Associations between two measures of music aptitude: Are the IMMA and the AMMA significantly correlated in a sample of 9- to 13-year-old children?

Participants

The sample comprised 89 (46 girls) 9- to 13-year-old children (M = 10 years; 9 months, SD = 8 months) recruited from volunteers listed in the database of the department of developmental psychology, and a secondary school in Germany. The mean IQ was M = 105.29 (SD = 12.63). In the sample, 21.6% of the children reported no former music education except for music as a school subject, 32.9% reported music education (private music lessons, single or in small groups) for 2 years or less, 21.6% reported 2 to 4 years of music education, and 23.9% reported a history of music education (private music lessons, single or in small groups) lasting for 4 years or more. The sample showed diversity with respect to parents’ education: 54.1% of households had no parent holding a university degree, 27% of households had one parent holding a university degree, and 18.9% of households had both parents holding a university degree. Parents’ education was correlated with children’s music education (r = .37, p = .001).

Measures

Amount of a child’s music lessons, socioeconomic status, and intelligence were measured. Beyond that, music aptitude was assessed with two different tests.

The amount of a child’s music training and socioeconomic status, measured by parents’ education, was assessed with a questionnaire. Formal music training (in months) was determined for each child from questions about current and former music education. When a child played more than one instrument, the number of months of instruction for each instrument was combined. Mothers’ and fathers’ education were initially coded individually as dichotomous variables (0 for “no university degree” and 1 for “a university degree”), and for the later statistical analyses parents’ education was collapsed into a single variable (0, 1, or 2 parents with a university degree).

A short version of the HAWIK III (Hamburg-Wechsler-Intelligenztest für Kinder; Tewes, Rossmann & Schallberger, 2000), which consisted of two verbal and two performance subtests, was administered to assess intelligence. The verbal subtests were the vocabulary test, and the information test; the performance subtests consisted of the picture arrangement test, and the mosaic test. Based on these four subtest scores, an estimate of full-scale IQ was computed according to the formula by Schallberger (2005). The short form of the HAWIK III explains at least 90% of the variance in full scale IQ and allows a good estimation of the participant’s IQ (Schallberger, 2005).

Musical aptitude was measured using the Intermediate Measures of Music Audiation (IMMA) (Gordon, 1982) and the Advanced Measures of Music Audiation (AMMA) (Gordon, 1989). To ensure a standardized procedure, both tests were CD-based.

The IMMA consisted of a tonal test, and a rhythm test. For each test, 20 minutes were allowed for the complete test administration. The IMMA offered a total score as well as separate tonal, and rhythm subscores. The CD recording consisted of four practice examples and 40 test questions for the tonal test, as well as two practice exercises and 40 test questions for the rhythm test. Each tone in the two phrases of the tonal test was in beats of equal length, and notes in the two phrases of the rhythm test were on the same pitch. The tonal phrases were all three tones in length. The rhythm phrases varied between 2/4 and 8/8 beats. The procedures for the tonal and the rhythm tests were the same: the child listened to both phrases of a pair, and decided whether the phrases sounded the same. If the two phrases sounded the same, the child drew a circle around a box with two faces that looked the same. In case of a difference between the two phrases of a pair, the child marked the box with two different looking faces (see Table 3 for scoring information).

The AMMA, like the IMMA, provided tonal and rhythm subscores as well as a total score. The CD recording contained the instruction for test taking, three practice exercises, and 30 test items. The complete test administration lasted about 30 minutes. Each test item consisted of two musical phrases. All items comprised 18 tones. The participant was asked to listen attentively to each item, and subsequently indicate (by filling a space on the answer sheet) whether the two musical phrases were the same or different. When the musical phrases were different, the participant had to decide whether the difference was a result of a tonal change or a rhythm change. In contrast to the IMMA, the answer sheet of the AMMA did not contain faces that should be marked. Instead of faces, the answer sheet contained 30 lines with three boxes in each line. Depending on their decision, participants could mark the box for tonal changes, rhythm changes, or no changes (same) (see Table 3 for scoring information). In contrast to the IMMA, in the AMMA the participant was asked to audiate tonality, keyality, melody, implied harmony, rhythm, meter, and tempo in one musical phrase together, and respond to tonal or rhythm aspects of the phrase at the same time.

