أحجام التأثير — d لكوهن وη² وV لكرامر وr

$$d = \frac{M_1-M_2}{SD_{pooled}},\quad SD_{pooled}=\sqrt{\frac{(n_1-1)SD_1^2+(n_2-1)SD_2^2}{n_1+n_2-2}}$$

$$SD_{pooled}=\sqrt{\frac{14(6.5)^2+14(5.9)^2}{28}}=\sqrt{\frac{592+487}{28}}=\sqrt{38.5}=6.21$$ $$d=\frac{82-76}{6.21}=\frac{6}{6.21}=\mathbf{0.97}\quad(\text{large})$$

$$\eta^2=\frac{SS_{between}}{SS_{total}},\quad \omega^2=\frac{SS_{between}-df_{between}\cdot MS_{within}}{SS_{total}+MS_{within}}\;(\text{less biased})$$ $$\text{Example: }SS_{between}=180,\;SS_{total}=520 \;\Rightarrow\; \eta^2=\frac{180}{520}=\mathbf{.346}\quad(\text{large})$$

$$V=\sqrt{\frac{\chi^2}{n\cdot\min(r-1,\;c-1)}}$$ $$\text{Example: }\chi^2=8.64,\;n=45,\;2\times2\text{ table} \;\Rightarrow\; V=\sqrt{\frac{8.64}{45\times1}}=\sqrt{.192}=\mathbf{.438}\quad(\text{large})$$

$$r=\frac{|z|}{\sqrt{N}}$$ $$\text{Example: }z=-2.45,\;N=30 \;\Rightarrow\; r=\frac{2.45}{\sqrt{30}}=\frac{2.45}{5.48}=\mathbf{.447}\quad(\text{medium-large})$$