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Related Concept Videos

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)...
Test for Homogeneity01:23

Test for Homogeneity

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...
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:
Correlation of Experimental Data01:23

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...
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...
McNemar's Test01:23

McNemar's Test

McNemar's Test is a nonparametric statistical test used to determine if there is a significant difference in proportions between two related groups when the outcome is binary (e.g., yes/no, success/failure). It is beneficial when we have paired data, such as pre-test/post-test designs, where the same subjects are measured under two different conditions. The test is named after the statistician Quinn McNemar, who introduced it in 1947. It is commonly used in situations where subjects are...

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Basics of Multivariate Analysis in Neuroimaging Data
06:35

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Published on: July 24, 2010

A test of location for exchangeable multivariate normal data with unknown correlation.

Dean Follmann1, Michael Proschan

  • 1Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, 6700B Rockledge Drive MSC 7609, Bethesda, MD 20892.

Journal of Multivariate Analysis
|November 30, 2011
PubMed
Summary
This summary is machine-generated.

This study addresses testing the common mean of multivariate normal data with unknown correlation. New methods are proposed to control type I error rates, offering robust solutions for statistical inference.

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Area of Science:

  • Statistics
  • Statistical Inference
  • Multivariate Analysis

Background:

  • Testing the common mean in multivariate normal distributions is crucial.
  • Unknown common correlation (ρ) presents challenges in statistical testing.
  • Existing methods may exhibit pathological behavior with certain correlation structures.

Purpose of the Study:

  • To develop robust statistical tests for the common mean of multivariate normal variables with unknown correlation.
  • To control Type I error rates under various correlation scenarios.
  • To provide reliable methods for applications like within-cluster resampling and combining p-values.

Main Methods:

  • Derivation of the standardized likelihood ratio test for known and unknown correlation.
  • Evaluation of performance by replacing unknown correlation with estimates.
  • Determination of critical values to control Type I error rates for the least favorable correlation.
  • Development of an alternate approach using confidence intervals for correlation.
  • Investigation of a simpler bound method for Type I error rate control.

Main Results:

  • A critical value c(n) is determined to control Type I error rates, which increases with n.
  • Pathological behavior observed when correlation depends on sample size and converges to zero.
  • An alternate method using confidence intervals provides exact Type I error control and performs well across sample sizes.
  • A simpler bound method offers less power but may be useful in specific contexts.

Conclusions:

  • The proposed confidence interval method offers a robust and well-performing approach for testing common means with unknown correlation.
  • The simpler bound method provides a practical alternative when exact control is not paramount.
  • These statistical tests have potential applications in diverse fields, enhancing data analysis techniques.