Question

You are testing the change in test scores following an intensive tutoring session.
You have the following data from a small group of students each student is tested before and after the tutoring session.
Each row represents one student.

|Time 1 |Time 2|
|---------|------|
|65 |77 |
|87 |100 |
|77 |75 |
|90 |89 |
|70 |80 |
|84 |81 |
|92 |91 |
|83 |96 |
|85 |84 |
|91 |89 |
|68 |88 |
|72 |100 |
|81 |81 |
|---------|------|

Q3.1 Calculate the appropriate non-paramentric test for these data by hand.

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Q3.2 Check your work using R

```{r}
# your code here
```

Answer 1

This is a simple problem of conducting the test of significance by the application of non parametric functions.

We will use the Kruskal Wallis test for the same.

Test in R

We shall provide the key inputs required to check for the validity of the data significance in two samples.

Firstly we shall take all data point in two samples and align as follows.

a = c(65,87,77,90,70,84,92,83,85,91,68,72,81)
b = c(77,100,75,89,80,81,91,96,84,89,88,100,81)

Then recall the following function to test for the similarity of variances of the two samples.

var.test(a,b)

Run it in R studio

We will get the following output

data: a and b
F = 3.74481, num df = 1, denom df = 24, p-value = 0.0648
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
   -2.80381 10.39254
sample estimates:
 ratio of variances  
1.2287