biostats lecture 3

why do we need sample size calculation or power analysis

• mainly to ensure the study will have sufficienct sample size to detect a true effect if exists

• sample size or power analysis should be conducted at the study planning stage, before the study starts

• most often, it is calculated based on the primary outcome

• most often, power is set to 80% or higher

before

• sample size or power analysis should be conducted at the study planning stage, __ the study starts

80%

• power is set to __ or higher

type 1 error

• rejecting H0 when H0 is true

• there is no difference but one concludes there is a difference

• false positive

• the maximum probabily of making this error is a (alpha) and is referred to as the level of the test or the significance level, often set at a=0.05

a (alpha)

• maximum allowable probability of making a type 1 error

• the level of the test or the significance level

• often set at a=0.05

type II error

• fail to reject H0 when H0 is false (there is a real difference, but one concludes there is no difference)

• false negative

• the maximum allowable probability of making type II error is B (beta)

• 1-B is the power of the test

B (beta)

• the maximum allowable probability of making type II error

1-B

• the power of the test

power

• if there is a real differnece, this tells us how likely one can correctly conclude there is a difference

• the generally acceptable level is at least 0.8

• 1-B

inversely

• type 1 error and type II error are ___ related

type 1 and type 2 error

• inversely related

• reduce the probability of type 1 errors will increase the probability of type II errors

• the relationship is not 1:1, reducing the probaility of making a type I error by 5% generally will not increase the probability of making a type II error by exactly 5%

• true IF nothing else changes

• type 1 error is positively related to power

positively

• type 1 error is ___ related to power

factors affecting power

• effect size

• population variations in the outcome

• type 1 error (a) or significance level

• sample size

• study design

effect size

• tells us how large is the difference in study outcome between two treatments under comparision

• positively associated with power

positively

• effect size and power are __ asssociated

variation of outcome (ó)

• negatively associated with power

• the larger the variation, the lower the power

type 1 error (a)

• postively associated with pwoer

• common practice a=0.05

sample size

• positively associated with power

• increasing increases power

• prior to a study, researchers have more control over sample size than other factors, subject to financial and time constraints

• power analysis and sample size determination/calculation are often used interchangeably

study design

• not directly entering the equation for power

• will affect the observed variation in the outcome

• can also affect the observed effect size

examples of study design issues

• number of comparison gorups

• how subjects are selected

• how frequently the outcomes are measured (repeated measure)

• equal or unequal number of subjects in each group

• instrument used to measure outcomes and its adminsitration