Estimation, Point estimation and Interval estimation

Estimation

Estimation.

It is defined as the statistical method of estimating the population parameter from the sample observation drawn from the population with the desired degree of precision. It helps to obtain a guess or estimate of the unknown true value from the sample data or past experience. The estimation o f population parameters like mean, variance, proportion etc. from the corresponding sample statistics with reasonable accuracy are very common problems of statistical inference. That’s why the sampling distribution of a statistic and its standard error plays a vital role in both the estimation of parameters and the testing of hypothesis. A sample statistic used to estimate a population parameter is called an estimator. Example The sample mean\(\overline{X}\) is an estimator of the population mean (µ).

A specific observed numerical value of the estimator is called on an estimate. For example, A random sample 200 students of Trichandra college give a mean height of 5.5ft with S.D of 0.25 ft, then if we use these specific values to estimate the mean height and S.D of the whole students, the values 5.5ft and 0.25 ft would be estimates of population mean and population standard derivation respectively.

The estimation of the population parameters can be done in either of the following two ways.

1. Point estimation.
2. Interval estimation.

Point estimation.

The procedure of estimating an unknown parameter from a single value is known as point estimation. It provides an exact value of the unknown parameter to be estimated under investigation. A single number that is used to estimate an unknown population parameter is called points estimate.

For example.

A sample mean \(\overline{X}\) and a sample standard deviation (S) are point estimates of the population mean (µ) and the population standard deviation (σ) respectively.

The number of enrollments in next year in BSC I year estimates by Trichandra college would be 900 is a point estimate. This process is called point estimation.

In this process, the main difficulty is to choose the best estimator for a parameter some criterion or proportions are needed to choose the best estimator among the possible estimators. The desired properties are the following . They are as follows.

1. Un-biassed.\
2. Consistency
3. Sufficiency
4. Efficiency.

Interval estimation.

This process of estimating an unknown population from a range of values is known as interval estimating. In point estimation, we give a range value while in interval estimation we give an interval to estimate a parameter. In interval estimation, a sample to the sample variation is also taken into consideration through standard error.

A range of values used to estimate a population parameter is called an interval estimation. There are two ways for indicating an error by the extent of its range and by the probability of the true population parameter lying in that range. In this estimation, the researcher or decision maker has a better idea of the reliability of his estimate.

For example.

The number of enrollments in BSc. I year in next year estimates by Trichandra campus would be 700 to 1100 is an interval estimate. This process of estimation is called interval estimation.

Point estimation sometimes may not exactly represent the population parameter to overcome. This drawback we need , a range of values to estimate the population parameter. As a rule of a point, estimate fluctuates from sample to sample interval estimates are preferable to point estimates. Also, the interval estimates indicate the accuracy of an estimate because the interval estimates provide a measure of the degree of uncertainty in terms of probability attached to the interval.

Reference

Kerlinger, F.N. Foundation of Behavioural Research. New Delhi: Surjeet Publication, 2000.

Kothari, C.R. Research Methodology. India: Vishwa Prakashan, 1990.

Singh, M.L. and J.M Singh. Understanding Research Methodology. 1998.

Singh, Mrigendra Lal. Understanding Research Methodology. Nepal: National Book centre, 2013.