Statistical Package for the Social Sciences (SPSS; Armonk, NY, IBM Corp.) is a statistical software application that allows for researchers to enter and manipulate data and conduct various statistical analyses. Step by step methods for conducting and interpreting over 60 statistical tests are available in Research Engineer. Videos will be coming soon. Click on a link below to gain access to the methods for conducting and interpreting the statistical analysis in SPSS.
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Comparison of independent groups on an outcomeNumber of groups, scales of measurement, and meeting statistical assumptions
Betweensubjects 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 betweensubjects designs, participants can only be part of one group (independence) and only observed once (independence of observations, IOO).
One chooses a betweensubjects 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 betweensubjects statistical tests and when they are utilized in applied quantitative research: 1. Chisquare Goodnessoffit  One group, categorical outcome, a priori hypothesis for dispersal of outcome 2. Onesample median test  One group, ordinal outcome, a priori hypothesis for median value 3. Onesample ttest  One group, continuous outcome, meet the assumption of IOO and normality, a priori hypothesis for mean value 4. Chisquare  Two independent groups, categorical outcome, and chisquare assumption (more than five observations in each cell) 5. Fisher's Exact test  Two independent groups, categorical outcome, and when the chisquare assumption is not met 6. MannWhitney U  Two independent groups, ordinal outcome, and when the assumption of homogeneity of variance for independent samples ttest is violated 7. Independent samples ttest  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, chisquare assumption, choose a reference category and compare each independent group to the reference 9. KruskalWallis  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 Parametric statistics are more powerful statisticsNonparametric statistics are used with categorical and ordinal outcomes
As we continue our journey to break through the barriers associated with statistical lexicons, here is another dichotomy of popular statistical terms that are spoken commonly but not always understood by everyone.
Parametric statistics are used to assess differences and effects for continuous outcomes. These statistical tests include onesample ttests, independent samples ttests, oneway ANOVA, repeatedmeasures ANOVA, ANCOVA, factorial ANOVA, multiple regression, MANOVA, and MANCOVA. Nonparametric statistics are used to assess differences and effects for: 1. Ordinal outcomes  Onesample median tests, MannWhitney U, Wilcoxon, KruskalWallis, Friedman's ANOVA, Proportional odds regression 2. Categorical outcomes  Chisquare, Chisquare Goodnessoffit, odds ratio, relative risk, McNemar's, Cochran's Q, KaplanMeier, logrank test, CochranMantelHaenszel, Cox regression, logistic regression, multinomial logistic regression 3. Small sample sizes (n < 30)  Smaller sample sizes make it harder to meet the statistical assumptions associated with parametric statistics. Nonparametric statistics can generate valid statistical inferences in these situations. 4. Violations of statistical assumptions for parametric tests  Normality, Homogeneity of variance, Normality of difference scores Research questions lead to choice of statistical designDifferences betweensubjects and withinsubjects designs
There are terms in statistics that many people do not understand from a practical standpoint. I'm a biostatistical scientist and it took me YEARS to wrap my head around some fundamental aspects of statistical reasoning, much less the lexicon. I would hypothesize that 90% of the statistics reported in the empirical literature as a whole fall between two different categories of statistics, betweensubjects and withinsubjects. Here is a basic breakdown of the differences in these types of statistical tests:
1. Betweensubjects  When you are comparing independent groups on a categorical, ordinal, or continuous outcome variable, you are conducting betweensubjects analyses. The "between" denotes the differences between mutually exclusive groups or levels of a categorical predictor variable. Chisquare, MannWhitney U, independentsamples ttests, odds ratio, KruskalWallis, and oneway ANOVA are all considered betweensubjects analyses because of the comparison of independent groups. 2. Withinsubjects  When you are comparing THE SAME GROUP on a categorical, ordinal, or continuous outcome ACROSS TIME OR WITHIN THE SAME OBJECT OF MEASUREMENT MULTIPLE TIMES, then you are conducting withinsubjects analyses. The "within" relates to the differences within the same object of measurement across multiple observations, time, or literally, "withinsubjects." Chisquare Goodnessoffit, Wilcoxon, repeatedmeasures ttests, relative risk, Friedman's ANOVA, and repeatedmeasures ANOVA are withinsubjects analyses because the same group or cohort of individuals is measured at several different timepoints or observations. 
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March 2016
AuthorEric Heidel, Ph.D. is Owner and Operator of Scalë, LLC. Categories
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