What is Statistical Inference| Point vs.Interval Estimation

Statistical Estimation

Estimation is the process of drawing conclusions about an unknown population parameter from a sample. An estimator is a statistic used to calculate the value of an unknown parameter.

A point estimate is, in some ways, the best estimate of the parameter based on a sample. It should go without saying that no point estimate is perfect. It is a guess based on a single random sample. The point estimate would be expected to vary from sample to sample if repeated random samples were taken from the population. 

In repeated sampling, a confidence interval is an estimate based on the assumption that a specified proportion of the confidence intervals include the true parameter. The confidence level determines how frequently the confidence interval contains the parameter. The term "95 percent" refers to the fact that in repeated sampling, 95 percent of the confidence intervals include the parameter. When more confidence is required, 99 percent is used, which means that in repeated sampling, 99 percent of the intervals include the true parameter.

A confidence level of less than 90% is uncommon because too many intervals would fail to include the parameter. Similarly, confidence levels greater than 99 percent are rarely used because the intervals become wider as the confidence level increases, necessitating large sample sizes to produce usable intervals.

Many people get confidence intervals wrong. A confidence interval does not predict that the parameter will fall within the interval with a given probability. The issue arises because the word confidence is interpreted incorrectly as implying probability. Probability statements about parameters are not possible in frequentist statistics. Because parameters are not random variables, a probability statement cannot be made about them. When a confidence interval is constructed, it either includes or excludes the parameter.