The article extends and applies previous approaches by Klauer and Fischer to the statistical evaluation of ability changes in tests conforming to the Rasch model (RM). Exact uniformly most powerful unbiased (UMPU) hypothesis tests and uniformly most accurate (UMA) confidence intervals (CIs) for the amount of change can be constructed for each testee separately. Under the H0 of no change, the individual p values of testees can be aggregated also within groups. The current results extend this method by an estimator for a group effect, an exact UMPU test of its significance, a corresponding UMA CI, and a likelihood ratio test for group comparisons. All these methods are applied to two sets of data concerning a highly controversial issue in literature: the so-called Mozart Effect (ME). As test material, a unidimensional test of spatial ability by Gittler and Arendasy was presented to two samples of testees (Studies I and II). On the basis of these data, the occurrence of a short-term effect of the experimental condition can be demonstrated which, however, seems to be related to the relaxation between pretest and posttest rather than to the musical priming.
AdlmannE. M. (2005). Unterschiede in der Raumvorstellung bei professionellen Musikern und Nicht-Musikern unter Berücksichtigung des “Mozart-Effekts” und der psychologischen Androgynie-Messung [Differences in spatial ability in professional musicians and non-musicians considering the “Mozart effect” and the psychological measures of androgyny](Unpublished master’s thesis). University of Vienna, Vienna, Austria.
2.
AndersenE. B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38, 123–140.
3.
AndersenE. B. (1980). Discrete statistical models with social science applications. Amsterdam, Netherlands: North-Holland.
4.
Barndorff-NielsenO. (1978). Information and exponential families in statistical theory. New York, NY: Wiley.
5.
BeverT. G.ChiarelloR. J. (1974). Cerebral dominance in musicians and nonmusicians. Perceptual and Motor Skills, 60, 31–36.
6.
BrownT. L.WilsonT. L. (1997). Reexamination of the effect of Mozart’s music on spatial-task performance. Journal of Psychology, 131, 365–370.
7.
ChabrisC. F. (1999). Prelude or requiem for the “Mozart effect”?Nature, 400, 826–827.
8.
CollinsL. M. (1996). Is reliability obsolete? A commentary on “Are simple gain scores obsolete?”Applied Psychological Measurement, 20, 289–292.
9.
CollinsL. M.HornJ. L. (Eds.). (1991). Best methods for the analysis of change. Washington, DC: American Psychological Association.
10.
CrncecR.WilsonS. J.PriorM. (2006). No evidence for the Mozart Effect in children. Music Perception, 23, 305–317.
11.
CronbachL. J.FurbyL. (1970). How should we measure change, or should we?Psychological Bulletin, 74, 68–80.
12.
DavidF. N.KendallM. G.BartonD. E. (1966). Symmetric function and allied tables. Cambridge, England: Cambridge University Press.
13.
DouglasK. M.BilkeyD. K. (2007). Amusia is associated with deficits in spatial processing. Nature Neuroscience, 10, 915–921.
14.
EggenT. J. H. M. (2000). On the loss of information in conditional maximum likelihood estimation of item parameters. Psychometrika, 65, 337–362.
15.
EmbretsonS. E. (2006). The continued search for nonarbitrary metrics in psychology. American Psychologist, 61, 50–55.
16.
FischerG. H. (1974). Einführung in die Theorie psychologischer Tests [Introduction to mental test theory]. Bern, Switzerland: Huber.
17.
FischerG. H. (1976). Some probabilistic models for measuring change. In de GruijterD. N. M.van der KampL. J. T. (Eds.), Advances in psychological and educational measurement (pp. 97–110). New York, NY: Wiley.
18.
FischerG. H. (1987). Applying the principles of specific objectivity and generalizability to the measurement of change. Psychometrika, 52, 565–587.
19.
FischerG. H. (1995a). Derivations of the Rasch model. In FischerG. H.MolenaarI. W. (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 15–38). New York, NY: Springer-Verlag.
20.
FischerG. H. (1995b). Some neglected problems in IRT. Psychometrika, 60, 459–487.
21.
FischerG. H. (2001). Gain scores revisited under an IRT perspective. In BoomsmaA.van DuijnM. A. J.SnijdersT. A. B. (Eds.), Essays on item response theory. Lecture Notes in Statistics 157 (pp. 43–68). New York, NY: Springer-Verlag.
22.
FischerG. H. (2003). The precision of gain scores under an item response theory perspective: A comparison of asymptotic and exact conditional inference about change. Applied Psychological Measurement, 27, 3–26.
23.
FischerG. H.MolenaarI. W. (Eds.). (1995). Rasch models. Foundations, recent developments, and applications. New York, NY: Springer-Verlag.
24.
FischerG. H.Ponocny-SeligerE. (1998). Structural Rasch modeling. Handbook of the usage of LPCM Win 1.0. Groningen, Netherlands: SciencePlus.
25.