Procedure

The testing procedure consisted of an individual testing session (40 minutes) and a group testing session (80 minutes including a 10-minute break). In the individual testing session, we assessed intelligence; children were tested in a quiet room by a female assistant trained in administering the test. The group session comprised the assessment of musical aptitude with the IMMA and the AMMA. The order of the musical aptitude tests was counterbalanced: 45 participants worked at first on the IMMA and completed the AMMA afterward, and 44 participants completed the tests in the opposite order. Three female assistants carried out the group sessions. The questionnaire assessing music education and socioeconomic status was sent via mail or email to the participants, and participants handed it in at the individual testing session. At the end of the group session children received a certificate, and a voucher to thank them for their participation.

Data analysis

In preliminary analyses, we looked at Pearson correlations for both musical aptitude tests to determine whether total test score and subtests were correlated. Note that all correlational analyses reported in the results are two-tailed. Secondly, we used a nonparametric test, the Wilcoxon test, to compare the average achievement on the music aptitude tests. In the next step, the sample distributions were inspected more closely. The skewness and kurtosis value were z-transformed and compared to the critical z-score to obtain information about their significance. This had two implications: first, significant skewness yields information about experienced difficulty of the tests (too easy, appropriate, too difficult). Second, a significant skewness or kurtosis indicates a deviance from normal distribution. Thus, where possible, appropriate nonparametrical tests were applied in the analyses.

The main analyses contained correlations between music aptitude, socioeconomic status, amount of music lessons, and IQ and three hierarchical multiple regression models (first step IMMA measures, second step control variables). In the first model the AMMA total score was the criterion measure and the IMMA total score as well as SES, amount of music lessons, and IQ were the predictors. In the second model the AMMA tonal score was the criterion measure and the IMMA tonal score as well as SES, amount of music lessons, and IQ were the predictors. In the third model the AMMA rhythm score was the criterion measure and the IMMA rhythm score as well as SES, amount of music lessons, and IQ were the predictors.

Preliminary analyses

Mean, standard deviation, and minimum as well as maximum scores of age, SES, IQ, and amount of music lessons are shown in Table 1.

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Table 1.

Mean, standard deviation, and minimum as well as maximum scores of age, SES, IQ, and amount of music lessons.

	Age(in months)	SES (parents’ education)	IQ	Amount of music lessons (in months)
Minimum	108	0.00	80.00	0.00
Maximum	159	2.00	136.00	228.00
Mean	129.27	0.65	105.29	33.98
Standard deviation	8.64	0.78	12.63	38.77

Note. Parents’ education was collapsed into a single variable (0, 1, or 2 parents with a university degree).

Correlations between the subtests and the total test score of the IMMA are shown in Table 2. All correlations were significant. Also, for the AMMA the correlations between the subtests and the total test score were significant (see Table 2).

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Table 2.

Correlations between subtest and total test score for the Intermediate Measures of Music Audiation (IMMA) and the Advanced Measures of Music Audiation (AMMA).

IMMA					AMMA
	Total		Rhythm		Total		Rhythm
	r	p	r	p	r	p	r	p
Tonal	.58 +	.00	.20 +	.01	.74 +	.00	.67 +	.00
Rhythm	.69 +	.00			.78 +	.00

Note. ⁺Non-parametric correlation coefficient (τ).

