Parametirc test or not:
Test statistic:
p-value:
decision:
Is There A Difference Between the Means?
6.7 6.2 3.1 3
10.3 10 5 5.5
6.9 5.5 3.3 3.1
10.5 6.3 4.3 5.4
4.5 4.6 1.8 2
5.6 5.6 2 2.6
5.9 6.1 2.1 2.5
8 11.7 4 4.6
8 7.4 3.3 3.1
5.8 5.2 3.1 2.9
6 7.3 3.0 3.2
8.7 5.3 2.7 3
6 5.5 2.1 2.2
7.2 6.3 3.5 3.2
5.9 4.6 2.9 3.4
6 7.4 3 3.3
7.2 7.8 3.7 3.4
8.6 9.4 5.1 5.7
7.2 8.1 2.8 3.1
5.8 5.4 2.2 1.8
3.3 4 1.7 1.8
6.8 5.1 2 1.8
3.7 3.5 2.2 2.1
12 10.8 5.7 5.8
9.5 6.9 4.4 3.2
21.4 15.4 7.2 6.9
6.5 7 3.5 3
4.6 6.4 3.2 2.7
3.9 4.2 2.9 2.4
4.6 3.6 1.4 1.7
9.1 11.2 4.5 5.1
3.3 3 1.7 1.5
8 7.7 4 3.6
15.3 15.2 12 6.1
6.8 5.6 3.3 2.6
10.5 7.4 5.8 3.9
5.2 4.2 1.8 2.6
7.2 5.5 2.8 2.7
14.2 12.4 7.6 5.3
11.7 11.4 6.8 6.2
8 8.2 4.9 4.1
10 10 4.7 5.3
6.1 9.7 1.9 2.3
4.5 5.1 2.6 2.3
4 3.4 2 1.9
12.9 10 4.4 4
6.5 7.5 3.5 2.3
17.3 7.9 6.4 8.1
We will assume parametric setup for this problem
Here we will use ANOVA test to check whether the means are different.
that is to test,
H0: means of all 4 groups are same
vs
H1: at least 2 groups are different means
To test this we will use Excel software and the output is
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
Column 1 | 48 | 377.7 | 7.86875 | 13.6255984 | ||
Column 2 | 48 | 348 | 7.25 | 8.538297872 | ||
Column 3 | 48 | 177.9 | 3.70625 | 3.821449468 | ||
Column 4 | 48 | 168.3 | 3.50625 | 2.384428191 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 760.2539 | 3 | 253.418 | 35.73069977 | 2.54521E-18 | 2.652645615 |
Within Groups | 1333.379 | 188 | 7.092443 | |||
Total | 2093.633 | 191 |
Test statistic: F=35.73069977
p-value: 0.00000
decision: we will reject H0 and claim that groups has
significantly different means.
Is There A Difference Between the Means?
YES. There is significant difference in means.
Parametirc test or not: Test statistic: p-value: decision: Is There A Difference Between the Means?
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