M. Drew LaMar
April 13, 2022
“…a hypothesis test tells us whether the observed data are consistent with the null hypothesis, and a confidence interval tells us which hypotheses are consistent with the data.”
- William C. Blackwelder
The main assumptions of all statistical techniques is that your data come from a random sample.
Definition: In a
random sample , each member of a population has an equal and independent chance of being selected.
Random sampling
Definition: The
sampling distribution represents the distribution of the point estimatesbased on samples of a fixed size from a certain population. It is useful to think of a particular point estimate as being drawn from such a distribution. Understanding the concept of a sampling distribution is central to understanding statistical inference.
Definition: The standard deviation associated with an estimate is called the
standard error . It describes the typical error or uncertainty associated with the estimate.
The standard error is also the standard deviation of the sampling distribution.
http://www.zoology.ubc.ca/~whitlock/kingfisher/SamplingNormal.htm
If a sample consists of at least 30 independent observations and the data are not strongly skewed, then the sampling distribution for the mean is well approximated by a normal model even if the population is not normally distributed.
Definition: The standard error represents the standard deviation associated with the estimate, and roughly 95% of the time the estimate will be within 2 standard errors of the parameter.
An approximate 95% confidence interval for a point estimate is given by \[ \textrm{point estimate} \pm 1.96\times SE \]
Note: For a huge number of computed 95% confidence intervals, the population parameter will be contained in 95% of the confidence intervals.