Results

Repeated Measures ANOVA

Data from Perham & Sykora (2012). The authors investigated how music influences performance on a memory task.

In the Repeated Measures Factors box supply a name for the first within-subject (repeated-measures) variable. The first repeated-measures variable we’re going to enter is the type of sound (quiet, liked or disliked), so replace the word RM Factor 1 with the word Sound. In this case, there were three type of sound, so enter the 3 types into the box. Repeat this process for the second independent variable, the position of the letter in the list, by entering the word Position into the space labelled New Factor and then, because there were eight levels of this variable, enter them below. Then, in the box labelled Repeated Measures Cells enter the variables corresponding to each combination of factors (they are in the same order here, so you can shift-click them all and easoly add all of them at once).

Within Subjects Effects
Cases	Sphericity Correction	Sum of Squares	df	Mean Square	F	p	ω²ₚ
Sound	Greenhouse-Geisser	2.368	1.621	1.461	9.459	< .001	0.104
Residuals	Greenhouse-Geisser	6.007	38.895	0.154
Position	Greenhouse-Geisser	13.474	3.830	3.518	41.432	< .001	0.396
Residuals	Greenhouse-Geisser	7.805	91.923	0.085
Sound ✻ Position	Greenhouse-Geisser	0.565	6.391	0.088	1.435	0.201	0.008
Residuals	Greenhouse-Geisser	9.453	153.389	0.062

Note. Type III Sum of Squares
ᵃ Mauchly's test of sphericity indicates that the assumption of sphericity is violated (p < .05).

The main ANOVA summary table (which, as I explain in the book, I have edited to show only the Greenhouse-Geisser correct values) shows a significant main effect of the type of sound on memory performance F(1.62, 38.90) = 9.46, p < .001. Looking at the earlier plot below, we can see that performance was best in the quiet condition, poorer in the disliked music condition and poorest in the liked music condition. However, we cannot tell where the significant differences lie without looking at some contrasts or post hoc tests. There was also a significant main effect of position, F(3.83, 91.92) = 41.43, p < .001, but no significant position by sound interaction, F(6.39, 153.39) = 1.44, p = .201.

Between Subjects Effects
Cases	Sum of Squares	df	Mean Square	F	p
Residuals	11.487	24	0.479

Note. Type III Sum of Squares

Descriptives

Descriptives plots

The Descriptives Plots tab is a convenient way to plot the means for each level of the factors (although really you should do some proper plots before the analysis). Add Position to the space labelled Horizontal Axis and to the space labelled Separate Lines. I also selected to include error bars representing a 95% CI.

The resulting plot displays the estimated marginal means of letters recalled in each of the positions of the lists when no music was played (white dots), when liked music was played (black dots) and when disliked music was played (white squares). The chart shows that the typical serial curve was elicited for all sound conditions (participants’ memory was best for letters towards the beginning of the list and at the end of the list, and poorest for letters in the middle of the list) and that performance was best in the quiet condition, poorer in the disliked music condition and poorest in the liked music condition.

Assumption Checks

Test of Sphericity
	Mauchly's W	Approx. Χ²	df	p-value	Greenhouse-Geisser ε	Huynh-Feldt ε	Lower Bound ε
Sound	0.766	6.134	2	0.047	0.810	0.861	0.500
Position	0.050	64.153	27	< .001	0.547	0.664	0.143
Sound ✻ Position	1.164×10^-4	173.403	104	< .001	0.457	0.640	0.071

Mauchly’s test shows that the assumption of sphericity has been broken for both of the independent variables and also for the interaction. In the book I advise you to routinely interpret the Greenhouse-Geisser corrected values for the main model anyway, but for these data this is certainly a good idea.

Post Hoc Tests

Post Hoc Comparisons - Sound
			95% CI for Mean Difference						95% CI for Cohen's d
		Mean Difference	Lower	Upper	SE	df	t	Cohen's d	Lower	Upper	p_holm
Quiet	Liked	0.154	0.044	0.263	0.042	24	3.616	0.625	0.123	1.127	0.004	**
	Disliked	0.068	-0.003	0.138	0.028	24	2.451	0.275	-0.031	0.581	0.040	*
Liked	Disliked	-0.086	-0.175	0.003	0.035	24	-2.489	-0.350	-0.735	0.035	0.040	*

* p < .05, ** p < .01
Note. P-value and confidence intervals adjusted for comparing a family of 3 estimates (confidence intervals corrected using the bonferroni method).
Note. Results are averaged over the levels of: Position

The main effect of position was significant because of the production of the typical serial curve (see plot above), so post hoc analyses were not conducted.

However, we did conduct post hoc comparisons on the main effect of sound. These Holm corrected post hoc tests revealed that performance in the quiet condition (level 1. was significantly better than both the liked condition (level 2), p = .004, and in the disliked condition (level 3), p = .040. Performance in the disliked condition (level 3) was significantly better than in the liked condition (level 2), p = .040. We can conclude that liked music interferes more with performance on a memory task than disliked music.