# Interval Estimation and Point Estimation: A Quick Guide 2012

The problem with using a point estimate is that although it is the single best guess you can make about the value of a population parameter, it is also usually wrong. Interval estimate overcomes this problem using interval estimation technique which is based on point estimate and margin of error.

### Point Estimation

Point estimation involves calculating a single value from sample data to estimate a population parameter. The examples of point estimation are: (i) Estimating the population mean using the sample mean and (ii) Estimating the population proportion using the sample proportion. The common point estimators are:

• Sample mean $\overline{x}$ for population mean ($\mu$).
• Sample proportion ($\hat{p}$​) for population proportion ($P$).
• Sample variance ($s^2$) for population variance ($\sigma^2$).

### Interval Estimation

Interval estimation involves calculating a range of values (set of values: an interval) from sample data to estimate a population parameter. The range constructed has a specified level of confidence. The Components of an interval are:

• Confidence level: The probability that the true population parameter lies within the interval.
• Margin of error: The maximum allowable error (difference between the point estimate and the true population parameter).

The common confidence intervals for the population mean are:

• Confidence interval for a large sample (or known population standard deviation):
$\overline{x} \pm Z_{\alpha/2} \frac{s}{\sqrt{n}}$
• Confidence interval for small sample (or unknown population standard deviation):
$\overline{x} \pm t_{\alpha/2, n-1} \frac{s}{\sqrt{n}}$
• Confidence interval for the population proportion
$\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p} {1-\hat{p}}}{n}}$

• A major advantage of using interval estimation is that you provide a range of values with a known probability of capturing the population parameter (e.g. if you obtain from SPSS a 95% confidence interval you can claim to have 95% confidence that it will include the true population parameter.
• An interval estimate (i.e., confidence intervals) also helps one not to be so confident that the population value is exactly equal to the single-point estimate. That is, it makes us more careful in interpreting our data and helps keep us in proper perspective.
• Perhaps the best thing to do is to provide both the point estimate and the interval estimate. For example, our best estimate of the population mean is the value of $32,640 (the point estimate) and our 95% confidence interval is$30,913.71 to \$34,366.29.
• By the way, note that the bigger your sample size, the more narrow the confidence interval will be.
• Remember to include many participants in your research study if you want narrow (i.e., exact) confidence intervals.

In essence, interval estimation is a game-changer in the field of statistics. Interval estimation, acknowledges the uncertainty inherent in data, providing a range of probable values (interval estimates) instead of a single (point estimate), potentially misleading, point estimate. By incorporating it into the statistical analysis, one can gain a more realistic understanding of the data and can make more informed decisions based on evidence, not just a single number.

https://gmstat.com