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In a significance test, the null hypothesis is rejected if the p-value is less than or equal to a predefined threshold value , which is referred to as the alpha level or significance level. α {\displaystyle \alpha } is not derived from the data, but rather is set by the researcher before examining the data.
[15] [16] But if the p-value of an observed effect is less than (or equal to) the significance level, an investigator may conclude that the effect reflects the characteristics of the whole population, [1] thereby rejecting the null hypothesis. [17] This technique for testing the statistical significance of results was developed in the early ...
It is less stringent than the Bonferroni correction, but only slightly. For example, for α {\displaystyle \alpha } = 0.05 and m = 10, the Bonferroni-adjusted level is 0.005 and the Šidák-adjusted level is approximately 0.005116.
The Shapiro–Wilk test tests the null hypothesis that a sample x 1, ..., x n came from a normally distributed population. The test statistic is = (= ()) = (¯), where with parentheses enclosing the subscript index i is the ith order statistic, i.e., the ith-smallest number in the sample (not to be confused with ).
The concentrations of nickel, copper, and zinc were less than 0.005, less than 0.04, and less than 0.02 milligrams per liter in the upper reaches and the lower reaches. The arsenic, cadmium, and lead concentrations were less than 0.005, less than 0.001, and less than 0.01 milligrams per liter both reaches. [2]
In normalized notation, the exponent is chosen so that the absolute value (modulus) of the significand m is at least 1 but less than 10. Decimal floating point is a computer arithmetic system closely related to scientific notation.
If the n + 1 digit is greater than 5 or is 5 followed by other non-zero digits, add 1 to the n digit. For example, if we want to round 1.2459 to 3 significant figures, then this step results in 1.25. If the n + 1 digit is 5 not followed by other digits or followed by only zeros, then rounding requires a tie-breaking rule. For example, to round ...
The probability of having numbers larger than 16 is p =0.0029, of having numbers larger than 15 is p =0.0094, and of having numbers larger than 14 is p =0.0246. For a random distribution, this means that numbers larger than 14 correspond to 2 σ deviations and numbers larger than 16 correspond to 3 σ deviations.