# chapter 7 notes for HLTA10

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Published on 24 Apr 2011
School
Department
Course
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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