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# Statistics pres 3.31.2014

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### Statistics pres 3.31.2014

1. 1. A D L T 6 7 3 : T E A C H I N G A S S C H O L A R S H I P I N M E D I C A L E D U C A T I O N M O N D A Y , M A R C H 3 1 , 2 0 1 4 An Overview of Quantitative Data Analysis
2. 2. Outline of Today’s Class  Analytic Methods  Summary Measures  Hypothesis Testing  Statistical Methodologies  Group Discussion  Sample Size Determination  Group Discussion  Additional Resources
3. 3. Analytic Methods: Summary Measures  Representative Measures  Reflect the most “typical” or “average” data value.  Continuous Measurements:  Mean (Average), Median and Mode  Categorical Measurements:  Frequencies and Proportions
4. 4. Analytic Methods: Summary Measures  Measures of Variability  Reflect how much the values differ from one another.  Continuous Measurements:  Standard deviation, range, interquartile range  Categorical Measurements:  None that are meaningful (sorry!)
5. 5. “Normally” Distributed Data “Skewed” Data Analytic Methods: Summary Measures
6. 6. “Normally” Distributed Data “Skewed” Data Analytic Methods: Summary Measures
7. 7. Analytic Methods: Summary Measures  Measures of Association  Continuous Measures: Correlation Coefficient (ρ): -1 < ρ < 1  Correlations close to 1 indicate two measurements are highly predictive and “track” with one another.  Correlations close to -1 indicate two measurements are highly predictive and have inverse relationship.  Correlations close to 0 indicate little association.  Categorical Measures: Odds Ratio (OR): 0 < OR < ∞  OR greater than 1 indicates outcome (e.g., passed test) more likely in test group than in control.  OR less than 1 indicates outcome less likely in test group than in control.  OR ≈ 1 indicates little difference in outcomes between groups.
8. 8. Analytic Methods: Hypothesis Testing  Most commonly accepted format of providing quantitative evidence.  Consists of 5 Steps:  Translate research question into a set of testable hypotheses.  Select most appropriate statistical test for your hypotheses.  Collect your data.  Calculate test statistic and/or p-value.  Make Decision.
9. 9. Analytic Methods: Hypothesis Testing  Translating Research Question into Testable Hypotheses  Identify parameter: population Mean (μ), proportion (p) or difference (e.g., μ1-μ2).  Identify statements made about that parameter.  Should be in the form of: <, ≤, >, ≥, = or ≠  Write research question in symbolic form, and find its opposite.  Opposite of “<“ is “≥”  “≤” is opposite of “>”  “≠” is opposite of “=“
10. 10. Analytic Methods: Hypothesis Testing  Example:  Does an active learning curriculum improve the proportion of students passing their board examinations compared to students receiving the standard curriculum?  Parameter: proportion passing board exams  p  Statement: pactive is greater than pstandard  Symbolic Form: pactive > pstandard or pactive – pstandard > 0  Opposite of Symbolic Form: pactive ≤ pstandard or pactive – pstandard ≤ 0
11. 11. Analytic Methods: Hypothesis Testing  Testable Hypotheses:  Null Hypothesis: Statement that parameter (or difference) is equal to zero.  Any statement in symbolic form with a ≤, ≥ or = is automatically the null (note: we replace ≤ or ≥ with 0).  Alternative Hypothesis: Statement that parameter (or difference) is somehow different from zero.  Any statement in symbolic form with a <, > or ≠ is automatically the alternative.  Example:  pactive – pstandard > 0  becomes the alternative (HA)  pactive – pstandard ≤ 0  becomes the null (H0)
12. 12. Analytic Methods: Hypothesis Testing  Make Decision  Based on statistical methodology you use, you get a p-value.  Probability of observing outcomes that are more extreme than the data you actually observed, given the null hypothesis is true.  Plain English: If your study was ineffective, p-value is the probability of observing more extreme results than what you observed.  If this probability is high, then your results match with the null hypothesis, and you fail to reject the null (intervention didn’t work)  If this probability is low, then your results do not seem to match the null hypothesis, and you reject the null (intervention likely worked).  In practice: we compare p-value to significance level (α = 0.05).  If p-value ≥ 0.05, we fail to reject the null.  If p-value < 0.05, we reject the null.
