Question

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
17	11	31	10
28	8	17	16
5	31	13	11
17	9	47	32
12	22		12
	18		19

Shall we reject or not reject the claim that there is no difference in the population mean three-circle red-on-white sherd counts for the four sites? Use a 5% level of significance.

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

SSTOT	=
SSBET	=
SSW	=

b)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	=

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

d) What are the degrees of freedom?

(numerator) =

(denominator) =

e) Find the P-value of the sample test statistic.

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

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

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio
Between groups
Within groups
Total

Answer 1

Here we have data:

Site I	Site II	Site III	Site IV
17	11	31	10
28	8	17	16
5	31	13	11
17	9	47	32
12	22		12
	18		19

We are using Excel for calculation:

f)

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	5	79	15.8	70.7
Column 2	6	99	16.5	80.3
Column 3	4	108	27	237.3333
Column 4	6	100	16.66667	67.86667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	369.319	3	123.106	1.206	0.3377	3.197
Within Groups	1735.633	17	102.096
Total	2104.952	20

a)

SSTOT = 2104.952

SSBET = 369.319

SSW = 1735.633

B)

DFBET = 3

DFW = 17

MSBET = 123.106

MSW = 102.096

c)

F- statistics = 1.206

d)

Numerator = 3

Denominator = 17

e) P-value of the test statistics = 0.3377

Correct option "A"

P-value > 0.100