Question

help calculate the f ratio for these values and setting up steps thank you!

Country και η 7η k=3 Σ(x2) 358 Σ(x) Σ(x2) 38.83 7.33 22.83

Answer 1

Here, we consider a one-way anova to solve this problem.

Let xij denote the observations correspoind to ith level that is either city, suburb or country, i=1,2,3

For each level we have 6 observations i.e, for k=3 we have n1=n2=n3=6.

Therefore N=3*6=18

So, our model is

$x_{ij}=\mu + \alpha _{i}+e_{ij}$

where, i=1(|)3 and j=1(6)

The following formulas are used here to calculate the f ratio-

$G=\sum_{i=1}^{3}\sum_{j=1}^{6}x_{ij}$

$Correction factor(CF)=\frac{G^{2}}{N}$

$Total sum square(TSS)=\sum_{i=1}^{3}\sum_{j=1}^{6}x_{ij}^{2} - CF$

$Sum square due to level(SSA)=\sum_{i=1}^{3}\frac{T_{i0}^{2}}{n_{i}} - CF$

Sum square due to error (SSE)=TSS - SSA

Now, we draw the followinf table to calculate the above-

Level	City	Suburb	Country
	5	3	2
	10	5	1
	6	2	7
	2	4	2
	5	3	2
	3	5	3
Ti0	31	22	17
Ti02	961	484	289

G=70 , CF=272.2222

TSS = 85.7778 , SSA = 16.7778 , SSE = 69

Now we find the degrees of freedom of each

df(TSS)=N-k=18-1=17

df(SSA)=k-1=3-1=2

df(SSE)=N-k=18-3=15

Now, we calculate the mean sum of squares which are given by,

MSA=SSA/df = 8.3889

MSE = SSE/df =4.6

Therefore, f ratio = MSA/MSE = 1.8236