Question

Follow the questions below to conduct a One-way ANOVA test for the sample problem used in the lecture (with some slight data modifications):

A travel journal is comparing the ratings of three local cupcake shops to see who’s the best.
N = 30; send 10 to each shop (assume alpha of .05)

Shop A: M = 1, SD = 3.00

Shop B: M = 5, SD = 3.16

Shop C: M = 6, SD = 3.32

Compute SS_{B ,} Compute df_B, Compute MS_B

Answer 1

treatment	A	B	C
count, ni =	10	10	10
mean , x̅ i =	1.000	5.00	6.000
std. dev., si =	3.000	3.160	3.320
sample variances, si^2 =	9.000	9.986	11.022
total sum	10	50	60		120	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	4.00
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	9.000	1.000	4.000
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	90.000	10.000	40.000		140
SS(within ) = SSW = Σ(n-1)s² =	81.000	89.870	99.202		270.0720

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   30
df within = N-k =   27
  
mean square between groups , MSB = SSB/k-1 =    70.0000
  
mean square within groups , MSW = SSW/N-k =    10.0027
  
F-stat = MSB/MSW =    6.9981

anova table
	SS	df	MS	F	p-value	F-critical
Between:	140.0000	2	70.000	6.998	0.0036	3.354
Within:	270.0720	27	10.003
Total:	410.0720	29
					α =	0.05

SSB=140

dfb = 2

MSB = 70