FisherR. A. (1932). Statistical methods for research workers (5th ed.). Edinburgh, Scotland: Oliver & Boyd.
26.
FormannA. K. (1981). Über die Verwendung von Items als Teilungskriterium für Modellkontrollen im Modell von Rasch [About the use of items as dividing criteron for model control in the model of Rasch]. Zeitschrift für Experimentelle und Angewandte Psychologie, 28, 541–560.
27.
GittlerG.ArendasyM. (2003). Endlosschleifen: Psychometrische Grundlagen des Aufgabentyps EP [Endless loops: The psychometric basis of item type EP]. Diagnostica, 49, 164–175.
28.
GlasC. A. W.VerhelstN. D. (1995). Testing the Rasch Model. In FischerG. H.MolenaarI. W. (Eds.), Rasch Models. Foundations, recent developments, and applications (pp. 69–95). New York, NY: Springer.
29.
GulliksenH. (1950). Theory of mental tests. New York, NY: Wiley.
30.
HarrisC. W. (Ed.). (1963). Problems in measuring change. Madison, WI: University of Wisconsin Press.
31.
HasslerM. (1992). Testosterone, estradiol, ACTH, and musical, spatial and verbal performance. International Journal of Neuroscience, 65, 45–60.
HetlandL. (2000). Listening to music enhances spatial-temporal reasoning: Evidence for the “Mozart Effect.”. Journal of Aesthetic Education, 34, 105–148.
34.
IvanovV. K.GaekeJ. G. (2003). The Mozart effect and primary school children. Psychology of Music, 31, 405–413.
35.
JänckeL. (2001). Was ist so Besonders an den Gehirnen von professionellen Musikern? [What is so special about the brains of professional musicians?]. Zeitschrift für Medizinische Psychologie, 10, 107–114.
36.
JohanssonB. B. (2006). Music and brain plasticity. European Review, 14, 49–64.
37.
KenealyP.MonsefA. (1994). Music and IQ tests. The Psychologist, 7, 346.
38.
KlauerK. C. (1991). An exact and optimal standardized person test for assessing consistency with the Rasch model. Psychometrika, 56, 213–228.
39.
KnellU. (2006). Zum “Mozart-Effekt”: Stellen musikalische Begabung und Befindlichkeit Einflussfaktoren dar? [The “Mozart effect”: musical talent and mental states as influencing factors?](Unpublished master’s thesis). University of Vienna, Vienna, Austria.
40.
KolataG. (1999). Muddling fact and fiction and policy. New York Times, WK5.
41.
LeeD. J.ChenY.SchlaugG. (2003). Corpus callosum: Musician and gender effects. NeuroReport, 14, 205–209.
42.
LehmannE. L. (1986). Testing statistical hypotheses (2nd ed.). New York, NY: John Wiley.
43.
LinnM. C.PetersenA. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child Development, 56, 1479–1498.
44.
LiouM. (1993). Exact person tests for assessing model-data fit in the Rasch model. Applied Psychological Measurement, 17, 187–195.
45.
LiouM.ChangC.-H. (1992). Constructing the exact significance level for a person fit statistic. Psychometrika, 57, 169–181.
46.
LordF. M. (1956). The measurement of growth. Educational and Psychological Measurement, 16, 421–437.
47.
LordF. M. (1963). Elementary models for measuring change. In HarrisC. W. (Ed.), Problems in measuring change (pp. 21–38). Madison: University of Wisconsin Press.
48.
LordF. M. (1983). Unbiased estimators of ability parameters, of their variances, and their parallel-forms reliability. Psychometrika, 48, 233–245.
49.
LordF. M.NovickM. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
50.
LordF. M.WingerskyM. S. (1984). Comparison of IRT true-score and equipercentile observed-score equatings. Applied Psychological Measurement, 8, 453–461.
51.
MastersG. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.
52.
McCutcheonL. E. (2000). Another failure to generalize the Mozart effect. Psychological Reports, 87, 325–330.
53.
McKelvieP.LowJ. (2002). Listening to Mozart does not improve children’s spatial ability: Final curtains for the Mozart effect. British Journal of Developmental Psychology, 20, 241–258.
54.
McLaneS.BirkoffG. (1988). Algebra (3rd ed.). New York, NY: Chelsea.
55.
M.I.N.D. Institute. (2006). Retrieved April 11, 2006, fromwww.mindinst.org
56.
NaderI. W.GittlerG.WaldherrK.PietschnigJ. (2010). Chew on this: No support for facilitating effects of gum on spatial task performance. Archives of Oral Biology, 55, 712–717.
57.
NantaisK. M.SchellenbergE. G. (1999). The Mozart effect: An artifact of preference. Psychological Science, 10, 370–373.
58.
NewmanJ.RosenbachJ. H.BurnsK. L.LatimerB. C.MatochaH. R.VogtE. R. (1995). An experimental test of the Mozart Effect: Does listening to his music improve spatial ability?Perceptual and Motor Skills, 81, 1379–1387.
