SCRIPT TO TEST ASSIGNMENT 3 FUNCTIONS.

Read the function definitions.

```
> source("http://www.cs.utoronto.ca/~radford/csc120/a3funs.r")
```

Set up a test data frame.

```
> dt <- data.frame (list (treatment=c("drug","drug","placebo","placebo"),
+ A=c(6,2,4,0), B=c(1,9,3,5)))
```

Find effects and p-values for this test data, using a large number of permutations.

```
> set.seed(1)
> print_effects_with_pvalues(dt,c("A","B"),nperm=10000)
```

```
A B
effect 2.0000 1.0000
pvalue 0.3349 0.5035
Number of subjects: 4
```

The correct effects are 2 for A and 1 for B, since the means for the drug group are 4 for A and 5 for B, while the means for the placebo group are 2 for A and 4 for B. The correct pvalues are 1/3 for a, ½ for b. To see this, consider the six possible results of permuting the treatment variable (D=drug, P=placebo,):

```
> # D D P P A effect: 4-2 = 2 B effect: 5-4 = 1
> # D P D P A effect: 5-1 = 4 B effect: 2-7 = -5
> # D P P D A effect: 3-3 = 0 B effect: 3-6 = -3
> # P D D P A effect: 3-3 = 0 B effect: 6-3 = 3
> # P D P D A effect: 1-5 = -4 B effect: 7-2 = 5
> # P P D D A effect: 2-4 = -2 B effect: 4-5 = -1
```

Of these, 2 out of 6 have A effect of at least 2, and 3 out of 6 have B effect of at least 1, giving the p-values of 2/6 = 1/3 and 3/6 = ½.