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 Chisquare vs. Fisher's Exact TestMeeting chisquare assumption of at least five observations per cell
There is a fundamental difference between chisquare and Fisher's Exact test. They are often used interchangeably both in everyday empirical discourse and also in the literature. There are many calculators available for free on the internet that will calculate inferential statistics for chisquare tests of independence and fisher's exact test. Without the proper statistical competencies, researchers can employ the wrong test. Here is how to know which of these tests to use with your research data:
1. Chisquare  This nonparametric test is used when you are looking at the association between dichotomous categorical variables. The primary inference yielded from this test is the unadjusted odds ratio with 95% confidence interval. EACH CELL of the 2x2 table MUST have at least five observations. 2. Fisher's Exact Test  This nonparametric test is employed when you are looking at the association between dichotomous categorical variables. The primary inference here is also the unadjusted odds ratio with 95% confidence interval. However, the Fisher's Exact Test is used instead of chisquare if ONE OF THE CELLS in the 2x2 has LESS than five observations. 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 Chisquare pvalueOdds ratio with 95% confidence interval should be reported and interpreted
Most people that need statistics are focused only on the almighty pvalue of less than .05. When running Chisquare analyses between a dichotomous categorical predictor and a dichotomous categorical outcome, pvalues are not the primary inference that should be interpreted for practical purposes. The lack of precision and accuracy in categorical measures coupled with sampling error makes the pvalues yielded from Chisquare analyses virtually worthless in the applied sense.
The correct statistic to run is an unadjusted odds ratio with 95% confidence interval. This is the best measure for interpreting the magnitude of the association between two dichotomous categorical variables collected in a retrospective fashion. Relative risk can be calculated when the association is assessed in a prospective fashion. The width of the 95% confidence interval and it crossing over 1.0 dictate the significance and precision of the association between the variables. With smaller sample sizes, the 95% confidence interval will be wider and less precise. Larger sample sizes will yield more precise effects. 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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