Question

An investigator wonders if slow-tempo music is more complex than fast-tempo music – since with slower music, the listener has more time to process the incoming musical information. To study this, he examines three samples of pop songs by the Beatles that differ in tempo: slow (group 1), moderate (group 2), and fast (group 3). 20 Beatles songs are sampled in each category (so, 60 songs total). As a measure of musical complexity, the investigator counts the number of different chords that appear in each song (a chord is a group of notes played at the same time). He then compares the three tempo groups to see if they differ in average number of chords each song contains. Analyze the data using JASP, SPSS, or an online calculator, and answer the following question

do post hoc comparisons using Tukey’s HSD with a = 0.05. Report which means are reliably different, and what the basis for that decision is (in terms of the decision rule).

group	chords
1	9
1	9
1	10
1	11
1	11
1	11
1	12
1	12
1	12
1	13
1	13
1	13
1	14
1	14
1	14
1	14
1	14
1	15
1	17
1	19
2	5
2	5
2	6
2	6
2	6
2	7
2	7
2	7
2	8
2	8
2	8
2	9
2	9
2	9
2	9
2	10
2	10
2	11
2	12
2	14
3	2
3	4

3	4
3	4
3	5
3	6
3	6
3	6
3	6
3	7
3	7
3	7
3	7
3	8
3	9
3	9
3	9
3	10
3	10
3	11

Answer 1

Using an online calculator, the output is:

Empty cells or non-numeric cells will be ignored

Group1 contains 20 values
Group2 contains 20 values
Group3 contains 20 values
validation:success

Hover over the cells for more information.

Source	DF	Sum of Square	Mean Square	F Statistic	P-value
Groups (between groups)	2	392.033333	196.016667	34.136728	1.79246e-10
Error (within groups)	57	327.299968	5.742105
Total	59	719.333301	12.192090

One Way ANOVA test, using F distribution df(2,57) (right tailed)

1. H0 hypothesis
Since p-value<α, H0 is rejected.
Some of the groups' averages consider to be not equal.
In other words, the difference between the averages of some groups is big enough to be statistically significant.

2. P-value
p-value equals 1.79246e-10, [p( x ≤ F ) = 1.00000 ]. This means that the chance of type1 error (rejecting a correct H0) is small: 1.792e-10 (1.8e-8%)
The smaller the p-value the stronger it support H1

3. The statistics
The test statistic F equals 34.136728, is not in the 95% critical value accepted range: [-∞ : 3.1588]

4. Effect size
The observed effect size f is large (1.09). That indicates that the magnitude of the difference between the averages is large.
The η2 equals 0.54. It means that the group explains 54.5% of the variance from the average (similar to R2 in the linear regression)

5. Tukey HSD / Tukey Kramer
The means of the following pairs are significantly different: x1-x2, x1-x3.

Tukey HSD / Tukey Kramer

Pair	Difference	SE	Q	Lower CI	Upper CI	Critical Mean	p-value
x1-x2	4.550000	0.535822	8.491626	2.726496	6.373504	1.823504	4.21384e-7
x1-x3	6.000000	0.535822	11.197748	4.176496	7.823504	1.823504	3.16771e-10
x2-x3	1.450000	0.535822	2.706122	-0.373504	3.273504	1.823504	0.144140

Group	x2	x3
x1	4.55	6.00
x2	0.0	1.45