Many course participants of non-statistics background always find the word “estimation” in statistics rather abstract and difficult to apprehend. To overcome this, one can get a clear picture with the following explanations.
In carrying out statistical analysis, we must appreciate an important point that we are always trying to understand the characteristics or features of a larger phenomenon (called population) from the data analysis of samples collected from this population.
Then let’s differentiate the meanings of the words “parameter” and “statistic”.
A parameter is a statistical constant or number describing a feature of the entire phenomenon or population, such as population mean m, or population standard deviation σ, whilst a statistic is any summary number that describes the sample such as sample standard deviation s.
One of the major applications used by statisticians is estimating population parameter from sample statistics. For example, sample means are used to estimate population means, sample proportions to estimate population proportions.
In short, estimation refers to the process by which one makes inferences about a population, based on information obtained from one or more samples. It is basically the process of finding the values of the parameters that make the statistical model fit the data the best.
In fact, estimation is one of the two common forms of statistical inference. Another one is the null hypothesis tests of significance, including the analysis of variance ANOVA.
Generally we can express an estimate of a population parameter in two ways:
Point estimate. A point estimate of a population parameter is a single value of a statistic, such as the sample mean is a point estimate of the population mean.
Interval estimate. An interval estimate is defined by a range of two numbers, between which a population parameter is said to likely lie upon with certain degree of confidence. For example, the expression X + U or –U < X < +U gives the range of uncertainty estimate of the population mean.
It is to be noted that point estimates and parameters represent fundamentally different things. For example:
- Point estimates are calculated from the data; parameters are not.
- Point estimates vary from study to study; parameters do not.
- Point estimates are random variables: parameters are constants.