Question

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[9 total pt(s)] A one-way analysis of variance was conducted on 5 groups. The total standard devation was calculated to be 2. The total degrees of freedom was found to be 13 and the resulting p-value was found to be 0.05. Use the given information to fill out the rest of the ANOVA table. What is the number of treatment degrees of freedom? 4 [1 pt(s)] You are correct. Your receipt no. is 159-1431 Previous Tries What is the denominator degrees of freedom for the test statistic? 9 [1 pt(s)] You are correct. Your receipt no. is 159-6077 Previous Tries How many total observations were there? 14 [1 pt(s)] You are correct. Your receipt no. is 159-6444 Previous Tries What is the value of Fobs? [1 pt(s)] Incorrect. Tries 3/3 Previous Tries Calculate SST [1 pt(s)] Satan. Incorrect. Tries 2/3 Previous Tries Calculate SSE [1 pt(s)] A Tries 0/3 Calculate SSA [1 pt(s)] Sabri Tries 0/3 Calculate the MSE [1 pt(s)] S Tries 0/3 Calculate MSA

Answer 1

Note: Final answers are highlighted in colour.

No of treatment Degrees of freedom= No of groups(k)-1= 5-1= 4

Denomenator degrees of freedom for test statistic(df_error)= Total degrees of freedom- No of treatment Degrees of freedom(df_between)

= 13-4= 9

Total observations(n)= Total degrees of freedom+1= 13+1= 14

Value of F_obs= F.INV.RT(0.05,4,9)= 3.633089

Sum of Squares total (SST)= Variance * (n-1)= (2^2)*(14-1)= 52

Lets say SSA= x,

SSE= 52-x

F= MSA/MSE= $\frac{SSA/df_{between}}{SSE/df_{error}}$

   $\frac{x/4}{(52-x)/9}$ = 3.633089

Solving for x gives x= 32.11

Therefore SSA= 32.11

SSE= 52- SSA= 19.89

MSE= SSE/df_Error = 19.89/9= 2.21

MSA= SSA/df_Between = 32.11/4= 8.028

The final Anova table is as shown below

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	32.11132	4	8.027831	3.633089	0.05
Within Groups	19.88868	9	2.209853
Total	52	13