# ANOVA Visualization (Interactive Simulation)

INSTRUCTOR: This demo shows how a balanced one-way analysis of variance
works, also known as ANOVA. Let’s consider three experiments, each with 10 measurements
shown as the blue circles. Here, capital I is the
number of experiments, so three in this case. And J sub I is the number of measurements in the Ith experiment. Each experiment has 10 measurements, so J one equals J two
equals J three equals 10. And let’s define capital
N as the total number of measurements in all the experiments, so 10 plus 10 plus 10 is 30 in this case. So, now let’s calculate the mean in each experiment, also
known as the sample mean and shown on the plot as the red dots. Now let’s calculate the grand mean, also known as the mean of the sample means and indicated as the black
dashed line on the plot. Now let’s calculate the variance within each experiment shown visually with the green bars. And let’s calculate the difference between each sample mean and the grand mean shown visually with the orange bars. A one-way ANOVA is a special
type of hypothesis test that tells us if one of these experiments differs
significantly from the others. So, to get a test statistic
which we call capital F, we compare the treatment sum of squares which is related to the
sum of the squared length of the orange bars to the ever sum of squares which is related to the sum of the length of the green bars. So, we get a P value
for this hypothesis test from the F distribution and traditionally if our
P value is less than .05, we say that one of these datasets differs from the others. We can also change the spread and the offset in each one of
these individual experiments and we can see how that affects the treatment sum of squares, the ever sum of squares, the test statistic F and our P value.

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