Statistics formula — definition, units and applicable conditions

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Statistics

unbiased sample variance

s^2=\frac1{n-1}\sum_{i=1}^n(x_i-\bar x)^2

estimates the population variance corrected with degrees of freedom.

Statistics

\bar x\pm t_{1-\alpha/2,n-1}\frac{s}{\sqrt n}

expresses the coverage of the population mean by a repeated sampling procedure.

Statistics

r=\frac{\sum_i(x_i-\bar x)(y_i-\bar y)}{\sqrt{\sum_i(x_i-\bar x)^2\sum_i(y_i-\bar y)^2}}

measures the linear association between two sets of paired data.

Statistics

\chi^2=\sum_i\frac{(O_i-E_i)^2}{E_i}

compares the observed frequency of a category with the model expected frequency.