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Related Concept Videos

Interpretation of Confidence Intervals01:19

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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A Bootstrap Confidence Interval Based on a Correlation Corrected for Range Restriction.

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    Summary
    This summary is machine-generated.

    Bootstrapping the corrected correlation coefficient provides accurate confidence intervals for population correlation (rho). Sample size is crucial for interval accuracy and stability, especially with smaller rho values.

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    Area of Science:

    • Statistics
    • Psychometrics
    • Quantitative Psychology

    Background:

    • Range restriction attenuates correlation coefficients.
    • Accurate estimation of population correlation (rho) is essential.
    • Bootstrapping offers a method for confidence interval estimation.

    Purpose of the Study:

    • To evaluate the accuracy and stability of bootstrap confidence intervals for the corrected correlation coefficient.
    • To assess the influence of population correlation (rho) size and data distribution on interval performance.
    • To determine the impact of sample size on the reliability of the bootstrapping technique.

    Main Methods:

    • Computer simulations were used to test the bootstrapping method.
    • The corrected correlation coefficient was bootstrapped across various rho values and distributions (normal, mixed, skewed).
    • Confidence interval accuracy and stability were analyzed based on simulation outcomes.

    Main Results:

    • Bootstrap confidence intervals for the corrected correlation coefficient were accurate across all tested distributions.
    • The magnitude of rho generally did not impact interval accuracy but affected stability.
    • Small rho values and small sample sizes led to erratic interval behavior.
    • Sample size emerged as the most critical factor for both accuracy and stability.

    Conclusions:

    • Bootstrapping the corrected correlation coefficient is a reliable method for estimating confidence intervals for population correlation (rho).
    • The technique is particularly effective for moderate to large sample sizes (n > 50).
    • Researchers can confidently use this method to obtain robust estimates of population correlation, even with range restriction.