# Significance Tests on Trend Plots

${\displaystyle e_{a+b}^{2}={\frac {[n_{a}(n_{a}-1)e_{a}^{2}+n_{b}(n_{b}-1)e_{b}^{2}+(n_{a}n_{b})/(n_{a}+n_{b})(m_{a}-m_{b})^{2}]}{(n_{a}+n_{b})(n_{a}+n_{b}-1)}}}$
where ${\displaystyle n_{a}}$ is the effective sample size of the first group, ${\displaystyle e_{a}^{2}}$ is the squared standard error of the first group, ${\displaystyle m_{a}}$ is the relevant statistic (proportion, mean or coefficient, depending upon the data) of the first group and the second group’s terms are denoted with the subscript b (see: Baker, R. W. R. and J. A. Nissim (1963), "Expressions for Combining Standard Errors of Two Groups and for Sequential Standard Error," Nature, 198 (8 June 1963).