Question

A researcher examined whether the time of day someone exercises affects memory retention in college courses.  Participants were assigned to one of three exercise groups: morning, afternoon, evening, and their performance on a memorization task was measured.  This data is below:

Morning	Afternoon	Evening
6	4	7
7	5	6
8	6	8
5	4	6
6	5	5
Mean = 6.40	Mean = 4.80	Mean = 6.40
s = 1.14	s =.84	s = 1.14

Assuming the researcher wants to know whether the performance was different in these groups (alpha = .05).  What is the Total Sum of Squares (SS_T)?  Round to two decimal places.

Answer 1

First be need to find grand mean so

$\bar{x}=\frac{5\cdot \left (6.40+4.80+6.40 \right )}{15}=5.87$

Now,

$SS_{between}=n_{1}(\bar{x}_{1}-\bar{x})^{2}+n_{2}(\bar{x}_{2}-\bar{x})^{2}+n_{3}(\bar{x}_{3}-\bar{x})^{2}=5\cdot (6.40-5.87)^{2}+5\cdot (4.80-5.87)^{2}+5\cdot (6.40-5.87)^{2}=8.53$

and

$SS_{within}=(n_{1}-1)s^{2}_{1}+(n_{2}-1)s^{2}_{2}+(n_{3}-1)s^{2}_{3}=13.22$

Therefore

$SS_{total}=SS_{between}+SS_{within}=21.75$