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# Confidence Interval Definition

Confidence Interval Definition

A confidence interval shows a range of values within which an unknown population parameter lies. Loosely speaking, it shows the confidence that one has that a given population parameter lies within a given range. For instance, one can say, “I am confident that 95 percent confident that between 45 and 56 percent of Americans love cooking their food more than eating out.”

A Little More on What is a Confidence Interval

A confidence interval does not show the true value of a population parameter but a range of values within which the true value lies. If, for instance, a student wants to find the percentage of Americans who love hockey, a random sample will be taken and the participants asked whether they love hockey. Since the sample is random, the CI constructed from the data will be random.

The most common CI is 95 percent but others, such as 99 and 90 percent are used. The higher the CI, the broader the range of values and the lower the CI, the narrower the range of values. When constructing CI range, one should consider the size of the sample they choose and the variability of the sample and the CI chosen.

The introduction of CI into statistics in 1937 is credited to Jerzy Neyman.

Conceptual basis

Interval estimation is not the same as point estimation. While a point estimate is an estimate of a population parameter of interest, for instance, the mean of a given quantity, interval estimate specifies a range within which a population parameter is estimated to lie. CI is usually reported in graphs or tables together with point estimates to show the reliability of the estimates.

For instance, a confidence interval is useful in determining the reliability of survey results. Consider election-voting intentions where 40 percent of the respondents want to vote for a certain party. Using a 99 percent confidence interval for the whole population, the results may be between 30 and 50 percent. If the same data is used with a 90 percent confidence interval, the results may be between 37 and 43 percent. The size of the used sample determines the length of the CI.

Meaning and interpretation

There are different interpretations of confidence interval taking an example of 90 percent CI.

•         CI is expressed as samples or repeated samples. If this procedure was to be reused on different samples, fraction of calculated CI that shows the true population parameter tends towards 90 percent.
•         CI is expressed as a single sample. In this case, there is a 90 percent probability that calculated CI as from future experiment shows the true value of an unknown population parameter. This statement is more about probability than confidence interval. The statement considers the probability associated with CI.
•         The CI can also be said to represent values of population parameter in which the difference between the observed estimate and the parameter is not significant statistically at 10 percent level.

For each of the above, if the true value of the parameter falls outside the 90 percent CI, it shows that there is a sampling event has happened, which in this case is a point estimate, and which had a probability of 10 percent or less of happening.