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The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H 1, H 2, ..., H m. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant.
Even if a study meets the benchmark requirements for and , and is free of bias, there is still a 36% probability that a paper reporting a positive result will be incorrect; if the base probability of a true result is lower, then this will push the PPV lower too. Furthermore, there is strong evidence that the average statistical power of a study ...
This should result in 5% of hypotheses that are supported being false positives (an incorrect hypothesis being erroneously found correct), assuming the studies meet all of the statistical assumptions. Some fields use smaller p-values, such as p < 0.01 (1% chance of a false positive) or p < 0.001 (0.1% chance of a false positive).
The former report is adequate, the latter gives a more detailed explanation of the data and the reason why the suitcase is being checked. Not rejecting the null hypothesis does not mean the null hypothesis is "accepted" per se (though Neyman and Pearson used that word in their original writings; see the Interpretation section).
More formally, the LPM can arise from a latent-variable formulation (usually to be found in the econometrics literature [2]), as follows: assume the following regression model with a latent (unobservable) dependent variable:
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If the resulting p-value of Levene's test is less than some significance level (typically 0.05), the obtained differences in sample variances are unlikely to have occurred based on random sampling from a population with equal variances. Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference ...
As you know, actual events and results can differ materially from these forward-looking statements, and the company does not undertake a duty to update any forward-looking statements. With that, I ...