Statistics pres 3.31.2014

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

Outline of Today’s Class
 Analytic Methods
 Summary Measures
 Hypothesis Testing
 Statistical Methodologies
 Group Discussion
 Sample Size Determination
 Group Discussion
 Additional Resources

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

 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!)

“Normally” Distributed
Data
“Skewed” Data

 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.

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.

 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 “=“

 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

 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)

 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.

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

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

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).

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

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

 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

 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%).

 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

 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)

 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

 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

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.

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.

 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)

 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

Statistics pres 3.31.2014

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Statistics pres 3.31.2014