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Symbol used in drawings Standard penetration test N values from a surficial aquifer in south Florida. The standard penetration test (SPT) is an in-situ dynamic penetration test designed to provide information on the geotechnical engineering properties of soil. This test is the most frequently used subsurface exploration drilling test performed ...
Since the square root introduces bias, the terminology "uncorrected" and "corrected" is preferred for the standard deviation estimators: s n is the uncorrected sample standard deviation (i.e., without Bessel's correction) s is the corrected sample standard deviation (i.e., with Bessel's correction), which is less biased, but still biased
This reduces the chi-squared value obtained and thus increases its p-value. The effect of Yates's correction is to prevent overestimation of statistical significance for small data. This formula is chiefly used when at least one cell of the table has an expected count smaller than 5. = =
n}. If np and np(1 − p) are large (sometimes taken as both ≥ 5), then the probability above is fairly well approximated by (+ /) where Y is a normally distributed random variable with the same expected value and the same variance as X, i.e., E(Y) = np and var(Y) = np(1 − p).
The Bonferroni correction can also be applied as a p-value adjustment: Using that approach, instead of adjusting the alpha level, each p-value is multiplied by the number of tests (with adjusted p-values that exceed 1 then being reduced to 1), and the alpha level is left unchanged.
Correction factor versus sample size n.. When the random variable is normally distributed, a minor correction exists to eliminate the bias.To derive the correction, note that for normally distributed X, Cochran's theorem implies that () / has a chi square distribution with degrees of freedom and thus its square root, / has a chi distribution with degrees of freedom.
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For example, for = 0.05 and m = 10, the Bonferroni-adjusted level is 0.005 and the Šidák-adjusted level is approximately 0.005116. One can also compute confidence intervals matching the test decision using the Šidák correction by computing each confidence interval at the (1 − α) 1/m % level.