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

Answer:

$MSE = 10$

Step-by-step explanation:

Given

$SSTR = 200$

$SST = 800$

Required

Determine MSE

This is calculated as:

$MSE = \frac{1}{ddf} * SSE$

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:

$MSE = \frac{1}{ddf} * SSE$

$MSE = \frac{1}{60} * 600$

$MSE = 10$