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- 1. Page 1 of 6 HOW TO INTERPRET COMMONLY USED STATISTICS IN MEDICAL RESEARCH WHY LEARN HOW TO READ STATISTICS ?Several studies have reported the error rate in reporting and/or interpreting statistics in the medical literature is between 30-90% (Novak et al., 2006).Understanding basic statistical concepts will allow you to become a more critical consumer of the medical literature, and ultimately be able to produce better research and make better clinical decisions. THREE MAJOR CATEGORIES OF STATISTICAL TESTSDescriptive Statistics:These are numbers used simply to describe the sample population of the study. They do not actually test any hypotheses,or yield any p-values. Example descriptive statistics: Frequencies, mean, median, percentages, standard deviation.Parametric (distribution-dependent) Statistics:These are the most powerful type of statistics we use. Unfortunately, researchers must make sure their data meets anumber of assumptions (or rules) before these tests can be used properly. In research, you always want to use parametricstatistics if possible. Example parametric statistics: Independent t-test, Pearson r correlation, Analysis of Variance (ANOVA)Nonparametric Statistics:A less-powerful group of statistical analyses that are used either when the researcher has violated the assumptions (i.e.broke the rules) necessary to run parametric statistics or when using categorical or ordinal variables. They are also used totest the risk or odds of someone an outcome occurring. These tests are extremely common due to the nature of manyresearch studies, and parametric statistics have a nonparametric counterpart that tests the same type of hypotheses. Someresearch questions can only be asked non-parametrically (e.g. odds of developing cancer based on smoker/non-smoker). Example nonparametric statistics:Mann-Whitney U (independent t-test equivalent), Odds/Risk, Survival Analysis, Logistic Regression, Spearman Rho (Pearson r equivalent), and Kruskall-Wallis (ANOVA equivalent) DIFFERENT TYPES OF STATISTICAL TESTSTests of Relationships:These analyses look at the relationship between a set of variables. Specifically, they seek to determine how an outcome(dependent) variable changes in response to changes in one or more predictor (independent) variables. Example tests of relationships: Pearson r correlation, Spearman Rho correlation, multiple regression.Tests of Group Differences:This group of statistical tests focuses on determining the average difference between two or more groups of independentparticipants. They compare the mean (average) score for each group on an outcome (dependent) variable. Example tests of group differences: Independent t-test, between-subjects analysis of variance (ANOVA), analysis of covariance (ANCOVA).Tests of Repeated Measures:A group of tests which looks at the difference in average score on an outcome (dependent) variable between two or moretime-points using the same group of participants. These tests are used to compare pretest and posttest scores, or otherchanges over time. Example tests of repeated measures: Dependent t-test, repeated-measures analysis of variance. Prepared By: Tiffany Smith, Patrick Barlow, and Eric Heidel
- 2. Page 2 of 6Tests of Odds / Risk:A group of Non-Parametric tests which look at the odds or risk (risk is prospective, odds is retrospective) of an eventoccurring or not occurring based on one or more predictor variables (independent). These tests involve categoricalvariables as the independent variables and a dichotomous dependent variable (i.e. develops cancer, yes or no). Example tests of odds/risk: Chi-square, Odds Ratio / Relative Risk, Logistic Regression, Survival Analysis. COMMONLY USED STATISTICAL TESTS:Pearson R Correlation: A statistical analysis that tests the relationship between two continuous variables. Commonly Associated Terms:bivariate correlation, relationship, r-value, scatterplot, confidence interval, relationship, association, direction, magnitude. What to interpret: p-values (<.05), EFFECT SIZE (square the r-value to obtain effect size), magnitude of the relationship (between -1.0 and 1.0), direction (positive or negative), weak |.1|-|.3|, moderate |.3|-|.5|, strong |.5|- |1.0| How to interpret: There is a significant positive relationship between the two variables, where as one increases, the other also increases. There is a significant negative relationship between the two variables, where as one increases the other decreases. Non-Parametric Equivalent: Spearman RhoLinear/Multiple Regression: A statistical analysis that tests the relationship betweenmultiple predictor variables andonecontinuousoutcome variable. Commonly Associated Terms:multivariate,beta weight,r2-value, relationship, model, forward regression, backward regression, sequential/hierarchical regression,standard/simultaneous regression, statistical/stepwise regression, confidence interval, correlation, association, direction, magnitude. What to interpret: p-values (<.05), EFFECT SIZE (square the r-value to obtain effect size), magnitude of the relationship beta weights: beta < 1 = protective effect/negative relationship, beta > 1 = positive relationship. How to interpret: Beta is positive: There is a significant positive relationship between the predictor and outcome variables, whereas the predictor increases by 1 unit (e.g. 1lbs to 2lbs), the outcome variable also increases by (beta) after controlling for *at least one* other covariate. Beta is negative:There is a significant negative relationship between the two variables, whereas the predictor