BIOL2300 Biostatistics Chapter 7 - Boston College

[Pages:91]BIOL2300 Biostatistics Chapter 7

Point estimates, confidence intervals and minimum sample size for proportion, mean and variance

Inferential statistics

? estimate a population parameter (proportion, mean, variance)

? confidence interval for point estimate

? hypothesis testing

? H1: patients taking Vioxx (Merck) have MORE heart attacks and strokes than those not taking Vioxx

? H0: NULL hypothesis, EQUAL number of heart attacks and strokes in control and treatment groups

Merck

? The arthritis medication Vioxx was removed from US market on Sep 30, 2004, after data from a clinical trial showed an increased risk of heart attack, stroke, blood clots and other cardiovascular illnesses.

? FDA announced in 2004 that patients taking Vioxx have a 50 percent greater chance of heart attacks and sudden cardiac death, and that patients taking the highest recommended daily dosage of Vioxx had a 300 percent greater chance of heart attack and sudden cardiac death.

? source of information from this paragraph is

ESTIMATING PROPORTIONS

Requirements to check before approximating population proportion

? Simple random sample ? Sampling with replacement (binomial)

? fixed number of trials ? trials independent ? 2 outcomes: success, failure

? Conditions allowing approximation of binomial by normal are satisfied:

where p,q are estimated by p-hat (resp. q-hat), the proportion of successes (resp. failures) in sample

? point estimate: a single value used as approximation for a population parameter

? confidence interval: a real interval

such that we are 1- confident that p lies in that interval

Rationale for confidence interval

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