A researcher investigated the effect of volume of background noise on participan
ID: 3291162 • Letter: A
Question
A researcher investigated the effect of volume of background noise on participants’ error rates while performing a boring task. He tested three groups of randomly selected students and obtained the following error data.
Low Volume
Moderate Volume
High Volume
n
61.5
5
65.5
5
48.25
5
ANOVA Table
Source
Sum of Squares (SS)
df
Mean Square (MS)
F
Between
Within
Total
652.16
612.75
1264.92
(a) Complete the ANOVA Table
(b) What is your statistical decision?
(c) Compute and interpret the effect size
(d) Conduct the appropriate post-hoc tests
(e) Report the results using APA format
Low Volume
Moderate Volume
High Volume
n
61.5
5
65.5
5
48.25
5
Explanation / Answer
Question a)
Source
Sum of Squares (SS)
df
Mean Square (MS)
F
Between
652.16
2
326.08
6.386
Within
612.75
12
51.0625
Total
1264.92
14
Df (between) = k – 1 = 3 – 1 = 2
Df (within) = n – k = 15 – 3 = 12
Df (total) = 2 + 12 = 14
MS (between) = 652.16/2 = 326.08
MS (within) = 612.75/2 = 51.0625
F = MS (between)/MS (within)
= 326.08 / 51.0625
= 3.386
Question b)
The critical F at 5% level of significance for 2,12 degrees of freedom is given by 3.885. The value of the test statistics is less than the critical F. We reject the null hypothesis. We conclude that all the population means are not equal.
Question c)
eta-square = SS between / SS total = 652.16 / 1264.92 = 0.5156
Question d)
Here we use Tukey Post Hoc test.
HSD = q * sqrt (MSW/n)
= 3.78 * sqrt (51.0625/5)
= 12.080
Low Volume – Moderate Volume = | 61.5 – 65.5 | = 4
Low Volume – High Volume = |61.5 – 48.25| = 13.25 (>12.08) --- It is significant
Moderate Volume – High Volume = |48.25 – 65.5|= 17.25 (>12.08) --- It is significant
The difference between Low Volume and High Volume is significant.
The difference between moderate volume and high volume is significant.
Source
Sum of Squares (SS)
df
Mean Square (MS)
F
Between
652.16
2
326.08
6.386
Within
612.75
12
51.0625
Total
1264.92
14
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