increases by 1 unit (e.g. 1lbs to 2lbs), the outcome variable also decreases by (beta) after controlling for *at least one* other covariate.Independent T-Test: A statistical analysis that tests differences between two independent groups at one time-point. Commonly Associated Terms:two sample t-test, student’s t-test, means, group means, standard deviations, mean differences, case-control, group difference, confidence interval, group comparison. What to interpret: p-values (<.05), large mean differences and small standard deviations based on your judgment of the variables included (via literature review, clinical expertise, etc.), EFFECT SIZE How to interpret: There is a significant difference between the two groups where one group has a significantly higher/lower score on the dependent variable than the other. Non-Parametric Equivalent: Mann-Whitney UOne-Way Between Subjects Analysis of Variance (ANOVA): A statistical analysis that tests differences between twoor more independent groups at one time-point. Commonly Associated Terms:two or more groups, means, standard deviations, confidence interval, group differences, group comparisons, F-test, interactions, post-hoc tests (tukey HSD, bonferroni, scheffe, dunnett, etc.). What to interpret: main effect, post-hoc, p-values (<.05), large mean differences between two or more groups and small standard deviations based on your judgment of the variables included, EFFECT SIZE How to interpret: Prepared By: Tiffany Smith, Patrick Barlow, and Eric Heidel
- 3. Page 3 of 6 Main Effect – There was an overall significant difference among the groups of the independent variable on the dependent variable, however we must figure out where that difference is through the post-hoc test that was performed in the study. Post-Hoc: There is a significant difference between the two groups where one (or more) group(s) has a significantly higher/lower score on the dependent variable than the other(s). Non-Parametric Equivalent: Kruskall-Wallis with follow-up Mann-Whitney U testsDependent T-Test: A statistical analysis that tests differences of one group between two time-points. Commonly Associated Terms:pre and posttest, matched pairs, means, standard deviations, mean differences, confidence interval, paired samples, time. What to interpret: p-values (<.05), large mean change between two time-points and small standard deviations based on your judgment of the variables included, EFFECT SIZE How to interpret: There is a significant difference between the pretest and posttest where the score on the posttest was significantly higher/lower on the dependent variable than the pretest. Non-Parametric Equivalent: Wilcoxon Matched PairsRepeated Measures ANOVA: A statistical analysis that tests differences of one group between two or more time-points. Commonly Associated Terms:multiple time-points (e.g. pretest, posttest, follow-up; not JUST pre and post), means, standard deviations, confidence interval, mean differences, time series, F-test, interactions, repeated measures, post-hoc tests (Tukey HSD, Bonferroni, Scheffe, Dunnett, etc.). What to interpret: main effect, post-hoc, p-values (<.05), large mean change between two or more time-points and small standard deviations based on your judgment of the variables included, EFFECT SIZE, direction of change (Do scores increase between each time-point? Do they decrease at each? Is it a mix of both?) How to interpret: Main Effect – There was an overall significant difference among the different time-points on the dependent variable, however we must figure out where that difference is through the post-hoc test that was performed in the study. Post-Hoc: There is a significant difference between the pretest, posttest, and follow-up where scores at one or more time-points were significantly higher/lower on the dependent variable than the other time- point(s). Non-Parametric Equivalent: Friedman ANOVA with follow-up Wilcoxon Matched Pairs testsOTHER ANOVAs: Mixed ANOVA: A statistical analysis that tests differences between two or more independent groups at two or more time-points. ANCOVA:A statistical analysis that tests differences between two or more independent groups at one time-point while controlling for other variables. Multivariate ANOVA (MANOVA):A statistical analysis that tests differences between two or more independent groups on multiple dependent variables.Odds Ratios / Relative Risk:A statistical analysis that tests the odds or risk of an event occurring or not occurring basedon one or more predictor variables (independent). These tests involve categorical variables as the independent variablesand a dichotomous dependent variable (i.e. develops cancer, yes or no). (A Fisher’s Exact Test is used when you have asmall sample size (n < 20) or when one of the cells of a 2x2 table has fewer than 5 observations. It is interpreted the exactsame way as a Chi Square.) Commonly Associated Terms:unadjusted odds ratio (OR), relative risk, 2x2, chi-square, absolute riskreduction, absolute risk, relative risk reduction, odds, confidence intervals, protective effect, likelihood, forest plot. What to interpret: p-values (<.05), confidence interval (should not cross over 1.0), odds ratio (<1 is a protective effect, >1 is increased odds/risk) How to interpret: Prepared By: Tiffany Smith, Patrick Barlow, and Eric Heidel
