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Some statisticians have proposed abandoning p-values and focusing more on other inferential statistics, [3] such as confidence intervals, [17] [18] likelihood ratios, [19] [20] or Bayes factors, [21] [22] [23] but there is heated debate on the feasibility of these alternatives.
The p-value was introduced by Karl Pearson [6] in the Pearson's chi-squared test, where he defined P (original notation) as the probability that the statistic would be at or above a given level. This is a one-tailed definition, and the chi-squared distribution is asymmetric, only assuming positive or zero values, and has only one tail, the ...
The confidence interval summarizes a range of likely values of the underlying population effect. Proponents of estimation see reporting a P value as an unhelpful distraction from the important business of reporting an effect size with its confidence intervals, [7] and believe that estimation should replace significance testing for data analysis ...
Critics of significance testing have advocated basing inference less on p-values and more on confidence intervals for effect sizes for importance, prediction intervals for confidence, replications and extensions for replicability, meta-analyses for generality :. [88] But none of these suggested alternatives inherently produces a decision.
The confidence interval can be expressed in terms of probability with respect to a single theoretical (yet to be realized) sample: "There is a 95% probability that the 95% confidence interval calculated from a given future sample will cover the true value of the population parameter."
The procedure proposed by Dunn [2] can be used to adjust confidence intervals. If one establishes m {\displaystyle m} confidence intervals, and wishes to have an overall confidence level of 1 − α {\displaystyle 1-\alpha } , each individual confidence interval can be adjusted to the level of 1 − α m {\displaystyle 1-{\frac {\alpha }{m}}} .
For example, if z = 2.2 is observed and a two-sided p-value is desired to test the null hypothesis that =, the p-value is 2 Φ(−2.2) = 0.028, where Φ is the standard normal cumulative distribution function. To obtain a confidence interval for ρ, we first compute a confidence interval for F():
In statistics, the Šidák ... is a method used to counteract the problem of multiple comparisons. ... p-values, or confidence intervals. Usage