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# Commonly Used Statistics in Medical Research Part I

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This presentation covers a brief introduction to some of the more common statistical analyses we run into while working with medical residents. The point is to make the audience familiar with these statistics rather than calculate them, so it is well-suited for journal clubs or other EBM-related sessions. By the end of this presentation the students should be able to: Define parametric and descriptive statistics
• Compare and contrast three primary classes of parametric statistics: relationships, group differences, and repeated measures with regards to when and why to use each
• Link parametric statistics with their non-parametric equivalents
• Identify the benefits and risks associated with using multivariate statistics
• Match research scenarios with the appropriate parametric statistics
The presentation is accompanied with the following handout: http://slidesha.re/1178weg

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### Commonly Used Statistics in Medical Research Part I

1. 1. Tiffany Smith Patrick BarlowStatistical and Research Design Consultants, OMERAD
2. 2.  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.
3. 3. Descriptive StatisticsParametric StatisticsNon-Parametric Statistics
4. 4.  Null Hypothesis Alternative Hypothesis Mean Standard Deviation Correlation Confidence Interval
5. 5.  Fitthe statistics to the research question, not the other way around! First, ask yourself, “Am I interested in….  Describing a sample or outcome?”  Looking at how groups differ?”  Looking at how outcomes are related?”  Looking at changes over time?” Second, “How am I measuring my outcomes?” Finally, “How is my outcome distributed in the sample?”
6. 6.  DescriptiveStatistics Parametric Statistics  Common tests of relationships  Pearson r  Linear/multiple regression  Common tests of group differences  Independent t-test  Between subjects analysis of variance (ANOVA)  Common tests of repeated measures  Dependent t-test  Within subjects ANOVA Activity
7. 7.  Numbers used to describe the sample They do not actually test any hypotheses (or yield any p-values) Types:  Measures of Center -  Mean  Median  Mode  Measures of Spread -  Quartiles  Standard Deviation  Range  Variance  Frequencies
8. 8.  Most powerful type of statistics we use Researchers must make sure their data meets a number of assumptions (or parameters) before these tests can be used properly.  Some key assumptions  Normality  Independence of observations Inresearch, you always want to use parametric statistics if possible.
9. 9. Pearson r correlationLinear/Multiple Regression
10. 10.  What is it?  A statistical analysis that tests the relationship between two continuous variables. Commonly Associated Terms:  Bivariate correlation, relationship, r-value, scatterplot, association, direction, magnitude.
11. 11. No Relationship: Weak Relationship: r ≈ |.00| r ≈ |.10| ModerateRelationship: r ≈ |.30| Strong Relationship: r > .50 11
12. 12. Each has a Pearson Correlation of r=.82, is & is statistically significant 12Anscombe, F.J., Graphs in Statistical Analysis, American Statistican, 27, 17-21
13. 13.  What you read:  Study found a relationship between age and number of medications an individual is taking, r=.35, p = .03. What to interpret:  Results show r = .35, p = .03, R2=.12 How to interpret:  There is a weak, significant positive relationship between age and number of medications an individual is taking. As age increases, number of medications also increases.
14. 14.  What is it?  A statistical analysis that tests the relationship between multiple predictor variables and one continuous outcome variable.  Predictors: Any number of continuous or dichotomous variables, e.g. age, anxiety, SES  Outcome: 1 Continuous variable, e.g. ER visits per Month Commonly Associated Terms:  Multivariate, beta weight, r2-value, model, forward/backward regression, sequential/hierarchical regression, standard/simultaneous regression, statistical/stepwise regression. 14
15. 15.  What to interpret?  p-values (<.05)  R2 Value, magnitude of the relationship B/beta weights: B/beta < 1 = protective effect/negative relationship, beta > 1 = positive relationship. How to interpret?  B(β) is positive (e.g. 1.25): as the predictor increases by 1 unit (1lbs to 2lbs), the outcome variable also increases by B(β) (LDL Cholesterol increases by 1.25 mg/dl).  B(β) is negative (e.g. -1.25): as the predictor increases by 1 unit (1lbs to 2lbs), the outcome variable decreases by B(β) (LDL decreases by 1.25 mg/dl).
16. 16.  What you readTable 3: Predictors of Number of Surgical Site Infections Regression Coefficient1 Predictor p-value2 B(SE) βLength of Stay .25 (.06) .30 <.001Age -.75 (.05) -.45 <.0011B = Unstandardized coefficient, SE=standard error, and β = standardizedcoefficient2-Overall: F(2, 317)=17.19, p<.001, R=.31, R2 =.10  What to interpret:  “B’s” for each predictor: LoS=.25 and Age= -.75  p-value of each predictor: both <.001  p-value for the model: <.001.  R2 value for the model: .10
17. 17.  How to interpret:  Overall: Both length of stay and age significantly predict a patient’s number of surgical site infections, and account for 10% of the variance.  For Length of Stay: For every additional day a patient spends in the hospital, their number of surgical site infections increases by .25  For Age: For every additional year of age, a patient’s number of surgical site infections decreases by .75
18. 18. Independent t-testBetween Subjects Analysis of Variance (ANOVA)
19. 19.  What is it?  Tests the difference between two groups on a single, continuous dependent variable. Commonly associated terms:  Two sample t-test, student’s t-test, means, group means, standard deviations, mean differences, group difference, confidence interval, group comparison.
