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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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 Ordinal measures and normalityOrdinal level measurement can become interval level with assumed normality
Here is an interesting trick I picked up along the way when it comes to ordinal outcomes and some unvalidated measures. If you run skewness and kurtosis statistics on the ordinal variable and its distribution meets the assumption of normality (skewness and kurtosis statistics are less than an absolute value of 2.0), then you can "upgrade" the variable to a continuous level of measurement and analyze it using more powerful parametric statistics.
This type of thinking is the reason that the SAT, ACT, GRE, MCAT, LSAT, and validated psychological instruments are perceived at a continuous level. The scores yielded from these instruments, by definition, are not continuous because a "true zero" does not exist. Scores from these tests are often norm or criterionreferenced to the population so that they can be interpreted in the correct context. Therefore, with the subjectivity and measurement error associated with classical test theory and item response theory, the scores are actually ordinal. With that being said, if the survey instrument or ordinal outcome is used in the empirical literature often and it meets the assumption of normality as per skewness and kurtosis statistics, treat the ordinal variable as a continuous variable and run analyses using parametric statistics (ttests, ANOVA, regression) versus nonparametric statistics (Chisquare, MannWhitney U, KruskalWallis, McNemar's, Wicoxon, Friedman's ANOVA, logistic regression). 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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