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Point Estimate and Confidence Interval Estimate

Point Estimate and Confidence Interval Estimate

Point Estimate

A point estimate gives statisticians a single value as the estimate of a given population parameter. For example, the sample mean X̄ is the point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion p when binomial modeling is involved.

A point estimate is a specific outcome that takes a single numerical value.  It has two main characteristics:

  1. A point estimate is a single numerical value specific to a given sample.
  2. A point estimate has no sampling distribution.

Point estimates are subject to bias. In this context, bias refers to the difference between the expected value of the estimator and the true value of the population parameter involved. Each point estimate has a well-defined formula used in its calculation. Statisticians use the method of maximum likelihood or the method of moments to find good unbiased point estimates of the underlying population parameters.

Confidence Interval Estimate

We design a confidence interval estimate such that there is a range (lower confidence limit and upper confidence limit) within which analysts are confident that a population parameter lies. A probability is assigned indicating the likelihood that the designed interval contains the true value of the population parameter.

Breaking Down the Confidence Interval Estimate

There are three parts that collectively form an interval estimate:

  1. A confidence level.
  2. A statistic.
  3. A margin of error.

A confidence interval has a lower limit and an upper limit which serve as the bounds of the interval. The level of confidence highlights the uncertainty associated with samples and sampling methods. The precision of an interval estimate depends on the sample statistic and the margin of error. The interval estimate appears as: Sample statistic ± Margin of error.

The Confidence Level

Imagine that you have been tasked to compute an interval estimate with 90% confidence level.  What would be your interpretation of this task?

We could interpret this to mean that if we were to draw multiple samples using the same sampling method and then compute different interval estimates, we would expect 90% of the constructed intervals to contain the true value of the population parameter.

The Margin of Error

The margin of error is the range of values below and above a sample statistic. For example, assume that pollsters have predicted that an independent candidate will receive 25% of votes cast in an election. The survey has a margin of error of 5% at the 95% confidence level. How do you interpret this?

It means we are 95% confident that the independent candidate will receive between 20% and 30% of the votes.

In conclusion, the two concepts are very useful in hypothesis testing and overall statistical analysis.

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