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Fundamentals of Statistics 1: Basic Concepts :: A Parameter and a Statistic
In applied statistical work we rarely have the opportunity to measure entire populations, instead we make inferences about the populations from samples drawn, ideally randomly from the population. We usually want to know averages from whole populations, but use the average from a sample as our best guess at the population average. The unknown population average is called a parameter. The known sample average is called a statistic. It's easy to remember because of the alliteration
P
arameter:
P
opulation and
S
tatistics :
S
ample. Parameters and statistics are often means, but they could be standard deviations, medians or proportions.
For example, let's say we're interested in improving reading speed and want to test to see if a new speedreading technique actually works while still allowing for sufficient retention of material.
We could bring in a group of 50 volunteers, teach 25 of them the new speed reading technique for 2 hours and then ask them to read some material as fast as they could, and then answer several comprehension questions. The other 25 we'd just chat with for 2 hours about sports, politics and religion and then ask them to read the same material and answer the same comprehension questions. What we want to know is if we tested everyone (half got the training and half didn't) is the average time to read the material faster for the training group and is the average number of correct questions higher for the training group? We'd have an average time to read from each group. These would be sample statistics. We'd use the average time to read to make inferences about the average time for the entire population. The unknown average times for each group is the parameter.
As a matter of convention, most statistical texts use greek symbols for population parameters and the English or Arabic letters for sample statistics. For example, a sample mean is often denoted as xbar
. Population means are denoted with the lowercase greek letter mu
μ
. I try and stick to that convention on this website as well (it's just a pain sometimes getting those special characters into HTML).
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