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Related Concept Videos

Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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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.
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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Uncertainty: Confidence Intervals00:54

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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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Confidence Intervals01:21

Confidence Intervals

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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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Confidence Coefficient01:24

Confidence Coefficient

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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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Finding Critical Values for Chi-Square01:18

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Consider a curve representing sample data drawn randomly from a normally distributed population. One must construct confidence intervals to estimate or to test a claim regarding the population standard deviation. For example, a 95% confidence interval covers 95% of the area under the curve, and the remaining 5% is equally distributed on either side of the curve. To achieve such confidence intervals, one must determine the critical values. The critical values are simply the values separating the...
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Critical Region, Critical Values and Significance Level01:16

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The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in  probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the...
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Informative simultaneous confidence intervals for graphical test procedures.

Werner Brannath1, Liane Kluge1, Martin Scharpenberg1

  • 1Competence Center for Clinical Trials Bremen, University of Bremen, Bremen, Germany.

Statistical Methods in Medical Research
|November 14, 2025
PubMed
Summary
This summary is machine-generated.

New simultaneous confidence intervals offer informative results for graphical testing procedures. These intervals provide a balance between gaining information and rejecting hypotheses, enhancing statistical analysis.

Keywords:
Simultaneous confidence intervalsgraphical testing procedureinformative confidence intervals

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Area of Science:

  • Statistics
  • Statistical inference
  • Multiple hypothesis testing

Background:

  • Traditional simultaneous confidence intervals (SCIs) compatible with closed test procedures can be uninformative.
  • The bounds of these SCIs may remain at the null hypothesis boundary, regardless of the point estimate's deviation.
  • This limitation has been observed for Bonferroni-Holm and fall-back procedures.

Purpose of the Study:

  • To extend the concept of informative simultaneous confidence intervals to graphical test procedures.
  • To develop SCIs that are more informative than traditional ones while maintaining strong family-wise error rate control.
  • To offer a practical alternative to existing multiple testing methods.

Main Methods:

  • Definition of SCIs using a family of dual graphs.
  • Application of the projection method for interval construction.
  • Development of a simple iterative algorithm for computing the proposed SCIs.

Main Results:

  • The newly suggested SCIs are free from the deficiency of traditional SCIs.
  • Information gained from these SCIs increases with evidence against the null hypothesis.
  • A simulation study demonstrated the effectiveness for a complex graphical test procedure.

Conclusions:

  • The proposed informative SCIs offer a valuable compromise between information gain and power in multiple hypothesis testing.
  • These intervals can serve as a replacement for initial multiple tests, providing strong family-wise error rate control.
  • The method is applicable to graphical test procedures, enhancing their interpretability and utility.