Analysis of variance

statistics

The most common inferential statistical procedure to analyze experiments b/c it has a lot of well-developed variations to cover different use-cases.

It uses the $F_{obt}$ and $F_{crit}$, which tells us if there is some significant difference between the factors. It doesn’t tell us which one it is. For that, we instead need to do post-hoc comparisons (but only after significance testing to ensure Type I error rate stays the same as $\alpha$).

$F_{obt}=\frac{{MS}_{bn}}{{MS}_{wn}}$

$H_0$ is true when $F_{obt}\approx 1$.

It’s reported in the text as

$F(2,12)=4.52,p<.05$ which is to say: $F(d{f}_{bn},d{f}_{wn})=F_{obt},p<\alpha$

Definitions

factor : an independent variable

level : a condition of the independent variable (number of these represented by $k$)

treatment : see level

treatment effect : the differences between the independent variables

one-way (or n-way) ANOVA : when there is one (or, for n-way, n) independent variables

between-subjects factor : the independent variable uses independent samples

between-subjects ANOVA : involves between-subjects factors

within-subjects factor : the independent variable uses related samples

within-subjects ANOVA : involves within-subjects factors.

post-hoc comparisons : like the comparisons of all pairs of means from a factor in t-tests, but for ANOVA.

mean square within groups : variability of scores within the conditions ${MS}_{wn}$

mean square between groups : differences between the means of conditions within a factor. ${MS}_{bn}$

f-ratio : $F_{obt}$

anova effect size : represented as ${\eta }^2$ (eta squared) w/ the formula ${\eta }^2=\frac{S{S}_{bn}}{S{S}_{tot}}$