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Related Concept Videos

Introduction to Test of Independence01:21

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
Comparing Experimental Results: Student's t-Test01:09

Comparing Experimental Results: Student's t-Test

The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the...
Bonferroni Test01:10

Bonferroni Test

The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...

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Related Experiment Video

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Advancing Dyslexia Assessment in Children Through Computerized Testing
09:00

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Published on: August 16, 2024

Asymptotic online FWER control for dependent test statistics.

Vincent Jankovic1, Lasse Fischer1, Werner Brannath1

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

Statistical Methods in Medical Research
|July 2, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for online multiple testing, enabling robust error rate control irrespective of data dependencies. The developed procedures maintain statistical power while ensuring familywise error rate control in sequential hypothesis testing.

Keywords:
asymptoticsdependent test statisticsfamilywise error rateonline multiple testingplatform trials

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Area of Science:

  • Statistics
  • Statistical Inference
  • Hypothesis Testing

Background:

  • Online multiple testing involves sequential decisions on hypotheses with limited data.
  • Existing methods often require independence or local dependence of test statistics.
  • A need exists for flexible procedures adaptable to unknown dependence structures.

Purpose of the Study:

  • To develop a novel framework for online multiple testing procedures.
  • To ensure asymptotic control of the familywise error rate (FWER).
  • To accommodate arbitrary dependence structures among test statistics.

Main Methods:

  • A new theoretical framework for deriving online multiple test procedures.
  • Development of concrete test procedure examples within the framework.
  • Asymptotic analysis of the familywise error rate control.

Main Results:

  • The proposed framework guarantees asymptotic FWER control for any dependence structure.
  • Simulation studies confirm type I error control for finite sample sizes.
  • Indication of improved statistical power compared to existing methods.

Conclusions:

  • The new framework offers a powerful and flexible approach to online multiple testing.
  • Procedures derived from this framework are robust to complex data dependencies.
  • This work advances the field by providing adaptable tools for sequential hypothesis testing.