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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. Typical ...
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4]
This approximate formula is for moderate to large sample sizes; the reference gives the exact formulas for any sample size, and can be applied to heavily autocorrelated time series like Wall Street stock quotes. Moreover, this formula works for positive and negative ρ alike. [12] See also unbiased estimation of standard deviation for more ...
It can be used in calculating the sample size for a future study. When measuring differences between proportions, Cohen's h can be used in conjunction with hypothesis testing . A " statistically significant " difference between two proportions is understood to mean that, given the data, it is likely that there is a difference in the population ...
For a confidence level, there is a corresponding confidence interval about the mean , that is, the interval [, +] within which values of should fall with probability . ...
N = the sample size The resulting value can be compared with a chi-square distribution to determine the goodness of fit. The chi-square distribution has ( k − c ) degrees of freedom , where k is the number of non-empty bins and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the ...
where N is the population size, n is the sample size, m x is the mean of the x variate and s x 2 and s y 2 are the sample variances of the x and y variates respectively. These versions differ only in the factor in the denominator (N - 1). For a large N the difference is negligible.
I edited the top parts of this page to make it more parallel to the t-test page, which defines a t-test as being any test for which the test statistic follows a t-distribution (rather than just covering the one-sample and two-sample t-tests). Nevertheless, I agree that the one-sample/two-sample tests need to be covered in detail.