Editing Effect size (section)

=== ''t''-test for mean difference of single group or two related groups ===
For a single group, ''M'' denotes the sample mean, ''μ'' the population mean, ''SD'' the sample's standard deviation, ''σ'' the population's standard deviation, and ''n'' is the sample size of the group. The ''t'' value is used to test the hypothesis on the difference between the mean and a baseline&nbsp;''μ''<sub>baseline</sub>. Usually, ''μ''<sub>baseline</sub> is zero. In the case of two related groups, the single group is constructed by the differences in pair of samples, while ''SD'' and ''σ'' denote the sample's and population's standard deviations of differences rather than within original two groups.
<math display="block">t := \frac{M - \mu_{\text{baseline}}}{\text{SE}} = \frac{M- \mu_{\text{baseline}}}{\text{SD}/\sqrt{n}}=\frac{\sqrt{n} \left( \frac{M-\mu}{\sigma} \right) + \sqrt{n} \left( \frac{\mu-\mu_\text{baseline}}{\sigma}\right) }{\frac{\text{SD}} \sigma}</math>
<math display="block">ncp=\sqrt{n} \left( \frac{\mu-\mu_\text{baseline}}{\sigma} \right) </math>
and Cohen's
<math display="block">d := \frac{M-\mu_\text{baseline}}{\text{SD}}</math>

is the point estimate of
<math display="block">\frac{\mu-\mu_\text{baseline}} \sigma.</math>

So,
:<math>\tilde{d}=\frac{ncp}{\sqrt n}.</math>