59.
NguyenN.ShawG. L.TranS. (1996). [Exploring the Mozart effect: Pilot work on the effect of a distractor task]. Unpublished raw data, University of California, Irvine.
60.
OverallJ. E.WoodwardJ.A. (1975). Unreliability of difference scores: A paradox for measurement of change. Psychological Bulletin, 82, 85–86.
PonocnyI. (2000). Exact person fit indexes for the Rasch model for arbitrary alternatives. Psychometrika, 65, 29–42.
63.
PonocnyI. (2001). Non-parametric goodness-of-fit tests for the Rasch model. Psychometrika, 66, 437–460.
64.
PrielerJ. A.RavenJ. (2002). The measurement of change in groups and individuals, with particular reference to the value of gain scores: A new IRT-based methodology for the assessment of treatment effects and utilizing gain scores. Horizons of Psychology. Official Journal of the Slovenian Psychology Association, 11, 119–150.
65.
RaschG. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen, Denmark: The Danish Institute of Educational Research. (Expanded edition, 1980. Chicago, IL: University of Chicago Press.)
66.
RauscheckerJ. P. (1999). Auditory cortical plasticity: A comparison with other sensory systems. Trends in Neuroscience, 22, 74–80.
67.
RauscherF. H. (1999). Reply: Prelude or requiem for the ‘Mozart effect’?Nature, 400, 827–828.
68.
RauscherF. H.ShawG. L. (1998). Key components of the Mozart effect. Perceptual and Motor Skills, 86, 835–841.
69.
RauscherF. H.ShawG. L.KyK. N. (1993). Music and spatial task performance. Nature, 365, 611.
70.
RauscherF. H.ShawG. L.KyK. N. (1995). Listening to Mozart enhances spatial-temporal reasoning: Toward a neurophysiological basis. Neuroscience Letters, 185, 44–47.
71.
RideoutB. E.DoughertyS.WernertL. (1998). Effect of music on spatial performance: A test of generality. Perceptual and Motor Skills, 86, 512–514.
72.
RideoutB. E.TaylorJ. (1997). Enhanced spatial performance following 10 minutes exposure to music: A replication. Perceptual and Motor Skills, 85, 112–114.
73.
RogosaD. R. (1988). Myths about longitudinal research. In SchaieK. W.CampbellR. T.MeredithW. M.RawlingsS. C. (Eds.), Methodological issues in aging research (pp. 171–209). New York, NY: Springer.
74.
SteeleK. M. (2001). “The Mozart Effect”: An example of the scientific method in operation. Psychology Teacher Network, 11, 2–5.
75.
SteeleK. M.BallT. N.RunkR. (1997). Listening to Mozart does not enhance backwards digit span performance. Perceptual and Motor Skills, 84, 1179–1184.
76.
SteeleK. M.BassK. E.CrookM. D. (1999). The mystery of the Mozart effect. Psychological Science, 10, 366–369.
77.
SteeleK. M.BrownJ. D.StoeckerJ. A. (1999). Failure to confirm the Rauscher and Shaw description of recovery of the Mozart effect. Perceptual and Motor Skills, 88, 843–848.
78.
SteeleK. M.Dalla BellaS.PeretzI.DunlopT.DaweL. A.HumphreyG. K.… OlmsteadC. G. (1999). Prelude or requiem for the ‘Mozart effect’?Nature, 400, 827.
79.
ThompsonW. F.SchellenbergE. G.HusainG. (2001). Arousal, mood, and the Mozart effect. Psychological Science, 12, 248–251.
80.
ThorndikeR. L.HagenE. P.SattlerJ. M. (1986). The Stanford-Binet Scale of intelligence. Chicago, IL: Riverside.
81.
TwomeyA.EsgateA. (2002). The Mozart effect may only be demonstrable in nonmusicians. Perceptual and Motor Skills, 95, 1013–1026.
82.
van den WollenbergA. L. (1979). The Rasch model and time limit tests. Doctoral Thesis, Nijmegen, Netherlands: Studentenpers.
83.
VollsetS. E. (1993). Confidence intervals for a binomial proportion. Statistics in Medicine, 12, 809–824.
84.
von EyeA. (Ed.). (1990). Statistical methods in longitudinal research. (Vols. 1 and 2), New York, NY: Academic Press.
85.
WarmT. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427–450.
86.
WillettJ. B. (1989). Some results on reliability for the longitudinal measurement of change: Implications for the design of studies of individual growth. Educational and Psychological Measurement, 49, 587–602.
87.
WilliamsR. H.ZimmermanD. W. (1996). Are simple gain scores obsolete?Applied Psychological Measurement, 20, 59–69.
88.
WittingH. (1985). Mathematische Statistik I [Mathematical statistics, Vol. I]. Stuttgart, Germany: Teubner.
