Question

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided.

SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
The mean square within treatments (MSE) is _____.
a. 10
b. 600
c. 50
d. 200

Answer 1

`MSE = 10`

Explanation:

Given

`SSTR = 200`

`SST = 800`

Required

Determine MSE

This is calculated as:

`MSE = (1)/(ddf) * SSE`

Where:

`SSE = SST - SSTR`

`ddf \to` denominator df

So, we have:

`SSE = 800 - 200`

`SSE = 600`

To calculate the df, we have:

`r = 13` --- observations

`n = 5` treatments

So:

`ddf = Total\ df - Numerator\ df`

`Total = n*r-1 = 5*13 -1 = 64`

`Numerator =n - 1 = 5 - 1 =4`

`ddf =64-4=60`

So, we have:

`MSE = (1)/(ddf) * SSE`

`MSE = (1)/(60) * 600`

`MSE = 10`