interval estimate

(noun)

A range of values used to estimate a population parameter.

Related Terms

Examples of interval estimate in the following topics:

  • Estimating the Target Parameter: Interval Estimation

    • Interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter.
    • Interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter.
    • The most prevalent forms of interval estimation are:
    • We need to estimate from the data in order to do this.
    • The method for calculating a confidence interval assumes that individual observations are independent.

  • Introduction to Estimation

    • This value of 0.53 is called a point estimate of the population proportion.
    • It is called a point estimate because the estimate consists of a single value or point.
    • Point estimates are usually supplemented by interval estimates called confidence intervals.
    • Confidence intervals are intervals constructed using a method that contains the population parameter a specified proportion of the time.
    • You will see how to compute this kind of interval in another section.

  • Introduction to confidence intervals

    • A point estimate provides a single plausible value for a parameter.
    • However, a point estimate is rarely perfect; usually there is some error in the estimate.
    • Instead of supplying just a point estimate of a parameter, a next logical step would be to provide a plausible range of values for the parameter.
    • In Section 4.5, we generalize these methods for a variety of point estimates and population parameters that we will encounter in Chapter 5 and beyond.
    • This video introduces confidence intervals for point estimates, which are intervals that describe a plausible range for a population parameter.

  • What Is a Confidence Interval?

    • A confidence interval is a type of interval estimate of a population parameter and is used to indicate the reliability of an estimate.
    • After calculating point estimates, we construct confidence intervals in which we believe the parameter lies.
    • A confidence interval is a type of estimate (like a sample average or sample standard deviation), in the form of an interval of numbers, rather than only one number.
    • It is an observed interval (i.e., it is calculated from the observations), used to indicate the reliability of an estimate.
    • The interval of numbers is an estimated range of values calculated from a given set of sample data.

  • Variation and Prediction Intervals

    • A prediction interval is an estimate of an interval in which future observations will fall with a certain probability given what has already been observed.
    • In predictive inference, a prediction interval is an estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed.
    • Prediction intervals predict the distribution of individual future points, whereas confidence intervals and credible intervals of parameters predict the distribution of estimates of the true population mean or other quantity of interest that cannot be observed.
    • Prediction intervals are also present in forecasts; however, some experts have shown that it is difficult to estimate the prediction intervals of forecasts that have contrary series.
    • Then, confidence intervals and credible intervals may be used to estimate the population mean $\mu$ and population standard deviation $\sigma$ of the underlying population, while prediction intervals may be used to estimate the value of the next sample variable, $X_{n+1}$.

  • Interpreting confidence intervals

    • A careful eye might have observed the somewhat awkward language used to describe confidence intervals.
    • Incorrect language might try to describe the confidence interval as capturing the population parameter with a certain probability.
    • Another especially important consideration of confidence intervals is that they only try to capture the population parameter.
    • Our intervals say nothing about the confidence of capturing individual observations, a proportion of the observations, or about capturing point estimates.
    • Confidence intervals only attempt to capture population parameters.

  • Non-normal point estimates

    • We may apply the ideas of confidence intervals and hypothesis testing to cases where the point estimate or test statistic is not necessarily normal.
    • The point estimate tends towards some distribution that is not the normal distribution.
    • For each case where the normal approximation is not valid, our first task is always to understand and characterize the sampling distribution of the point estimate or test statistic.
    • Next, we can apply the general frameworks for confidence intervals and hypothesis testing to these alternative distributions.

  • Level of Confidence

    • The proportion of confidence intervals that contain the true value of a parameter will match the confidence level.
    • If confidence intervals are constructed across many separate data analyses of repeated (and possibly different) experiments, the proportion of such intervals that contain the true value of the parameter will match the confidence level.
    • This is guaranteed by the reasoning underlying the construction of confidence intervals.
    • Confidence intervals consist of a range of values (interval) that act as good estimates of the unknown population parameter .
    • In applied practice, confidence intervals are typically stated at the 95% confidence level.

  • Introduction to Confidence Intervals

    • State why a confidence interval is not the probability the interval contains the parameter
    • This sample mean of 90 is a point estimate of the population mean.
    • A point estimate by itself is of limited usefulness because it does not reveal the uncertainty associated with the estimate; you do not have a good sense of how far this sample mean may be from the population mean.
    • Confidence intervals provide more information than point estimates.
    • Although the various methods are equal from a purely mathematical point of view, the standard method of computing confidence intervals has two desirable properties: each interval is symmetric about the point estimate and each interval is contiguous.

  • Summary of Formulas

    • ( lower value,upper value ) = ( point estimate − error bound,point estimate + error bound )
    • Formula 8.2: To find the error bound when you know the confidence interval
    • error bound = upper value − point estimate OR error bound = (upper value − lower value)/2
    • The confidence interval has the format ($\bar{x}$ − EBM, $\bar{x}$ + EBM) .
    • The confidence interval has the format (p' − EBP, p' + EBP) .