The central tendency of the IMMA, M = 68.33 (SD = 4.55), and the AMMA, M = 46.62 (SD = 6.66), indicated a difference of overall achievement in the tests. A Wilcoxon-test revealed that this difference was significant, z = 8.19, p < .001, d = 3.51. Because a ceiling effect might be possible for the IMMA (maximum score = 80), we analyzed the sample distribution of the IMMA scores to assess if the distribution deviates from a normal distribution. To this end, we calculated the skewness and kurtosis of our sample distribution (see Table 3) and compared the z-transformed skewness and kurtosis values to the critical z-scores. For the IMMA total score z_skewness = −1.91 and z_kurtosis = −0.17 were both lower than the critical z-score z_critical = 1.96, indicating that the sample distribution was not skewed and had no significant kurtosis.

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Table 3.

Overview of constitution of score values, mean, standard deviation, skewness, and kurtosis for the total score, the tonal, and the rhythm subtest of the Intermediate Measures of Music Audiation (IMMA) and the Advanced Measures of Music Audiation (AMMA).

Constitutionof scorevalues	IMMA total	IMMA tonal	IMMA rhythm	AMMA total	AMMAtonal	AMMArhythm
	Add up correct items for tonal and rhythm subtests	Count number of correct items for tonal subtest	Count number of correct items for rhythm subtest	Add up “adjusted” scores for the tonal and rhythm subtest	Count correct items for tonal subtest, add 20, subtract incorrect items for tonal subtest	Count correct items for rhythm subtest, add 20, subtract incorrect items for rhythm subtest
Minimum	55.00	28.00	23.00	33.00	12.00	17.00
Maximum	77.00	40.00	38.00	65.00	32.00	33.00
Mean	68.33	35.80	32.53	46.62	22.20	24.42
Standard deviation	4.55	2.52	3.17	6.66	3.71	3.59
Skewness	−0.49	−0.77	−0.54	0.53	0.32	0.17
Kurtosis	−0.09	0.39	−0.49	0.31	0.68	−0.49

With respect to the IMMA tonal score, the comparison of the z-transformed kurtosis and skewness scores revealed no significant kurtosis, z_kurtosis = 0.76, of the distribution, but a significant skewness, z_skewness = −3.04. The IMMA tonal distribution is significantly skewed to the right, which could indicate that the tonal subtest was relatively easy for our participants. Regarding the IMMA rhythm score, the z-scores for skewness, z_skewness = −2.13, exceeded the critical z-score. The distribution was skewed to the right side, which might indicate that the rhythm test was easy. The kurtosis, z_kurtosis = 0.19, did not exceed the critical z-score, z_critical = 1.96. Just like for the IMMA, we analyzed the sample distribution of the AMMA to assess the adequacy of this measurement for this particular age group. Concerning the AMMA total score, the comparison of the z-transformed kurtosis and skewness scores revealed a significant skewness, z_skewness = 2.06, but no significant kurtosis, z_kurtosis = 0.62, of the distribution. The sample distribution was skewed to the left side, pointing toward a higher difficulty of the test. With regard to the AMMA tonal sore, no significant skewness, z_skewness = 1.27, or kurtosis, z_kurtosis = 1.33, was revealed. With respect to the AMMA rhythm score, z-transformed skewness, z_skewness = 0.65, and kurtosis, z_kurtosis = −0.96, were both lower than the critical z-score, z_critical = 1.96, indicating that the sample distribution was not skewed and had no significant kurtosis. Furthermore, we analyzed whether the possible differences in test difficulty were reflected in correlations between age and test scores. There was no significant correlation between age and AMMA (tonal, rhythm, total); see Table 4. Age did not correlate significantly with IMMA total and tonal score (see Table 4). However, the IMMA rhythm score was significantly correlated with age, τ = .16, p = .04.

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Table 4.

Correlations between age in months, SES, IQ, and music lessons, and the Intermediate Measures of Music Audiation (IMMA) as well as the Advanced Measures of Music Audiation (AMMA).

