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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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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.
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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:
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Accuracy and Errors in Hypothesis Testing01:13

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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.
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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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The actual hypothesis testing begins by considering two hypotheses. They are termed  the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.
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The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm
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Privacy-Aware Distributed Hypothesis Testing.

Sreejith Sreekumar1, Asaf Cohen2, Deniz Gündüz3

  • 1Department of Electrical and Computer Engineering , Cornell University, Ithaca, NY 14850, USA.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary

This study examines distributed binary hypothesis testing with privacy constraints. We establish trade-offs between communication rate, error exponent, and privacy measures like equivocation and distortion.

Keywords:
Hypothesis testingcausal disclosuredistortionequivocationerror exponentprivacytesting against conditional independence

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Area of Science:

  • Information Theory
  • Distributed Systems
  • Signal Processing

Background:

  • Distributed binary hypothesis testing (HT) involves a remote observer and a detector.
  • The observer communicates via a rate-limited channel, aiming to maximize the type II error exponent under a type I error constraint.
  • Privacy is a key concern, measured by equivocation and average distortion.

Purpose of the Study:

  • To analyze the trade-off between communication rate, type II error exponent, and privacy in distributed binary hypothesis testing.
  • To establish bounds and characterizations for these trade-offs under various conditions.
  • To investigate the impact of privacy constraints on the strong converse property.

Main Methods:

  • Derivation of single-letter inner bounds for rate-error exponent-equivocation and rate-error exponent-distortion trade-offs.
  • Characterization of these trade-offs for specific cases, including testing against conditional independence and zero communication rate.
  • Development of a counter-example to demonstrate the impact of privacy on the strong converse.

Main Results:

  • Established single-letter inner bounds for the general distributed HT problem with privacy.
  • Obtained single-letter characterizations for specific scenarios, offering precise trade-off analyses.
  • Demonstrated that privacy constraints can invalidate the strong converse property.

Conclusions:

  • The study quantifies the fundamental trade-offs between performance (error exponent) and privacy in distributed hypothesis testing.
  • Privacy constraints significantly alter the theoretical limits and properties of distributed detection systems.
  • Future research may explore optimal strategies for balancing detection accuracy and data privacy.