Commonly Used Statistics in Medical Research Part I

Tiffany Smith
Patrick Barlow
Statistical and Research Design Consultants, OMERAD

 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.

Descriptive Statistics

Parametric Statistics

Non-Parametric Statistics

 Null Hypothesis
 Alternative Hypothesis
 Mean
 Standard Deviation
 Correlation
 Confidence Interval

 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?”

 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

 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

 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.

Pearson r correlation
Linear/Multiple Regression

 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.

No Relationship: Weak Relationship:
r ≈ |.00| r ≈ |.10|

Moderate
Relationship:
r ≈ |.30| Strong Relationship: r > .50

11

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

 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.

 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
 Multivariate, beta weight, r2-value, model,
forward/backward regression,
sequential/hierarchical regression,
standard/simultaneous regression,
statistical/stepwise regression.
14

 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).

 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

 “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

 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

Commonly Used Statistics in Medical Research Part I

Independent t-test
Between Subjects Analysis of Variance (ANOVA)

 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.

 p-values (<.05)
 Mean differences and standard deviations
 Confidence intervals
 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.

 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 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).

 p-values (<.05)
 Main effect: Shows overall significance
 Post-hoc tests: shows specific group differences
 Mean differences, standard deviations
 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

 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.
 _____________________________
 _____________________________
 ________________________________________________
________________________________________________
 ________________________________________________
________________________________________________

Dependent t-test
Within Subjects Analysis of Variance (ANOVA)

 What is it?
 Tests the differences for one group between two time-points
or matched pairs
 Pre and posttest, matched pairs, paired samples, time.
 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.

 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 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).
 Multiple time-points/matched pairs, repeated measures, post-
hoc.
 Main effect: p-values
 Post-hoc: p-values, mean change, direction of change.
 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.

 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.
 p-value=.12, not statistically significant
 Mean change=1.0 fewer readmissions at post-intervention

 The number of COPD-related readmissions did not
significantly change among any of the the three time
points.

Other Types of ANOVAs
Conclusion

 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

 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!

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)

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.

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.

Commonly Used Statistics in Medical Research Part I

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