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A Direct Method for Obtaining Approximate Standard Error and Confidence Interval of Maximal Reliability for

Tenko Raykov, Spiridon Penev

    Multivariate Behavioral Research
    |January 21, 2016
    PubMed

    Related Concept Videos

    Estimating Population Mean with Known Standard Deviation01:16

    Estimating Population Mean with Known Standard Deviation

    To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
    The confidence interval estimate will have the form as follows:
    (point estimate - error bound, point estimate +...
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    Interpretation of Confidence Intervals01:19

    Interpretation of Confidence Intervals

    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.
    Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
    Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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    Confidence Interval for Estimating Population Mean01:25

    Confidence Interval for Estimating Population Mean

    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.
    A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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    Uncertainty: Confidence Intervals00:54

    Uncertainty: Confidence Intervals

    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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    Estimating Population Mean with Unknown Standard Deviation01:22

    Estimating Population Mean with Unknown Standard Deviation

    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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    Confidence Intervals01:21

    Confidence Intervals

    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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