In: Statistics and Probability
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 SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)
SSTOT | = | |
SSBET | = | |
SSW | = |
b)Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)
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 |
Sum of |
Degrees of |
MS |
F |
Between groups |
||||
Within groups |
||||
Total |
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