COMMONLY USED STATISTICS IN

MEDICAL RESEARCH PART I

Tiffany Smith

Patrick BarlowStatistical and Research Design Consultants,

OMERAD

WHY LEARN HOW TO READ STATISTICS? 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.

THREE MAJOR CATEGORIES OF STATISTICAL TESTS:

Descriptive Statistics

Parametric Statistics

Non-Parametric Statistics

SOME KEY TERMS Null Hypothesis Alternative Hypothesis Mean Standard Deviation Correlation Confidence Interval

INITIAL QUESTIONS Fit the 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?”

IN THIS PRESENTATION Descriptive Statistics 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

DESCRIPTIVE STATISTICS

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

PARAMETRIC STATISTICS 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

In research, you always want to use parametric statistics if possible.

COMMON PARAMETRIC TESTS OF

RELATIONSHIPSPearson r correlation

Linear/Multiple Regression

TESTS OF RELATIONSHIPS:PEARSON r CORRELATION 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.

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WHAT TO INTERPRET?

Strong Relationship: r > .50

Moderate Relationship:

r ≈ |.30|

Weak Relationship:r ≈ |.10|

No Relationship

:r ≈ |.00|

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IMPORTANCE OF GRAPHS

Anscombe, F.J., Graphs in Statistical Analysis, American Statistican, 27, 17-21

Each has a Pearson Correlation of r=.82, is

& is statistically

significant

EXAMPLE 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.

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LINEAR/MULTIPLE REGRESSION 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.

INTERPRETATION 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).

EXAMPLE

Table 3: Predictors of Number of Surgical Site Infections

PredictorRegression Coefficient1

p-value2

B(SE) β

Length of Stay .25 (.06) .30 <.001

Age -.75 (.05) -.45 <.0011B = Unstandardized coefficient, SE=standard error, and β = standardized coefficient2 Overall: F(2, 317)=17.19, p<.001, R=.31, R2 =.10

What you read

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

EXAMPLE CONTINUED

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

REMEMBER: CORRELATION DOES NOT IMPLY CAUSATION

COMMON PARAMETRIC TESTS OF GROUP

DIFFERENCES

Independent t-test

Between Subjects Analysis of Variance (ANOVA)

TESTS OF GROUP DIFFERENCES: INDEPENDENT t-TEST

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.

INTERPRETATION What to interpret?

p-values (<.05)Mean differences and standard deviationsConfidence 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.

EXAMPLE 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: _______________________________________________

_________________________________________

BETWEEN SUBJECTS ANALYSIS OF VARIANCE (ANOVA) 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).

INTERPRETATION 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

EXAMPLE 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: ________________________________________________________

________________________________________ ________________________________________________________

________________________________________

COMMON PARAMETRIC TESTS OF REPEATED

MEASURES

Dependent t-test

Within Subjects Analysis of Variance (ANOVA)

DEPENDENT t-TEST 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.

EXAMPLE 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: _____________________________________________

_______________________________________________________________________________________

REPEATED MEASURES ANOVA 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.

EXAMPLE 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.

FINAL THOUGHTS

Other Types of ANOVAs

Conclusion

OTHER ANOVAS 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

WHY BE SO COMPLICATED? Using complicated statistics give the

researcher several advantages:Reduced statistical errorAbility to look at complex relationshipsCan control for confoundersAllows for a more complete and in-depth

interpretation of the phenomenon. No phenomenon you study exists in a vacuum!

Questions?

HANDOUT SPECIFICSTest Name Commonly Associated Terms

Those that are bolded are terms specific to the test in question

What to interpretWhat to look for to understand the

relevance/importance p-values, confidence, mean differences, effect

size, etc.

How to interpretProvides 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.

ACTIVITYWork 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.