13. 13. Analytic Methods: Continuous Data # of Measurements # of Samples Single Pre/Post Repeated Measures 1 Sample t-test Paired t-test Repeated Measures ANOVA (RMA) / Linear Mixed Model (LMM)* 2 Samples Two-sample t-test RMA / LMM* RMA / LMM* “k” Samples Analysis of Variance (ANOVA) RMA / LMM* RMA / LMM* Adjusting for Covariates: Multiple Linear Regression*, Analysis of Covariance (ANCOVA)*, Linear Mixed Models* *Will likely require statistical assistance
14. 14. Analytic Methods: Categorical Data # of Measurements # of Samples Single Pre/Post Repeated Measures 1 Sample z-test McNemar’s Test Generalized Linear Mixed Models (GLMM)* 2 Samples Chi-square Test GLMM* GLMM* “k” Samples Chi-square Test GLMM* GLMM* Adjusting for Covariates: Multiple Logistic Regression*, Generalized Linear Mixed Models* *Will likely require statistical assistance
15. 15. Analytic Methods: Group Discussion  Please break into groups by table  For the next 10-15 minutes, take turns discussing what analytic approaches are appropriate for your proposed study.  What are your null and alternative hypotheses?  Is your outcome continuous or categorical?  How many groups and measurements?  If your study is qualitative, discuss how statistical methodologies could be used (e.g. data summary, association).
16. 16. Sample Size Determination  As a general rule, larger sample sizes:  Lead to more representative samples  Lead to better estimation of parameters (e.g., representative measures)  Provide estimators with lower variability N=9 N=36 N=100
17. 17. Sample Size Determination Averages over 10,000 Simulations Sample Size Sample Mean Sample Std. Dev. Standard Error* 9 204.4 36.5 12.3 16 204.3 37.1 9.5 25 204.2 37.2 7.8 36 204.1 37.5 6.5 49 204.1 37.6 5.5 64 204.2 37.7 4.9 81 204.1 37.7 4.2 100 204.1 37.7 3.9 1000 204.1 37.7 1.2 *SE: explains variability in estimator; not the sample data
18. 18. Sample Size Determination  Possible Decisions  Power = 1 - β True State Decision H0 is “True” HA is True Reject H0 Type I Error α Correct Decision Fail to Reject H0 Correct Decision Type II Error β
19. 19. Sample Size Determination  Determinants of Required Sample Size  Significance Level (α): probability of rejecting H0 when it is true.  Power (1-β): probability of failing to reject H0 when it is false.  These values are selected during design phase  α = 5%  1-β = 80% (sometimes 90%).
20. 20. Sample Size Determination  Determinants of Required Sample Size  Measure of variability (usually standard deviation) inherent in study population.  As data become more variable…  Standard error of Test statistic increases…  p-value increases…  Ability to reject H0 decreases…  Power decreases.  Controlling variability:  Better measurement methodology  Homogeneous samples
21. 21. Sample Size Determination  Determinants of Required Sample Size  Effect Size: smallest difference or change in outcome that you are hoping to find  As difference you want to observe decreases…  Test statistic decreases…  p-value increases…  Ability to reject H0 decreases…  Power decreases.  Considerations:  Clinical significance  Clinical possibility (larger differences are easier to detect and harder to find)
22. 22. Sample Size Determination  Calculating Required Sample Size  Equations exist (involving α, β, variability and effect size) for simple analytic methods (t-test, chi-square, etc.).  Advanced methods require professional assistance.  Where do you find variability and effect size?  Previous literature of similar populations  Pilot study  Guess-timates
23. 23. Sample Size Determination  What if required sample size is too large?  Consider a different outcome  Continuous measures generally require smaller sample sizes than categorical measures  Consider multiple sections or sites  Will require more sophisticated analytic methods  Reconfigure study as a “pilot”  Emphasis switches from “hypothesis testing” to “estimation” and “data summary”  Goal is to provide data summaries and estimate confidence intervals  Summaries can be used to power larger study
24. 24. Sample Size Determination: Group Discussions  Please break into groups by table.  For the next 10-15 minutes, take turns discussing:  Whether you will be able to power your study.  Where to find information to perform power analysis.  Your options if you are unable to adequately power your study.
25. 25. Additional Resources  VCU Department of Biostatistics  18 full-time faculty  Can assist with: study design, sample size determination, interim and final analyses, dissemination  Grant funding (or prospects of funding) usually required.  BIOS 516 Biostatistical Consulting: graduate students available for FREE consultations  Contact Russ Boyle (boyle@vcu.edu) and provide a protocol.
26. 26. Additional Resources  VCU Center for Clinical and Translation Research  Research Incubator: study design, sample size determination, and other resources (e.g. grant writing)  Contact: Pam Dillon (pmdillon@vcu.edu)  Biomedical Informatics: data management and storage (e.g. REDCAP)  Support requested online: (http://www.cctr.vcu.edu/informatics/index.html)
27. 27. Additional Resources  Textbooks (i.e., shameless plug):  Statistical Research Methods: A Guide for Non-Statisticians  Sabo and Boone, Springer, 2013  Available on the web (\$45-\$65):  http://www.springer.com/statistics//life+sciences,+medicine +%26+health/book/978-1-4614-8707-4  http://www.amazon.ca/Statistical-Research-Methods-Guide- Non-Statisticians/dp/1461487072