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Related Concept Videos

Critical Values01:31

Critical Values

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A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...
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Confidence Coefficient01:24

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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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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.
A...
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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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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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The α-test: Rapid Cell-free CD4 Enumeration Using Whole Saliva
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An Approximate Confidence Interval for Maximum Coefficient Alpha.

G W Joe, J A Woodward

    Multivariate Behavioral Research
    |January 27, 2016
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    Summary
    This summary is machine-generated.

    This study develops a confidence interval for scale reliability, specifically coefficient alpha, when analyzing sampled individuals from a fixed scale. This aids in understanding the precision of reliability estimates in psychometric research.

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    Area of Science:

    • Psychometrics
    • Statistical modeling
    • Educational measurement

    Background:

    • Coefficient alpha is a widely used measure of internal consistency for scales.
    • Estimating the reliability of a scale is crucial for accurate measurement in various fields.
    • Existing methods for confidence intervals of coefficient alpha may have limitations.

    Purpose of the Study:

    • To develop an approximate confidence interval for the maximum coefficient alpha reliability.
    • To provide a method for assessing the precision of reliability estimates when persons are sampled from a fixed scale.

    Main Methods:

    • Development of an approximate confidence interval formula.
    • Application to scenarios with sampled persons and a fixed scale.

    Main Results:

    • An approximate confidence interval for maximum coefficient alpha reliability was successfully developed.
    • The method provides a way to quantify uncertainty around the reliability estimate.

    Conclusions:

    • The developed confidence interval offers a valuable tool for researchers assessing scale reliability.
    • This method enhances the interpretation of coefficient alpha in psychometric and educational research.