	IMMA						AMMA
	Total		Tonal		Rhythm		Total		Tonal		Rhythm
	r	p	r	p	r	p	r	p	r	p	r	p
Age	.16	.15	−.02 +	.82	.16 +	.04	.04 +	.64	.07	.49	.05	.65
SES	.26	.03	.21 +	.03	.12 +	.23	.06 +	.53	.10	.39	.12	.30
Music lessons	.19	.07	.16 +	.05	−.09 +	.27	.08 +	.32	.05	.62	.10	.36
IQ	−.002	.98	−.06 +	.47	−.03 +	.72	−.004 +	.96	−.01	.95	−.02	.82

Note. ⁺Non-parametric correlation coefficient (τ).

Correlations between musical aptitude, socioeconomic status, music lessons, and IQ

Socioeconomic status (SES) was not correlated with any test score of the AMMA. However, SES was significantly associated with the IMMA total score, r = .26, p = .03, and the IMMA tonal score, τ = .21, p = .03. SES was not correlated with the IMMA rhythm score; for details, see Table 4. Amount of music lessons in months was not correlated to any test score of the AMMA. However, amount of music lessons was significantly associated with the IMMA tonal score, τ = .16, p = .05; for details, see Table 4. Amount of music lessons was not correlated with IMMA total score or IMMA rhythm score. IQ was not significantly correlated with any test score of the AMMA or the IMMA (see Table 4).

Our study contains several correlations. Therefore, it should be taken into account that this affects the alpha level. Because 30 correlations were calculated in the principal analyses, it might be reasonable to adjust the alpha level. The adjusted alpha level is p = .002.

Associations between the Intermediate Measures of Music Audiation and the Advanced Measures of Music Audiation

Hierarchical multiple regression analysis was used to predict AMMA total score with the IMMA total score entered on the first step and SES, amount of music lessons, and IQ added on the second step. The IMMA total score accounted for only 4.0% of the variance in the AMMA total score, F(1, 72) = 3.02, p = .09. The addition of the control variables did not improve the fit of the model, Finc(3, 69) = 0.21, p = .89, accounting for an additional 0.9% of the variance in the AMMA total score. No variable contributed significantly, ps > .18. See Table 5 for more details.

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Table 5.

Regression table with IMMA scores, IQ, amount of music lessons, and SES as predictor variables and AMMA scores as outcome variables.

		B	SE B	β	T	p
Step 1
	Constant	25.57	12.07		2.12	.04
	IMMA total score	0.31	1.76	0.20	1.74	.09
Step 2
	Constant	30.38	14.94		2.03	.05
	IMMA total score	0.26	0.19	0.17	1.36	.18
	Socioeconomic status	0.57	1.12	0.07	0.51	.61
	Amount of music lessons	0.01	0.02	0.06	0.44	.66
	IQ	−0.21	0.07	−0.04	−0.33	.75
Note. R2 = .04 for step 1; ΔR2 = .009; R2 = .049 forstep 2 (all p values > .09).
Step 1
	Constant	25.07	6.12		4.1	.001
	IMMA tonal score	−0.08	0.17	−0.06	−0.47	.64
Step 2
	Constant	28.95	7.90		3.67	.001
	IMMA tonal score	−0.17	0.19	−0.12	−0.89	.38
	Socioeconomic status	0.53	0.63	0.11	0.84	.40
	Amount of music lessons	0.01	0.01	0.09	0.64	.52
	IQ	−0.01	0.04	−0.05	−0.37	.71
Note. R2 = .003 for step 1; ΔR2 = .021; R2 = .024 forstep 2 (all p values > .64).
Step 1
	Constant	16.26	4.48		3.63	.001
	IMMA rhythm score	0.25	0.14	0.21	1.8	.08
Step 2
	Constant	18.34	5.90		3.12	.003
	IMMA rhythm score	0.23	0.14	0.19	1.61	.11
	Socioeconomic status	0.33	0.60	0.07	0.56	.58
	Amount of music lessons	0.01	0.01	0.11	0.84	.40
	IQ	−0.02	0.04	−0.06	−0.52	.61
Note. R2 = .043 for step 1; ΔR2 = .02; R2 = .063 forstep 2 (all p values > .08).