20. 20.  What to interpret?  p-values (<.05)  Mean differences and standard deviations  Confidence intervals 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.
21. 21.  What you read:  Patients admitted to “academic” hospital clinics (M=.50, SD=.40) had lower average 90-day readmissions than patients seen by non-academic clinics (M=1.5, SD=.75), p = .02. What to interpret:  _____________________________  _____________________________  _____________________________ How to interpret:  ____________________________________________ ____________________________________________
22. 22.  What is it?  Tests the difference among more than two groups on a single, continuous variable.  Post-Hoc tests are required to examine where the differences are. Commonly associated terms:  F-test, interactions, post-hoc tests (tukey HSD, bonferroni, scheffe, dunnett).
23. 23.  What to interpret?  p-values (<.05)  Main effect: Shows overall significance  Post-hoc tests: shows specific group differences  Mean differences, standard deviations How to interpret?  Main Effect: There was an overall significant difference among the groups of the independent variable on the dependent variable.  Post-Hoc: Same interpretation as an independent t- test
24. 24.  What you read:  A researcher looks at differences in number of side effects patients had on three difference drugs (A, B, and C).  Main effect: Overall F=20.10, p=.01  Post-hoc: Comparison of Drug “A” to Drug “B” shows average side effects to be 4(SD=2.5) and 7(SD=4.8), respectively, p=.04. What to interpret:  _____________________________  _____________________________ How to interpret:  ________________________________________________ ________________________________________________  ________________________________________________ ________________________________________________
25. 25. Dependent t-testWithin Subjects Analysis of Variance (ANOVA)
26. 26.  What is it?  Tests the differences for one group between two time-points or matched pairs Commonly Associated Terms:  Pre and posttest, matched pairs, paired samples, time. What to interpret?  p-values (<.05)  Mean change between measurements (i.e. over time or between pairs) 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.
27. 27.  What you read:  An article shows a difference in average number of COPD-related readmissions before (M=1.5, SD=2.0) and after (M=.05, SD=.90) a patient education intervention, p=.08. What to interpret:  _____________________________  _____________________________ How to interpret:  ____________________________________________ ____________________________________________ ____________________________________________
28. 28.  What is it?  A statistical analysis that tests differences of one group between two or more time-points or matched pairs (e.g. pretest, posttest, & follow-up or treatment “A” patient, treatment “B” matched patient, & placebo matched patient). Commonly Associated Terms:  Multiple time-points/matched pairs, repeated measures, post- hoc. What to interpret?  Main effect: p-values  Post-hoc: p-values, mean change, direction of change. How to interpret:  Main Effect – There was an overall significant difference among the time points/matched pairs on the dependent variable.  Post-Hoc: Same as a dependent t-test.
29. 29.  What you read:  An article shows a difference in average number of COPD- related readmissions before (M=1.5, SD=2.0) and after (M=.05, SD=.90), and six months following a patient education intervention (M=0.80, SD=3.0).  Main effect: Overall F=3.59, p=.12. What to interpret:  p-value=.12, not statistically significant  Mean change=1.0 fewer readmissions at post-intervention How to interpret:  The number of COPD-related readmissions did not significantly change among any of the the three time points.
30. 30. Other Types of ANOVAs Conclusion
31. 31.  Mixed ANOVA: Used when comparing more than one group over more than one time-point on a measure  Example – Males vs. females, before and after smoking cessation intervention – Average cigarettes per day Factorial ANOVA: Comparing two or more separate independent variables on one dependent variable.  Example – Where the patient was seen (UTH, HSM, or UFP), AND Whether or not the diabetes regimen was intensified – Average readmissions Analysis of covariance (ANCOVA): Examining the differences among groups while controlling for an additional variable  Example – Whether or not the diabetes regimen was intensified, controlling for baseline A1C – Average readmissions All of these methods are used to test interaction effects
32. 32.  Using complicated statistics give the researcher several advantages:  Reduced statistical error  Ability to look at complex relationships  Can control for confounders  Allows for a more complete and in-depth interpretation of the phenomenon. No phenomenon you study exists in a vacuum!
33. 33. Questions? 
34. 34. Test Name Commonly Associated Terms  Those that are bolded are terms specific to the test in question What to interpret  What to look for to understand the relevance/importance  p-values, confidence, mean differences, effect size, etc. How to interpret  Provides test-specific ways to interpret results Non-Parametric Equivalent (where applicable)
35. 35. Remember: Just because a finding is not significant does not mean that it is not meaningful. You should always consider the effect size and context of the research when making a decision about whether or not any finding is clinically relevant.
36. 36. Work together (in pairs) to answer the questions on thehandout using your “Commonly Used Statistics” resource. Be prepared to share how you found your answers.