- 4. Page 4 of 6 Odds Ratio < 1:For every unit increase in the independent variable, the odds of having the outcome decrease by (OR) times. Odds Ratio > 1:For every unit increase in the independent variable, the odds of having the outcome increase by (OR) times. Odds Ratio = 1or CI crosses 1.0 or p > .05:You are no more or less likely to have the outcome as a result of the predictor variable. (this would be non-significant)Logistic Regression:A statistical procedure that attempts to correctly predict the occurrence or non-occurrence of anevent (i.e. dichotomous DV) based on multiple predictor variables (IVs). This is considered a multivariate (multiplevariables) approach to looking at research questions dealing with odds, risks, and proportions. Commonly Associated Terms:adjusted odds ratio(AOR), multivariate adjusted odds ratio,likelihood, protective effect, risk, odds, 95% confidence interval, classification table, dichotomous DV, backward regression, forward regression, standard/simultaneous regression, sequential/hierarchical regression, statistical/stepwise regression. What to interpret:OR (these are your measures for risk of the outcome occurring given the predictor variable), p- value for OR, confidence intervals for OR (should not cross over 1.0, should not be overly large e.g. 1.2 – 45.5), classification table (if it is provided). How to interpret: Odds Ratio < 1:For every unit increase in the independent variable, the odds of having the outcome decrease by (OR) times after controlling for *at least one* other covariate. Odds Ratio > 1:For every unit increase in the independent variable, the odds of having the outcome increase by (OR) times after controlling for *at least one* other covariate. Odds Ratio = 1 or CI crosses 1.0 or p > .05:You are no more or less likely to have the outcome as a result of the predictor variable after controlling for *at least one* other covariate. (this would be non- significant)Survival Analysis: A statistical procedure that deals with investigating the time it takes for a certain event to occur(disease, complication, death, etc.). With these analyses a research can look at simply the time it took for an event to occurbased on one IV (Kaplan Meier Analysis), or one can look at the time for an event to occur when multiple variables areconsidered at once (Cox Proportional Hazard). Commonly Associated Terms:survival, Kaplan Meier, life table, Cochran Mantel-Haenszel, Log-Rank, Breslow, Cox Regression, Cox Proportional Hazard,survival function, rate ratio (RR), hazard ratio (HR),odds ratio,likelihood, protective effect, risk, odds, 95% confidence interval, classification table, dichotomous DV, backward regression, forward regression, standard/simultaneous regression, sequential/hierarchical regression, statistical/stepwise regression. What to interpret:OR/RR/HR (these are your measures for risk of the event occurring given the predictor variable), p-value for OR, RR, or HR, Confidence intervals for OR/RR/HR (should not cross over 1.0, should not be overly large e.g. 1.2 – 45.5), survival curves (if they are included). How to interpret: Odds Ratio/Rate Ratio/Hazard Ratio < 1: For every unit increase in the independent variable, the odds of having the event occurring decrease by (OR) times. “Protective effect.” Odds Ratio/Rate Ratio/Hazard Ratio > 1: For every unit increase in the independent variable, the odds of the event occurring increase by (OR) times. Odds Ratio/Rate Ratio/Hazard Ratio = 1 or CI crosses 1.0 or p > .05: You are no more or less likely to have the event occurring as a result of the predictor variable (this would be non-significant). **Sometimes covariates may be used to account for the variance in the study. Prepared By: Tiffany Smith, Patrick Barlow, and Eric Heidel
- 5. Page 5 of 6 SENSITIVITY & SPECIFICITYSensitivity and Specificity are two areas of statistical analysis that are usually seen in diagnostic testing and/or theengineering field. They provide the probability that a test will yield a correct response. Commonly Associated Terms: True Positive: Test classified the patient as having a disease and the patient did have the disease True Negative: Test classified the patient as not having the disease and the patient did not have the disease. False Positive: Test classified the patient as having a disease and the patient did not have the disease. False Negative: Test classified the patient as not having the disease and the patient did have the disease. Sensitivity: Proportion of patients with a disease who will test positive for it. The ability of the test to identify positive results. Specificity: Proportion of patients without a disease who will test negative for it. The ability of the test to identify negative results. Positive Predictive Value: Proportion of True Positive classifications. The ability of the test to correctly classify patients with a disease. Negative Predictive Value: Proportion of True Negative classifications. The Ability of the test to correctly classify patients without a disease. Disease State + - Positive Predictive Value + True Positive False Positive Test Results Negative Predictive Value - False Negative True Negative Sensitivity = Specificity = Prepared By: Tiffany Smith, Patrick Barlow, and Eric Heidel
- 6. Page 6 of 6Remember: Just because a finding is not significant does not mean that it is not meaningful. You should always considerthe effect size and context of the research when making a decision about whether or not any finding is clinically relevant. "Absence of evidence is not evidence of absence!" -- Carl Sagan The University of Tennessee, Knoxville Office of Medical Education, Research, and Development Patrick Barlow, Eric Heidel, and Tiffany Smith University of Tennessee Medical Center Prepared By: Tiffany Smith, Patrick Barlow, and Eric Heidel

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