A second hierarchical multiple regression analysis was used to predict AMMA tonal score with the IMMA tonal score entered on the first step and SES, amount of music lessons, and IQ added on the second step. The IMMA tonal score accounted for only 0.3% of the variance in the AMMA tonal score, F(1, 72) = 0.23, p = .64. The addition of the control variables did not improve the fit of the model, Finc(3, 69) = 0.49, p = .69, accounting for an additional 2.1% of the variance in the AMMA tonal score. Again, no variable contributed significantly, ps > .38. See Table 5 for more details.

A third hierarchical multiple regression analysis was used to predict AMMA rhythm score with the IMMA rhythm score entered on the first step and SES, amount of music lessons, and IQ added on the second step. The IMMA rhythm score accounted for only 4.3% of the variance in the AMMA rhythm score, F(1, 72) = 3.25, p = .08. The addition of the control variables did not improve the fit of the model, Finc(3, 69) = 0.49, p = .69, accounting for an additional 2.0% of the variance in the AMMA rhythm score. Again, no variable contributed significantly, ps > .11. See Table 5 for more details.

Associations between IMMA and AMMA

The IMMA scores were no significant predictors of the AMMA scores. Furthermore, the variance explained by the different IMMA scores for the appropriate AMMA scores ranged between 0.3% up to 4.3% (depending on the measure). This indicates that not only is the association not significant, but that the practical significance is also trivial. This was surprising to us, and the question arises as to why these two tests were not significantly associated. First, age could play an important role in the formation of results. Participants’ age was within the extended age range of the IMMA (Gordon, 1989), but they were too young for the AMMA. Gordon himself reported successful application of the AMMA in 12-year-old children (Gordon, 2001). Our youngest participants were 9 years old, and therefore age might have been a problem. However, two points speak against an important contribution of age. On the one hand, age was not correlated at all with the AMMA. For the IMMA, only the subtest rhythm showed a significant correlation with age. However, the age range was not large and this might have contributed to the nonsignificant correlation. On the other hand, according to Gordon’s framework our sample was already in the stage of stabilized musical aptitude. Hence, influences of growing older and gaining more musical experience should be minimal. Second, differences in test difficulty might have contributed to missing significant associations. The existing difference between the means of the IMMA and the AMMA definitely suggested a difference in overall test difficulty. However, our investigation of the skewness of the distributions does not draw a supporting or conclusive picture. A direct comparison of the direction of skewness reveals that the IMMA and its subtest – if they differ from normal distribution – were skewed to the right (tonal subtest score and rhythm subtest score). Hence, if there is an effect, it indicates that the IMMA was relatively easy to work on. The AMMA (total test score), in contrast, was skewed to the left, which might indicate greater difficulty. These results are in accordance with reported differences in the means. However, the total score and subtest scores do not all show significant skewness. For the AMMA only the total score, and for the IMMA only the tonal and rhythm subtest scores were skewed. If the IMMA really was too easy, the subtest scores as well as the total score should have been skewed to the right. Similarly, if the AMMA was too difficult, all test scores should have shown a significant skewness to the left. Taken together, contributions of age and difficulty may (if they are involved at all) only partly explain our results. Our findings may indicate that the small to moderate associations between musical aptitude tests are not only caused by differences in structural models underlying the different tests, but that other factors might drive these low associations. If it was only an effect of different underlying structural models about musical aptitude, we should have found high and significant associations between two tests, which are based on the same model. Perhaps the small associations between musical aptitude tests are more a matter of validity problems. The tasks that both tests contain might only seem to be very similar on a superficial level. They may in fact differ, because the IMMA requests a more analytic judgment, whereas the AMMA relies more on a holistic decision about similarity. In addition, the response format might cause differences, because the required responses differ in the type of cognitive process they rely on. The response format of the IMMA is more similar to a discrimination task (same or different), whereas the response format of the AMMA includes a designation task: at first it is discrimination (same or different) but the second step requires the designation of a particular difference. Hence, the AMMA requests a two-step answer that might be cognitively more demanding. Beyond that, the AMMA comprises several musical features (i.e., pitch and rhythm not disentangled), whereas the IMMA presents musical features in a more isolated fashion. This fact might also contribute to differences in cognitive processing and task demand, which in turn might explain our non-significant correlations. Beyond that, it might be possible that successful test taking in the case of the IMMA and AMMA depends not only on musical aptitude, but also on other abilities.

