Question

#14

Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four different sites in an archaeological region, the number of such sherds was counted in local dwelling excavations.

Site I	Site II	Site III	Site IV
10	10	36	17
28	9	23	24
6	32	19	16
16	4	40	33
10	23		16
	13		14

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

SSTOT	=
SSBET	=
SSW	=

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

dfBET	=
dfW	=
MSBET	=
MSW	=

Find the value of the sample F statistic. (Use 3 decimal places.)


What are the degrees of freedom?
(numerator)
(denominator)

(f) Make a summary table for your ANOVA test.

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P Value	Test Decision
Between groups					---Select--- p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001	---Select--- Do not reject H0. Reject H0.
Within groups
Total

Answer 1

	Site I	Site II	Site III	Site IV
count, ni =	5	6	4	6
mean , x̅ i =	14.000	15.17	29.50	20.00
std. dev., si =	8.602	10.381	10.083	7.24
sample variances, si^2 =	74.000	107.767	101.667	52.400
total sum	70	91	118	120	399	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				19.00
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	25.000	14.694	110.250	1.000
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	125.000	88.167	441.000	6.000	660.1667
SS(within ) = SSW = Σ(n-1)s² =	296.000	538.833	305.000	262.000	1401.833

no. of treatment , k =   4
df between = k-1 =    3
N = Σn =   21
df within = N-k =   17
  
mean square between groups , MSB = SSB/k-1 =    220.0556
  
mean square within groups , MSW = SSW/N-k =    82.4608
  
F-stat = MSB/MSW =    2.6686
P value =   0.0806

----------------

SSTOT	=	2062.000
SSBET	=	660.167
SSW	=	1401.833

dfBET	=	3
dfW	=	17
MSBET	=	220.056
MSW	=	82.461

Value of the sample F statistic=2.669

the degrees of freedom?
(numerator)=3
(denominator)=17

ANOVA
Source of Variation	SS	df	MS	F	P-value	test decision
Between Groups	660.167	3	220.056	2.669	0.050 < p-value < 0.100	do not reject Ho
Within Groups	1401.833	17	82.461
Total	2062.000	20