Question

you read a report stating that correctional officers have very low job satisfaction. you take 3 samples of n=4 correctional officers who work in either a supermax,medium. and minimum security prison and ask them to self-report their level of stress on a 1-20point scale. the data are presented below Supermax: 17, 14, 13, 12, T1=56 SS1=14 meidum: 12, 14, 11, 13, T2=50 SS2=5 Minimum: 10, 8, 13, 9, T3=40 SS3=14 G=146 EX2=1842

Answer 1

This a one factor-ANOVA testing

Supermax	Medium	Minimum
17	12	10
14	14	8
13	11	13
12	13	9

Ho: All are equal VS H1 All u are not equal

F - Test Statistic = $\frac{MSS_{B}}{MSS_{R}}$

SSB MSSB 1
= $\frac{32.667}{2}=16.33$    (Variance between the treatments/ No. of treatment - 1)

$MSS_{R}=\frac{SS_{R}}{n-k}$$\frac{33}{9}=3.667$ (Variance between the residual / Total obs. - no. of treatment)

$SS_{B}=\sum \frac{y_{i.}^{2}}{n_{i}}-\frac{G^{2}}{N}$ = 32.667 ($y_{i}$. is the total of individual treatment scores eg. sum of supermax and is the total of all the scores)

$SS_{R}=SS_{T}-SS_{B}$ = 33

$SS_{T}=\sum \sum y_{ij}^{2}-\frac{G^{2}}{N}$ = 65.667 ($\sum \sum y_{ij}^{2}$ is the sum of individual squares of  scores)

Variance	df	SS	MS
Between	2	32.67	16.33
Residual	9	33	3.667
Total	11	65.667

F - Stat = $\frac{16.33}{3.667}$ $=4.455$

Using 5% level of significance the critical value

$F_{\alpha\%/2,k-1,n-k}=F_{2.5\%,2,9}=4.2565$

F - Stat > Critical Value

Decision : We reject the null hypothesis and conclude that there is a significant different between the level of stress under different level of correctional officers.