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Confidence intervals
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Lecture notes of 5 pages for the course Medicine at QUB (Statistics)
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CONFIDENCE INTERVALSPopulation parameters
A population is any collection of individuals in which
we are interested
The
frequency distribution of a variable in the
popu ation
is referred to as the population distribution
Summary values mean mode etc are referred to as
population parameters
A sample is any subset of a population and is ideally
selected to be representative of the population The
most
way to achieve this is by
likely a random
taking
It is taken in
sample way in which each member of
a
the public has an equal chance of being selected
Summary values calculated in samples are sample
statistics These are used to estimate population parameters
Accuracy or absence of bias if the samples were
repeatedly drawn from the population and the mean
calculated we would like the sample means to be
centred around the population mean
Precision or if samples were repeatedly
repeatability
drawn from the population and the mean calculated we
would like these samples to show little variation
, Sampling distribution and standard errors
Standard deviation A measure of the amount of
variation 1dispersion of a set of values A low standard
deviation indicates that the values tend to be close to
the mean of the set whilst a higher value means the
values are spread out over a wider
range
Sampling distribution of a statistic Frequency
distribution of that statistic over all possiblesamples of
a
given size selected from the population
The standard deviation of the sampling distribution
of a statistic is referred to as its standard error and is
used to calculate CIS
Example Bp in Queen's male students samples of 40
The sample mean varies from one to the next The
frequency distribution of the sample means is the
sampling distribution of the mean
The standard deviation of
the sample means or standard
error measures the
accuracy
with which sample distribution
a
represents a populationbyusing
standard deviation
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