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Null and Alternative Hypotheses

Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.
The null hypothesis, denoted by H0 is a statement of no difference between the variables—they are not related. This can often be considered the status quo. As a result if you cannot accept the null, it requires some action.
The alternative hypothesis, denoted by H1 or Ha, is a claim about the...

Hypothesis Test for Test of Independence

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 Homogeneity

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...

One-Way ANOVA: Unequal Sample Sizes

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:

Bonferroni Test

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...

Errors In Hypothesis Tests

Errors In Hypothesis Tests

When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.

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Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities

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Adaptive bootstrap tests for composite null hypotheses in the mediation pathway analysis.

Yinqiu He¹, Peter X K Song², Gongjun Xu³

¹Department of Statistics, University of Wisconsin, Madison, WI, USA.

Journal of the Royal Statistical Society. Series B, Statistical Methodology

|May 15, 2024

Summary

This summary is machine-generated.

We developed a new adaptive bootstrap framework to improve mediation analysis. This method enhances statistical power for testing mediation effects (ME) by addressing challenges posed by composite null hypotheses.

Keywords:

bootstrap composite hypothesis mediation analysis structural equation model

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Area of Science:

Statistics
Biostatistics
Epidemiology

Background:

Mediation analysis investigates how exposures influence outcomes via intermediate variables.
Current mediation effect (ME) testing faces challenges due to composite null hypotheses, leading to conservative and underpowered tests.
There is a growing need for robust mediation analysis across scientific disciplines.

Purpose of the Study:

To develop an adaptive bootstrap testing framework for mediation pathway analysis.
To enhance statistical power and provide type I error control under composite null hypotheses.
To address limitations of existing methods in mediation effect testing.

Main Methods:

An adaptive bootstrap testing framework was developed.
The framework accommodates various composite null hypotheses in mediation analysis.
Applied to product of coefficients and joint significance tests.

Main Results:

The proposed adaptive testing procedures offer improved type I error control.
The methodology significantly enhances statistical power compared to existing mediation tests.
Theoretical properties and numerical examples demonstrate the framework's effectiveness.

Conclusions:

The adaptive bootstrap framework offers a powerful solution for mediation analysis.
This approach improves the reliability and power of testing mediation effects.
The methodology is broadly applicable to various mediation pathway analyses.