And we build a model, as we've done before, using the ART command.

We formulate our model like we've seen, where we have our Y on the left.

Keyboard by posture is our study, and

we add this term in parenthesis one with a vertical bar and subject.

This is because the aligned rank transform,

the ART procedure under the hood here is using a linear mixed model.

We're not going to discuss that right now.

That'll be a topic later in the course.

But that's what that means and that's what's going on under the hood.

This notation is part of what tells it that subject is a random effect.

Again, we'll discuss that later, but also helps it know that subject is what to

use to correlate data across rows in our table.

So, let's go ahead and build that and then we'll report the ANOVA result.

Now remember, even though this isn't ANOVA.

It is a non parametric result, because the ART procedure used

the aligned rank transform on all of the data to build that model.

So that's what allows us to see interactions in an F test,

is how we'd report this, just like you've seen before,

but it's really a non parametric result.

Okay, so with this, we see that we have our F statistics for

keyboard posture and the interaction.

The degrees of freedom in the numerator as you've seen before.

And then the residual or denominator degrees of freedom.

And we see that all three results are statistically significant.

What that means is, for

all three main effects in the, or two main effects in the interaction.

We have statistically significant results.

It seems there's a main effective keyboard, a main effective posture and

we can tell from just looking at the graph obviously a significant interaction.

We can just for fun here,

test the normality of the residuals that the model provides.

Remember that one of the ANOVA assumptions is normality and specifically,

the normality of the residuals which are the difference and

the observations from the model predictions.

So we'll use our Shapiro–Wilk test.

And even though this is a non parametric test, we're ultimately still doing

an ANOVA, and so it would be nice to see that the residuals comply with normality.

The Shapiro-Wilk test is non significant, telling us that we don't have

a significant departure from normality, so that's nice to see.

And we can graph the residuals on a QQ plot as we've done in the past, and

see that the data points do seem to fall roughly equal to or

random around the normal line.

Which is the normal distribution line.

So that's good, so it seems that were conforming to the assumptions there

of ANOVA which can make us proceed with confidence.

So given the overall significant interaction effects and main effects here,

we can look a little bit further into pairwise comparisons.

Where do the differences lie?

One thing we might notice is in the sitting situation and the standing

situation, things between the keyboards don't seem to be all that different.

But in the walking situation, we see that they are quite different.

So that's going to be interesting for us to see.