Summary Research Methods - Data Analysis I

RM - Unit 101: Sampling distribution of a
mean

Micro-lectures

Inferential statistics - you use the sample to
say something about the population.

Sampling distribution - you take a sample
of the population several times and compute
the mean. You take the same sample size
every time.
The mean of the sampling
distribution will be very close or the same as
the population mean.
The first distribution is called the
sample mean. You use this in order to say
something about the population mean.
With random samples with a
substantial n from a population, the sampling
distribution will be (approximately) normal,
irrespective of the shape of the population
distribution. This is called the central limit
theorem.

The normal distributions are characterized by
their mean and their standard deviation.
If the sample size (n) is large than the
standard deviation is small, if the sample size
(n) is small then the standard deviation (sd) is
larger.
Choose a larger sample size in order not
to get a sample error. You’ll get closer to the
population mean.
The bigger the population standard
deviation, the bigger the sampling distribution
standard deviation.

A caveat - the idea of working with the sampling distribution is based on knowing the population
standard deviation when calculating the sampling distribution of the mean.
The population standard deviation is unknown, that’s why we use the standard deviation of the
sample.