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
Commonly Used Statistics in Medical Research Part I
1. Tiffany Smith
Patrick Barlow
Statistical and Research Design Consultants, OMERAD
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.
4. Null Hypothesis
Alternative Hypothesis
Mean
Standard Deviation
Correlation
Confidence Interval
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. 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. 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. 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.
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. No Relationship: Weak Relationship:
r ≈ |.00| r ≈ |.10|
Moderate
Relationship:
r ≈ |.30| Strong Relationship: r > .50
11
12. Each has a Pearson
Correlation of r=.82, is & is
statistically
significant
12
Anscombe, F.J., Graphs in Statistical Analysis, American Statistican, 27, 17-21
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. 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. 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. What you read
Table 3: Predictors of Number of Surgical Site Infections
Regression Coefficient1
Predictor p-value2
B(SE) β
Length of Stay .25 (.06) .30 <.001
Age -.75 (.05) -.45 <.001
1B = Unstandardized coefficient, SE=standard error, and β = standardized
coefficient
2-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. 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
20. 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.
21. 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.
22. 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:
____________________________________________
____________________________________________
23. 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).
24. 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
25. 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:
________________________________________________
________________________________________________
________________________________________________
________________________________________________
27. 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.
28. 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:
____________________________________________
____________________________________________
____________________________________________
29. 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.
30. 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.
32. 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
33. 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!
35. 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)
36. 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.
37. Work together (in pairs) to answer the questions on the
handout using your “Commonly Used Statistics” resource.
Be prepared to share how you found your answers.
Notes de l'éditeur
Null Hypothesis: The hypothesis that a difference or relationship between the variables does not exist. You are trying to reject this hypothesis in your test.Alternative Hypothesis: The hypothesis that a difference of relationship between the variables does exist. What you are trying to “prove” in statistical tests.Mean: A measure of central tendency that is the arithmetical average of a group of numbers. Standard Deviation: A measure of spread that quantifies how much the scores in a sample vary around the sample’s mean.Correlation: Implies a relationship (usually linear) between two variables. Terminology appropriately used when testing relationships between variables, but is commonly misused in other contexts.Confidence Interval: Derived from statistical tests. Provides 95% (usually) confidence that the true statistic of interest (i.e. mean, relationship, risk, etc.) lies within a given range. Greatly affected by things such as sample size and measurement error.
Etc: sample size, spherecity…
What to interpret:“B’s” for each predictor: LoS=.25 and Age= -.75p-value of each predictor: both <.001p-value for the model: <.001.R2 value for the model: .10