Various Topics of Interest to the Inquiring Orthopedist Richard Gerkin, MD, MS BGSMC GME Research

Probability of Obtaining a Test Statistic More Extreme than Actual Sample Value Given H 0 Is True Used to Make Rejection Decision – If p value > α, Do Not Reject H 0 – If p value < α, Reject H 0 p Value Test

p Values: Pitfalls A small p value does not prove that the alternative hypothesis is true If N is large enough, any desired p can be obtained. This type of situation must be interpreted with caution, looking for significant clinical results

p values: Pitfalls Sample size calculation: N = kσ 2 /d 2 No matter how small d is, N can be made large enough (have enough power) to detect that difference

Multiple Comparisons A p value of.05 would be expected by chance to occur once in 20 trials of a study in which there is no difference between groups If 14 tests are done within a study, the probability is greater than ½ that one of these will have a p of <.05

Multiple Comparisons Other than the primary outcome, all secondary outcomes and subgroup analyses should be considered exploratory In some instances, mathematical correction for multiple comparisons can be made.

Mean, , is unknown PopulationRandom Sample I am 95% confident that  is between 40 & 60. Mean X = 50 Estimation Process Sample

Estimate Population Parameter... with Sample Statistic Mean  Proportion pp s Variances 2 Population Parameters Estimated  2 Difference  -  12 x - x 12 X _ __

Provides Range of Values Provides Range of Values – Based on Observations from 1 Sample Gives Information about Closeness to Unknown Population Parameter Gives Information about Closeness to Unknown Population Parameter Stated in terms of Probability Stated 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 © T/Maker Co. Confidence Limits for Population Mean Error = Error = Error

90% Samples 95% Samples  x _ Confidence Intervals 99% Samples X _

Probability that the unknown Probability that the unknown population parameter falls within the interval Denoted (1 -  ) % = level of confidence e.g. 90%, 95%, 99% Denoted (1 -  ) % = level of confidence e.g. 90%, 95%, 99% –  Is Probability That the Parameter Is Not Within the Interval Level of Confidence

Data Variation Data Variation measured by  Sample Size Sample Size Level of Confidence (1 -  ) Level of Confidence (1 -  ) Factors Affecting Interval Width

Population Mean Equal to Population Mean Equal to Sampling Mean Sampling Mean The Standard Error (standard deviation) of the Sampling distribution is Less than Population Standard Deviation The Standard Error (standard deviation) of the Sampling distribution is Less than Population Standard Deviation Formula (sampling with replacement): Formula (sampling with replacement): Properties of Summary Measures As n increases, decreases.  x = x _ _