Understanding Statistical Significance: Explaining the 0.05 Level

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Discussion Overview

The discussion revolves around the interpretation of statistical significance at the 0.05 level, particularly in relation to the null hypothesis and the implications of rejecting it. Participants explore the nuances of probability in this context, addressing both theoretical and conceptual aspects.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant states that being "statistically significant at the 0.05 level" refers to the probability of rejecting a true null hypothesis, rather than the probability of the null hypothesis itself being true.
  • Another participant argues that the probability of the null hypothesis being true can vary based on individual knowledge, suggesting that it cannot be definitively assigned a value like 20% or 50% without context.
  • A further contribution attempts to clarify the relationship between type I error and the probability of the null hypothesis being true, proposing a conditional probability framework.
  • One participant questions whether the original post is a homework question, implying that the context of the discussion may affect its appropriateness.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of statistical significance and the implications for the null hypothesis. There is no consensus on the correct explanation, and the discussion remains unresolved.

Contextual Notes

Participants highlight the dependence of probability assessments on individual knowledge and the subtleties in the definitions of statistical terms, which may lead to varying interpretations.

jlo2006
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Heres the problem:

When asked to explain the meaning of "statistically significant at the 0.05 level," a student says, "This means there is only probability 0.05 that the null hypothesis is true." Is this an essentially correct explanation of statistical significance? Explain.


Help please. Appreciated.
 
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More specifically, it is the probability that you reject a true null hypothesis.

The difference in the statements is subtle.

The probability of the null hypothesis being true may be 20%, 50%, etc. -- but the probability of rejecting it is .05.
 
Well, you can't say anything about the probability of the null hypothesis being 20% or 50% right off the bat because probability is based on the amount of knowledge you have. For one person the probability of the null hypothesis being true might be 20% and for another person with more knowledge the probability of the same hypothesis being true might be 1.

But if the probability of a type I error is the probability that the null hypothesis is true and you reject it, then let A = the null hypothesis is true and let B = you reject the null hypothesis.
Then P(A n B) is the probability of a type I error, and P(A n B) = .05
But you know that P(B) = 1 since the test was significant. So P(A n B) = P(A) = .05 and the probability that the null hypothesis is true is .05.
 
Is this homework? If it is, it is not supposed to have been posted here. If it is not HW, why did you post it under HW help?
 

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