Can someone just quickly clarify if order matters when deciding on your design formula? In this post Anderson nicely explains that the design below is "Effect of treatment, accounting for the sample pairing"

```
~ Patient.ID + Treatment
```

But I thought that variables included in your design table (specifically referring to the Wilkinson Notation) just referred to the factors you wanted to take into account when creating your linear regression model.

What would be the difference between:

"Effect of treatment, accounting for the sample pairing"

```
~ Patient.ID + Treatment
```

and "Effect of sample pairing, accounting for the treatment"

```
~ Treatment + Patient.ID
```

**The same question is extended to interactions Patient.ID:Treatment and Treatment:Patient.ID)**

Also the design matrix does not change when specifying different orders in model.matrix()