Sampling
and sampling distributions
sample vs. population
parameter - measure used
to describe characteristic of a population (e.g., mu)
statistic - measure used
to describe characteristic of a sample (e.g., X bar)
inferential statistics
- how to use sample statistics to make inferences about population parameters
probability - relative
frequency in long run of repeated trials, expressed as proportion
probability sampling -
each unit of population has known probability for inclusion in sample
-
simple random sampling -
each case equally likely to be selected (e.g., using random number table,
etc.)
-
systematic sampling - select
every kth case (k = population size / desired sample size)
-
stratified random sampling
- proportionate and disproportionate
-
sampling error - difference
between sample statistic value and population parameter value
-
sampling distribution - theoretical
distribution of all possible sample statistic values
-
sampling distribution of
mean - theoretical distribution of all possible sample means
Central Limit theorem
-
sampling distribution of the mean = normal if sample size
is large enough, regardless of underlying population distribution
-
mean of sampling distribution = population mean (in long
run for large sample sizes)
-
standard error of the mean - standard deviation of the
sampling distribution of mean
-
in practice, sample sd used in place of pop sd
-
standard error influenced by sample size
-
standard error unrelated to population size
Rule for sample proportions
sampling distribution of proportions also distributed
normally if sample size sufficiently large
standard error for proportions (sd of sampling distribution
of a proportion)
-
SQRT ((pop proportion x (1 - pop proportion)) / sample
size)
applying Empirical rule to sample statistics and standard
errors
Summary:
parameter, statistic
sampling error
sampling distributions of mean and proportion are approximately
normal
standard error
increasing sample size decreases standard error