This problem will introduce the learner to a technique called Analysis of Varian
ID: 3046403 • Letter: T
Question
This problem will introduce the learner to a technique called Analysis of Variance. For this course, we will only conduct a simple One-Way ANOVA and touch briefly on the important elements of this technique. The One-Way ANOVA is an extension of the independent –t test that can only look at two independent sample means. We can use the One-Way ANOVA to look at three or more independent sample means. Use the following data to conduct a One-Way ANOVA:
Scores Group
1 1
2 1
3 1
2 2
3 2
4 2
4 3
5 3
6 3
Notice the group (grouping) variable, which is the independent variable or factor is made up of three different groups. The scores are the dependent variable.
Use the instructions for conduction an ANOVA on page 366 of the text for Excel.
a)What is the F-score; Are the results significant, and if so, at what level (P-value)?
b)If the results are significant to the following: Click Analyze, then click Compare Means, and then select One-Way ANOVA as you did previously. Now click Post Hoc. In this area check Tukey. If there is a significant result, we really do not know where it is. Is it between group 1 and 2, 1 and 3, or 2 and 3? Post hoc tests let us determine which group comparisons were significantly different. So if the results come back significant, conduct the post hoc test as I mentioned above and explain where the results were significant.
c)What do the results obtained from the test mean?
Explanation / Answer
Solution:
Using Statistical Software we calculate these results
a.F = 8.225, p = .015. The results are significant between the groups.
b.According to the Tukey HSD there is statistically significant differences only between groups one and three.
c.There are no significant differences between group 1 and group 2, or between group 2 and group 3. The only significant difference is between the values of group 1 and group 3 (p = .013).
ANOVA
Scores
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
14.100
2
7.050
8.225
.015
Within Groups
6.000
7
.857
Total
20.100
9
Multiple Comparisons
Scores
Tukey HSD
(I) Group
(J) Group
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
1.00
2.00
-1.00000
.70711
.385
-3.0825
1.0825
3.00
-3.00000*
.75593
.013
-5.2263
-.7737
2.00
1.00
1.00000
.70711
.385
-1.0825
3.0825
3.00
-2.00000
.70711
.059
-4.0825
.0825
3.00
1.00
3.00000*
.75593
.013
.7737
5.2263
2.00
2.00000
.70711
.059
-.0825
4.0825
*. The mean difference is significant at the 0.05 level.
Scores
Tukey HSDa,b
Group
N
Subset for alpha = 0.05
1
2
1.00
3
2.0000
2.00
4
3.0000
3.0000
3.00
3
5.0000
Sig.
.400
.064
Means for groups in homogeneous subsets are displayed.
a. Uses Harmonic Mean Sample Size = 3.273.
b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.
ANOVA
Scores
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
14.100
2
7.050
8.225
.015
Within Groups
6.000
7
.857
Total
20.100
9
Multiple Comparisons
Scores
Tukey HSD
(I) Group
(J) Group
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
1.00
2.00
-1.00000
.70711
.385
-3.0825
1.0825
3.00
-3.00000*
.75593
.013
-5.2263
-.7737
2.00
1.00
1.00000
.70711
.385
-1.0825
3.0825
3.00
-2.00000
.70711
.059
-4.0825
.0825
3.00
1.00
3.00000*
.75593
.013
.7737
5.2263
2.00
2.00000
.70711
.059
-.0825
4.0825
*. The mean difference is significant at the 0.05 level.
Scores
Tukey HSDa,b
Group
N
Subset for alpha = 0.05
1
2
1.00
3
2.0000
2.00
4
3.0000
3.0000
3.00
3
5.0000
Sig.
.400
.064
Means for groups in homogeneous subsets are displayed.
a. Uses Harmonic Mean Sample Size = 3.273.
b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.
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