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The statements "is an e-variable" and "if the null hypothesis is true, you do not expect to gain any money if you engage in this bet" are logically equivalent. This is because E {\displaystyle E} being an e-variable means that the expected gain of buying the ticket is the pay-off minus the cost, i.e. E − 1 {\displaystyle E-1} , which has ...
Since the probabilities must satisfy p 1 + ⋅⋅⋅ + p k = 1, it is natural to interpret E[X] as a weighted average of the x i values, with weights given by their probabilities p i. In the special case that all possible outcomes are equiprobable (that is, p 1 = ⋅⋅⋅ = p k), the weighted average is given by the standard average. In the ...
Comparison of the various grading methods in a normal distribution, including: standard deviations, cumulative percentages, percentile equivalents, z-scores, T-scores. In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured.
The goal of a forecaster is to maximize the score and for the score to be as large as possible, and −0.22 is indeed larger than −1.6. If one treats the truth or falsity of the prediction as a variable x with value 1 or 0 respectively, and the expressed probability as p , then one can write the logarithmic scoring rule as x ln( p ) + (1 − ...
A number of researchers have explored HADS data to establish the cut-off points for caseness of anxiety or depression. Bjelland et al (2002) [3] through a literature review of a large number of studies identified a cut-off point of 8/21 for anxiety or depression.
A number in the 0–9 range is considered to be normal while a number in the 10–24 range indicates that expert medical advice should be sought. [3] For instance, scores of 11–15 are shown to indicate the possibility of mild to moderate sleep apnea, where a score of 16 and above indicates the possibility of severe sleep apnea or narcolepsy. [3]
The interpretation of a p-value is dependent upon stopping rule and definition of multiple comparison. The former often changes during the course of a study and the latter is unavoidably ambiguous. (i.e. "p values depend on both the (data) observed and on the other possible (data) that might have been observed but weren't"). [69]
Performance indicators differ from business drivers and aims (or goals). A school might consider the failure rate of its students as a key performance indicator which might help the school understand its position in the educational community, whereas a business might consider the percentage of income from returning customers as a potential KPI.