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Difference between Z-test and t-test: Z-test is used when sample size is large (n>50), or the population variance is known. t-test is used when sample size is small (n<50) and population variance is unknown. There is no universal constant at which the sample size is generally considered large enough to justify use of the plug-in test.
Z tables use at least three different conventions: Cumulative from mean gives a probability that a statistic is between 0 (mean) and Z. Example: Prob(0 ≤ Z ≤ 0.69) = 0.2549. Cumulative gives a probability that a statistic is less than Z. This equates to the area of the distribution below Z. Example: Prob(Z ≤ 0.69) = 0.7549. Complementary ...
The Z-factor defines a characteristic parameter of the capability of hit identification for each given assay. The following categorization of HTS assay quality by the value of the Z-Factor is a modification of Table 1 shown in Zhang et al. (1999); [2] note that the Z-factor cannot exceed one.
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 formula given for 'Z' here is: Z = [ (x-μ)/σ ] Where: x is the raw score (the sample mean being tested) μ is the mean of the population; σ is the standard deviation of the population; s is the standard deviation of the sample; But, isn't that incorrect? The actual formula is the following: Z = [ (x-μ) / [σ/SqareRoot(N, the sample-size) ]
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If Z is a standard normal random variable, and V is a chi-squared distributed random variable with ν degrees of freedom that is independent of Z, then = + / is a noncentral t-distributed random variable with ν degrees of freedom and noncentrality parameter μ ≠ 0. Note that the noncentrality parameter may be negative.
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