higher mean VIQ score (107.8) than both the IBS group (97.5) and the IBD group (93.2), highlighting significant differences. However, there was no significant difference in VIQ between the IBD and IBS groups.
ANOVA
ANOVA - viq
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Cases Sum of Squares df Mean Square F p ω² |
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Groups 3365 2 1682.7 11.40 < .001 0.191 Residuals 12543 85 147.6 |
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Note. Type III Sum of Squares Descriptive Descriptive - viq groups N Mean SD SE Coefficient of variations |
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ibs 29 97.48 11.26 2.091 0.116 ibd 29 93.21 13.42 2.492 0.144 controls 30 107.87 11.67 2.131 0.108 |
Post Hoc Tests
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Standard (HSD) Post Hoc Comparisons – groups Mean Difference SE df t ptukey ibs ibd 4.276 3.190 85 1.340 .377 controls -10.384 3.163 85 -3.282 .004 ibd controls -14.660 3.163 85 -4.634 < .001 Note. P-value adjusted for comparing a family of 3 estimates |
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Following the one-way ANOVA, post hoc tests were conducted to clarify which specific group differences contributed to the significant findings. A repeated-measures ANOVA was used to evaluate the same group under four different conditions. The results showed a statistically significant difference among the four conditions, with F(3, 177) = 6.01, indicating that participants' scores differed across conditions. The p-value was less than .001, confirming statistical significance. The effect size, measured by ω² = 0.05, was small, representing a minor difference between conditions. Mauchly’s W of .004 showed sphericity was violated. After applying the Greenhouse-Geisser correction, the F statistic, F(1.2, 69.3), remained unchanged. Repeated Measures ANOVA
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Within-Subjects Effects Cases Sphericity Correction Sum of Squares df Mean F P ω² Square RM Factor 1 None 5556 ᵃ 3.000 ᵃ 1852.1 ᵃ 6.005ᵃ <. 001ᵃ 0.051 Greenhouse- Geisser 5556 1.174 4733.5 6.005. 013 0. 0.051 Residuals None 54591 177.000 308.4 Greenhouse- Geisser 54591 69.257 788.2 __________________________________________________________________________________+++++++++++++++Note. Type III Sum of Squares Mauchly's test of sphericity indicates that the assumption of sphericity is violated (p < .05). _Between-Subjects Effects__________________ Cases Sum of Squares df Mean Square F p Residuals 9587 59 501.5 Note. Type III Sum of Squares _____________________________________ Descriptive |
Condition 4 Descriptive RM Factor 1 N Mean SD SE Coefficient of variation
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Conditions 5
Kruskal-Wallis Test The Kruskal-Wallis test checks if ranks differ in non-parametric data for three or more groups. The following table shows a Kruskal-Wallis statistic of 11.03, which was statistically significant (p = .004), indicating differences among the groups. Dunn’s post hoc comparison revealed significant differences in ranks between groups 1 and 2 (p = 0.043) and between groups 1 and 3 (p < 0.001), but no significant difference between groups 2 and 3 (p = 0.206), clarifying where the group differences occurred. Overall, statistical tests revealed significant differences among groups by both ANOVA and Kruskal-Wallis analysis. Post hoc comparisons showed that the controls had higher scores than both the IBD and IBS groups, with no significant difference between the latter two. These findings were consistent across both parametric and non-parametric approaches.
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Factor Statistic df p group 11.03 2 .004 Dunn Dunn's Post Hoc Comparisons - group Comparison z Wi Wj rrb p pbonf pholm 1 - 2 -2.026 3.100 8.700 0.960 .043 .128 .086 1 - 3 -3.292 3.100 12.200 1.000 < .001 .003 .003 2 - 3 -1.266 8.700 12.200 0.680 .206 .617 .206 Note. Rank-biserial correlation based on individual Mann-Whitney tests |
. Data sourced from: Dancy, C., Reidy, J., & Rowe, R. (2012). Statistics for the Health Sciences. Sage Publications Ltd. UK.
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References:
Data sourced from: Dancy, C., Reidy, J., & Rowe, R. (2012). Statistics for the Health Sciences. Sage Publications Ltd. UK (Dancey et al., 2012)
Dancey & C.P. (2009). Cognitive Function in Inflammatory Bowel Disease: A Comparison with Irritable Bowel Syndrome and Healthy Controls. Journal of Clinical and Experimental Neuropsychology 31. https://repository.uel.ac.uk/download/a7a72000d88a5f25d1f8c0c1ed983a002124808bf76fdc274e04ecb78970c2e4/187081/Dancey%2C%20CP%20%282009%29%20IBD%2015%20%286%29%20852.pdf
Crawford, J.R. et al. (2022). Cognitive performance in patients with irritable bowel syndrome and inflammatory bowel disease: A comparative study. Journal of Clinical and Experimental Neuropsychology 44. https://pubmed.ncbi.nlm.nih.gov/35478469/
(n.d.). Interpret ANOVA Effect Sizes — interpret_omega_squared. easystats.github.io/effectsize/reference/interpret_omega_squared.html. https://easystats.github.io/effectsize/reference/interpret_omega_squared.html
(n.d.). Greenhouse-Geisser epsilon – Lancaster Glossary of Child Development. Lancaster University. https://www.lancaster.ac.uk/fas/psych/glossary/greenhouse-geisser_epsilon/
Dancey, Reidy, C., Rowe, J. & Richard. (2012). Statistics for the Health Sciences. SAGE Publications Ltd, UK. https://in.sagepub.com/en-in/sas/statistics-for-the-health-sciences/book234240
