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    Between-subjects statistics are used to compare independent groups

    ANOVA Test Between-subjects Chi-square Chi-square Goodness-of-fit Fisher's Exact Tests Independent Samples T-test Kruskal-Wallis Mann-Whitney U One-sample Median Tests One-sample T-test Scales Of Measurement Statistical Assumptions Unadjusted Odds Ratio

    Comparison of independent groups on an outcome

    Number of groups, scales of measurement, and meeting statistical assumptions

    Between-subjects statistics are used when comparing independent groups on an outcome. Independent groups means that the groups are "different" or "independent" from each other according to some characteristic. With between-subjects designs, participants can only be part of one group (independence) and only observed once (independence of observations, IOO).

    One chooses a between-subjects statistical test based on the following:

    1. Number of independent groups being compared (one group, two groups, or three or more groups)

    2. Scale of measurement of the outcome (categorical, ordinal, or continuous)

    3. Meeting statistical assumptions (independence of observations, normality, and homogeneity of variance)

    Here is a list of between-subjects statistical tests and when they are utilized in applied quantitative research:

    1. Chi-square Goodness-of-fit - One group, categorical outcome, a priori hypothesis for dispersal of outcome

    2. One-sample median test - One group, ordinal outcome, a priori hypothesis for median value

    3. One-sample t-test - One group, continuous outcome, meet the assumption of IOO and normality, a priori hypothesis for mean value

    4. Chi-square - Two independent groups, categorical outcome, and chi-square assumption (more than five observations in each cell)

    5. Fisher's Exact test - Two independent groups, categorical outcome, and when the chi-square assumption is not met

    6. Mann-Whitney U - Two independent groups, ordinal outcome, and when the assumption of homogeneity of variance for independent samples t-test is violated

    7. Independent samples t-test - Two independent groups, continuous outcome, meet the assumption of IOO, normality (skewness and kurtosis statistics), and homogeneity of variance (also known as homoscedasticity, tested with Levene's test)

    8. Unadjusted odds ratio - Three or more independent groups, categorical outcome, chi-square assumption, choose a reference category and compare each independent group to the reference

    9. Kruskal-Wallis - Three or more independent groups, ordinal outcome, and when the assumption of homogeneity of variance is violated

    10. ANOVA - Three or more independent groups, continuous outcome, meet the assumption of IOO, normality, and homogeneity of variance
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    Adjusted odds ratios in medicine

    Adjusted Odds Ratio Evidence-based Medicine Logistic Regression Medicine Unadjusted Odds Ratio

    Logistic regression yields adjusted odds ratios

    Adjusted odds ratios are easier generalized to clinical situations

    There is a strong need in clinical medicine for adjusted odds ratios with 95% confidence intervals. Medicine, as a science, often uses categorical outcomes to research causal effects. It is important to assess clinical outcomes (measured at the dichotomous categorical level) within the context of various predictor, clinical, prognostic, demographic, and confounding variables. Logistic regression is the statistical method used to understand the associations between the aforementioned variables and dichotomous categorical outcomes.

    Logistic regression yields adjusted odds ratios with 95% confidence intervals, rather than the more prevalent unadjusted odds ratios used in 2x2 tables. The odds ratios in logistic regression are "adjusted" because their associations to the dichotomous categorical outcome are "controlled for" or "adjusted" by the other variables in the model. The 95% confidence interval is used as the primary inference with adjusted odds ratios, just like with unadjusted odds ratios. If the 95% confidence interval crosses over 1.0, then there is a non-significant association with the outcome variable.  

    Adjusted odds ratios are important in medicine because very few physiological or medical phenomena are bivariate in nature. Most disease states or physiological disorders are understood and detected within the context of many different factors or variables.  Therefore, to truly understand treatment effects and clinical phenomena, multivariate adjustment must occur to properly account for clinical, prognostic, demographic, and confounding variables.