Associations between the IMMA as well as the AMMA and confounding variables

Indeed, the differing correlations that we found between the IMMA and the confounding variables compared to the AMMA and its confounding variables support this notion. Both tests were not correlated with general cognitive abilities. This finding is in accordance with the assumption Gordon postulates about his tests: that they should be independent of IQ. The IMMA was correlated with SES and music training, whereas the AMMA was not. These results may be interpreted as supportive evidence for the notion that different abilities are needed to perform successfully on these tests. The correlation of the IMMA with music training contradicts Gordon’s postulation that his tests assess musical aptitude in a way that is not influenced by music training. However, with an adjusted alpha level, these correlations were not significant. Thus, applying a more conservative approach means Gordon’s assumption could be right.

Taken together, our results indicate that it might be necessary to evaluate the Gordon tests again. Quite possibly, the AMMA assesses musical aptitude in a purer fashion than the IMMA does. Furthermore, our findings highlight how difficult it is to assess musical aptitude.

Limitations and future directions

When interpreting the results reported above, it is important to keep some limitations in mind. Neither the IMMA nor the AMMA were perfectly adequate for the age group under investigation. However, if someone wants to compare these two tests in one sample this problem will always be present. Since the Gordon tests were designed to measure musical aptitude across a wide age range (from 3-year-old children up to university students), the sequential application of different tests should cause no problems. It might therefore be expected that all tests would yield similar estimates of musical aptitude in a person as he or she grows older. Otherwise, the whole idea of constructing musical aptitude tests for such a large developmental span would be of no use.

What might also limit our results is the relatively small sample size. It cannot be ruled out that with a larger sample the correlations might be closer to significance. However, if the observed coefficients reflect the truth, we would need a sample of at least 700 to 12,000 participants (depending on the coefficient under inspection) to reveal a significant correlation with 95% probability (Faul, Erdfelder, Buchner, & Lang, 2009; Faul, Erdfelder, Lang, & Buchner, 2007).

Another limitation of our study might be the correlational design, which only allows a comparison of the IMMA and the AMMA at one point in time. It could be interesting to compare their results repeatedly in a longitudinal approach. However, the realization of such a longitudinal design remains up to future studies.

Beyond these limitations, it is also important to keep in mind that we only tested 9- to 13-year-old children, and therefore can only make conclusions about this age group. It is not clear if the same results would be obtained in children older than 13 years.

Our study has shown that it is a difficult endeavor to measure musical aptitude, but it is important to have reliable and valid musical aptitude tests. Hence, it might be useful for future research to critically evaluate and improve already existing musical aptitude tests, or create promising new measurements. Our findings might thus contribute to the improvement of tests. When one plans to apply tests of a similar type across a wider age range, even small attempts to facilitate the test for younger age groups (e.g., disentangle rhythm tasks from pitch tasks), as is the case for the IMMA, seem to make a crucial difference. Thus, test constructors should try to find another way of making a test suitable for younger age groups than isolating musical features. In this regard, it might also be important to use musical material instead of artificial stimuli. Another point raised by our findings is the potential problem of assessing musical aptitude independently of musical experience (e.g., music lessons). Although Gordon aimed at assessing musical aptitude without the influence of music experience effects, the IMMA seems to be related to amount of music lessons, at least in our sample. Hence, for the future it is important to be aware of this impurity problem. On the one hand, our findings could yield the assumption that it is not possible to measure musical aptitude purely, which comes as no surprise when taking into account reasonable definitions of musical aptitude (Gembris, 2003). On the other hand, this result highlights the importance of controlling for the influences of music experience when constructing a musical aptitude test.