Populations and Samples

Populations and Samples

Concepts

Population

A complete group of measurements or individuals of interest.

Sample

A subset of a population used for a measurement or treatment.

Sampling

Measuring a few individuals from a population to get a sense of the whole.

Often it is prohibitively expensive or time-consuming to measure all of the members of a population. Sampling is a group of techniques that allow us to measure a smaller sample that reflects the overall population.

Statistical Inference

The use of a sample to determine the characteristics of the larger population.

Hypothesis Testing

The practice of determining whether an observed difference is due to random fluctuations or the experiment (drug, education, etc).

Statistical Significance

A measure of the probability that the mean of a random sample from a subpopulation was randomly drawn from the larger population.

For example, if you drew 10 random SSU students and they were all taller than 6 feet, this probably wasn't random but was at basketball team practice.

Effect Size

This is the difference in the mean between an original distribution and the distribution after a treatment or from looking at a subpopulation.

Central Limit Theorem

The more observations you have in your sample, the higher the probability that the mean of your observation will be close to the population mean.

Sample Mean

This is the mean of a sample of data we take from a larger population.

We are often concerned with how well this sample mean predicts the mean of the overall population.

Standard Error

If you repeatedly take sample means, the standard error is the amount of spread these sample means have. This amount of spread goes down as you include more data in each of the repeated samples.