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Related Concept Videos

Types of Hypothesis Testing01:11

Types of Hypothesis Testing

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 ≠ 0.5.
Null and Alternative Hypotheses01:16

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 population that is...
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...
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...
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance, comparing...
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...

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Related Experiment Video

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A Two-interval Forced-choice Task for Multisensory Comparisons
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A Two-interval Forced-choice Task for Multisensory Comparisons

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Bayesian hypothesis testing in two-arm trials with dichotomous outcomes.

Boris G Zaslavsky1

  • 1FDA, CBER HFM-219, 1401 Rockville Pike, Rockville, Maryland 20852-1448, USA. Boris.Zaslavsky@FDA.HHS.gov

Biometrics
|September 26, 2012
PubMed
Summary

This study compares Bayesian and frequentist statistical methods for superiority and noninferiority tests. Bayesian posterior probabilities can mimic frequentist p-values with adjusted parameters, offering flexibility in hypothesis testing.

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Area of Science:

  • Statistics
  • Biostatistics
  • Hypothesis Testing

Background:

  • Comparing Bayesian and frequentist statistical inference is crucial for robust data analysis.
  • One-sided superiority and noninferiority tests are common in clinical trials and research.

Purpose of the Study:

  • To investigate Bayesian one-sided superiority and noninferiority tests.
  • To compare Bayesian inferences with frequentist approaches using the binomial distribution.
  • To explore the relationship between posterior probabilities and frequentist p-values.

Main Methods:

  • Utilized Bayesian tests for one-sided superiority and noninferiority.
  • Employed conjugate beta priors with integer parameters for the binomial distribution.
  • Transformed posterior probabilities into frequentist probabilities of Bernoulli trials with adjusted parameters.

Main Results:

  • Bayesian posterior probabilities were expressed using credible limits.
  • The transformation allowed a direct comparison with frequentist Bernoulli trial probabilities.
  • Posterior probabilities could be made smaller or larger than frequentist p-values by selecting appropriate prior parameters.

Conclusions:

  • Bayesian methods, specifically with conjugate priors, can be adapted to resemble frequentist test formulations.
  • The choice of prior parameters in Bayesian testing offers flexibility in influencing the outcome relative to frequentist p-values.
  • This approach provides a bridge between Bayesian and frequentist statistical inference for specific hypothesis testing scenarios.