Department

Health Studies

Course Code

HLTB15H3

Professor

Caroline Barakat

Health Studies

Section 3; Chapter 7.1

Calculation of Sample Size, Statistical Significance and Sampling

The Sampling Unit

Member of the sample population

Investigator must calculate how many clinics, doctors, and patients are needed in the

sample

Hierarchical statistical techniques (multilevel models) have been developed for the

analysis of multilevel studies

The different levels of data are referred to as ‘nested’

Ecological fallacy – inferences about groups are drawn from individuals

Calculation of Sample Size and Statistical Power

Size of the sample aimed for should be calculated at the design stage

Power calculation – statistical approach to determining sample size in evaluation

studies

oMeasure of how likely the study is to produce a statistically significant result

for a difference between groups of a different magnitude

oProbability = power

Considerations in Determination of Sample Size

Must consider need for sub-group analysis, issue of item and total non-response and

sample attrition in the case of longitudinal designs

Testing Hypothesis, Statistical Significance, the Null Hypothesis

Hypotheses are in the form of either a substantive hypothesis (represents a predicted

association between variables, or a null hypothesis (statistical artifice and always

predicts the absence of a relationship between the variables

Hypothesis testing is based on the logic that the substantive hypothesis is tested by

assuming that the null hypothesis is true

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Probability Theory

Statistical tests of significance apply probability theory to work out the chances of

obtaining the observed result

If the null hypothesis is not rejected, it cannot be conclude that there is no difference,

only that the method of study detected no difference

Bayesian theory is based on a principle which states that information arising from

research should be based only on the actual data observed, and on induction of the

probability of the true observation given the data

oStarts with the probability distribution of given data and adds new evidence

to produce a posterior

Frequentist theory involves the calculation of P values which take into account the

probability of observations more extreme than the actual observations, and the

deduction of the probability of the observation

Type I and Type II Errors

Sample size is determined by balancing both statistical and practical considerations

Two types of error to consider when making these decisions

Type I error – alpha error; error of rejecting a true null hypothesis that there is no

difference

oAnd, by corollary, acceptance of a hypothesis that there are differences which

is actually false

Type II error – beta error; failure to reject a null hypothesis when it is actually false

oAcceptance of no differences when they do exist

Sample Size and Type I and I I Errors

The larger the sample, then the smaller will be the sampling error, and statistically

significant results are more likely to be obtained in larger samples

With a very large sample, it is almost always possible to reject any null hypothesis

(type I error) simply because statistics are sensitive to sample size; therefore the

investigator must be careful not to report findings

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