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Related Concept Videos

Types of Hypothesis Testing01:11

Types of Hypothesis Testing

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There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p...
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Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

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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...
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Null and Alternative Hypotheses01:16

Null and Alternative Hypotheses

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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...
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What is a Hypothesis?01:14

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A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about a  property of the population. It can be stated for any field observations or experiments. A hypothesis statement cannot be said to be right or wrong as it is merely a statement. It needs to be tested through an elaborate data collection process and an appropriate statistical test. A hypothesis should be a general but not a vague...
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Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5%...
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Hypothesis: Accept or Fail to Reject?01:17

Hypothesis: Accept or Fail to Reject?

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The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, an appropriate test statistic, an appropriate confidence level, the critical values, and P-values. However, when the evidence suggests that the null hypothesis cannot be rejected, is it right to say, 'Accept' the null hypothesis?
There are two ways to indicate that the null hypothesis is not rejected. 'Accept' the null...
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Setting Limits on Supersymmetry Using Simplified Models
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Hypothesis testing near singularities and boundaries.

Jonathan D Mitchell1, Elizabeth S Allman1, John A Rhodes1

  • 1Department of Mathematics & Statistics, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA.

Electronic Journal of Statistics
|November 9, 2020
PubMed
Summary
This summary is machine-generated.

A new distribution improves hypothesis testing near model boundaries and singularities. This method offers more accurate statistical tests compared to the standard chi-squared (χ²) distribution in these challenging scenarios.

Keywords:
Primary 62E17boundarychi-squaredcoalescenthypothesis testinglikelihood ratio statisticphylogenomicssecondary 92D15singularity

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Area of Science:

  • Statistics
  • Statistical inference
  • Computational statistics

Background:

  • The likelihood ratio statistic is commonly used for hypothesis testing.
  • Its asymptotic chi-squared (χ²) distribution is reliable at regular model points.
  • However, this distribution can be inaccurate near model singularities and boundaries.

Purpose of the Study:

  • To develop a novel distribution for hypothesis testing near model singularities and boundaries.
  • To address the limitations of the standard chi-squared (χ²) distribution in these regions.
  • To provide a more accurate statistical tool for likelihood ratio tests in specific contexts.

Main Methods:

  • Development of a new asymptotic distribution for the likelihood ratio statistic.
  • Asymptotic analysis to ensure agreement with the likelihood ratio statistic.
  • Simulation studies and application to trinomial models in evolutionary tree inference.

Main Results:

  • The proposed distribution accurately reflects the behavior of the likelihood ratio statistic near singularities and boundaries.
  • Simulations demonstrate superior performance compared to the chi-squared (χ²) distribution.
  • The new distribution yields more reliable hypothesis tests in these problematic regions.

Conclusions:

  • The newly developed distribution is a more appropriate tool for hypothesis testing near model singularities and boundaries.
  • It overcomes the limitations of the chi-squared (χ²) distribution in such cases.
  • This advancement has practical implications for statistical inference, particularly in fields like evolutionary biology.