Various Topics of Interest to Various Topics of Interest to the Inquiring Orthopedistthe Inquiring Orthopedist

Richard Gerkin, MD, MSRichard Gerkin, MD, MS

BGSMC GME ResearchBGSMC GME Research

Probability of Obtaining a Test Statistic Probability of Obtaining a Test Statistic More Extreme than Actual Sample More Extreme than Actual Sample Value Given HValue Given H00 Is True Is True

Used to Make Rejection DecisionUsed to Make Rejection Decision– If p value > If p value > αα, Do Not Reject H, Do Not Reject H00

– If p value < If p value < αα, Reject H, Reject H00

p Value Test

p Values:p Values:PitfallsPitfalls

A small p value does not prove that the A small p value does not prove that the alternative hypothesis is truealternative hypothesis is true

If N is large enough, any desired p can If N is large enough, any desired p can be obtained. This type of situation must be obtained. This type of situation must be interpreted with caution, looking for be interpreted with caution, looking for significant significant clinicalclinical results results

p values:p values:PitfallsPitfalls

Sample size calculation: N = kSample size calculation: N = kσσ22/d/d22

No matter how small d is, N can be No matter how small d is, N can be made large enough (have enough made large enough (have enough power) to detect that differencepower) to detect that difference

Multiple ComparisonsMultiple Comparisons

A p value of .05 would be expected by A p value of .05 would be expected by chance to occur once in 20 trials of a chance to occur once in 20 trials of a study in which there is no difference study in which there is no difference between groupsbetween groups

If 14 tests are done within a study, the If 14 tests are done within a study, the probability is greater than ½ that one of probability is greater than ½ that one of these will have a p of < .05 these will have a p of < .05

Multiple ComparisonsMultiple Comparisons

Other than the primary outcome, all Other than the primary outcome, all secondary outcomes and subgroup secondary outcomes and subgroup analyses should be considered analyses should be considered exploratoryexploratory

In some instances, mathematical In some instances, mathematical correction for multiple comparisons can correction for multiple comparisons can be made.be made.

Mean, , is unknown

Population Random Sample

I am 95% confident that is between 40

& 60.

Mean X = 50

Estimation Process

Sample

Estimate PopulationParameter...

with SampleStatistic

Mean

Proportion p ps

Variance s2

Population Parameters Estimated

2

Difference - 1 2

x - x 1 2

X_

__

• Provides Range of Values Provides Range of Values – Based on Observations from 1 SampleBased on Observations from 1 Sample

• Gives Information about Closeness Gives Information about Closeness to Unknown Population Parameterto Unknown Population Parameter

• Stated in terms of ProbabilityStated in terms of Probability Never 100% Sure Never 100% Sure

Confidence Interval Estimation

Confidence Interval

Sample Statistic

Confidence Limit (Lower)

Confidence Limit (Upper)

A Probability That the Population Parameter Falls Somewhere Within the

Interval.

Elements of Confidence Interval Estimation

Parameter = Statistic ± Its Error

© 1984-1994 T/Maker Co.

Confidence Limits for Population Mean

X Error

= Error = X

XX

XZ

xZ

XZX

Error

Error

X

90% Samples

95% Samples

x_

Confidence Intervals

xx .. 64516451

xx 96.196.1

xx .. 582582 99% Samples

nZXZX X

X_

• Probability that the unknown Probability that the unknown

population parameter falls within the intervalpopulation parameter falls within the interval

• Denoted (1 - Denoted (1 - ) % = level of ) % = level of confidence confidence

e.g. 90%, 95%, 99%e.g. 90%, 95%, 99%

Is Probability That the Parameter Is Not Is Probability That the Parameter Is Not Within the IntervalWithin the Interval

Level of Confidence

• Data VariationData Variation

measured by measured by • Sample SizeSample Size

• Level of ConfidenceLevel of Confidence

(1 - (1 - ))

Factors Affecting

Interval Width

n/XX

• Population MeanPopulation Mean Equal Equal toto

Sampling MeanSampling Mean• TheThe Standard ErrorStandard Error (standard deviation)(standard deviation)

of the Sampling distribution isof the Sampling distribution is Less thanLess than PopulationPopulation Standard DeviationStandard Deviation

• Formula (sampling with replacement):Formula (sampling with replacement):

Properties of Summary Measures

x

As n increases, decreases. x =

xn__