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    Parametric vs. non-parametric statistics

    ANCOVA Test ANOVA Test Chi-square Chi-square Goodness-of-fit Cochran-Mantel-Haenszel Cochran's Q Test Cox Regression Factorial ANOVA Friedman's ANOVA Homogeneity Of Variance Independent Samples T-test Kruskal-Wallis Log-Rank Test Logistic Regression MANCOVA Mann-Whitney U MANOVA McNemar's Test Multinomial Logistic Regression Multiple Regression Non-parametric Statistics Normality Normality Of Difference Scores Odds Ratio With 95% CI One-sample Median Tests One-sample T-test Parametric Statistics Proportional Odds Regression Relative Risk Repeated-measures ANOVA Statistical Assumptions Wilcoxon

    Parametric statistics are more powerful statistics

    Non-parametric 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 one-sample t-tests, independent samples t-tests, one-way ANOVA, repeated-measures ANOVA, ANCOVA, factorial ANOVA, multiple regression, MANOVA, and MANCOVA. 

    Non-parametric statistics are used to assess differences and effects for:

    1. Ordinal outcomes - One-sample median tests, Mann-Whitney U, Wilcoxon, Kruskal-Wallis, Friedman's ANOVA, Proportional odds regression

    2. Categorical outcomes - Chi-square, Chi-square Goodness-of-fit, odds ratio, relative risk, McNemar's, Cochran's Q, Kaplan-Meier, log-rank test, Cochran-Mantel-Haenszel, 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.  Non-parametric 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
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    95% confidence intervals

    95% Confidence Interval Adjusted Odds Ratio Confidence Interval Hazard Ratio Measurement Odds Ratio With 95% CI P-value Relative Risk Statistics

    Precision and consistency of treatment effects

    95% confidence intervals are dependent upon sample size

    If there is ANY statistical calculation that holds true value for researchers and clinicians on a day-to-day basis, it is the 95% confidence interval wrapped around the findings of inferential analyses. Statistics is not an exact mathematical science as far as other exact mathematical sciences go, measurement error is inherent when attempting to measure for anything related to human beings, and FEW tried and true causal effects have been proven scientifically. Statistics' strength as a mathematical science is in its ability to build confidence intervals around findings to put them into a relative context.  

    Also, 95% confidence intervals act as the primary inference associated with unadjusted odds ratios, relative risk, hazard ratios, and adjusted odds ratios. If the confidence interval crosses over 1.0, there is a non-significant effect. Wide 95% confidence intervals are indicative of small sample sizes and lead to decreased precision of the effect. Constricted or narrow 95% confidence intervals reflect increased precision and consistency of a treatment effect.

    In essence, p-values should not be what people get excited about when it comes to statistical analyses. The interpretation of your findings within the context of the subsequent population means, odds, risk, hazard, and 95% confidence intervals IS the real "meat" of applied statistics.
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    Chi-square p-values are not enough

    95% Confidence Interval Chi-square Odds Ratio With 95% CI P-value Relative Risk Sampling Error

    Chi-square p-value

    Odds ratio with 95% confidence interval should be reported and interpreted

    Most people that need statistics are focused only on the almighty p-value of less than .05. When running Chi-square analyses between a dichotomous categorical predictor and a dichotomous categorical outcome, p-values 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 p-values yielded from Chi-square 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.
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    Statistical Designs

    ANOVA Test Between-subjects Chi-square Chi-square Goodness-of-fit Friedman's ANOVA Independent Samples T-test Kruskal-Wallis Mann-Whitney U Odds Ratio With 95% CI Relative Risk Repeated-measures ANOVA Repeated-measures T-test Wilcoxon Within-subjects

    Research questions lead to choice of statistical design

    Differences between-subjects and within-subjects 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, between-subjects and within-subjects. Here is a basic breakdown of the differences in these types of statistical tests:

    1. Between-subjects - When you are comparing independent groups on a categorical, ordinal, or continuous outcome variable, you are conducting between-subjects analyses. The "between-" denotes the differences between mutually exclusive groups or levels of a categorical predictor variable. Chi-square, Mann-Whitney U, independent-samples t-tests, odds ratio, Kruskal-Wallis, and one-way ANOVA are all considered between-subjects analyses because of the comparison of independent groups.  

    2. Within-subjects - 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 within-subjects analyses. The "within-" relates to the differences within the same object of measurement across multiple observations, time, or literally, "within-subjects." Chi-square Goodness-of-fit, Wilcoxon, repeated-measures t-tests, relative risk, Friedman's ANOVA, and repeated-measures ANOVA are within-subjects analyses because the same group or cohort of individuals is measured at several different time-points or observations.
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    Prevalence vs. Incidence

    Cohort Cross-sectional Incidence Odds Ratio With 95% CI Prevalence Prospective Cohort Relative Risk

    Prevalence and incidence used correctly

    Difference in important epidemiological measures

    The terms prevalence and incidence are often used interchangeably. However, they are extremely different in their utility and interpretability within epidemiology.

    Prevalence is the proportion of cases or disease states that exist in a population at any given time.  Prevalence is established using cross-sectional research designs.  Measures of prevalence can be used to generate odds ratios for outcomes occurring given an exposure or non-exposure.  It is calculated when data is collected in a retrospective fashion. 

    Incidence is the number of new cases or disease states that occur in a population.  Incidence is established in cohort designs.  Measures of incidence are used to establish the relative risk of an outcome given treatment or no treatment.  It is calculated when data is collected in a prospective fashion.

    ​Click on the Epidemiology button below to continue.