Notwithstanding the prevalence of multidimensional constructs in marketing research, very few reliability analyses have taken into account the multidimensional structure of their empirical data. In this article, the author argues that if a scale can be divided into two or more distinct though related dimensions, its internal consistency should be evaluated by coefficients designed for such cases. This article presents stratified alpha as a viable alternative to the common practices of computing alpha for the whole scale and averaging alpha values. It also illustrates, using D’Astous and Lévesque’s store personality scale, that the discrepancy between stratified alpha and alpha (or alpha mean) might be substantial. Thus, it would seem more scientifically sound to compute and report stratified alpha.
AakerJ.L. (1997). Dimensions of brand personality. Journal of Marketing Research, 34(3), 347–356.
2.
AzoulayA., & KapfererJ.-N. (2003). Do brand personality scales really measure brand personality?Journal of Brand Management, 11(2), 143–155.
3.
BaumgartnerH., & SteenkampJ.-B. (2006). An extended paradigm for measurement analysis of marketing constructs applicable to panel data. Journal of Marketing Research, 43(3), 431–442.
4.
BeardenW.O., MoneyR.B., & Nevins.J.L. (2006). A measure of long-term orientation: Development and validation. Journal of the Academy of Marketing Science, 34(3), 456–467.
5.
BeardenW.O., NetemeyerR.G., & HawsK.L. (2011). Handbook of marketing scales: Multi-item measures for marketing and consumer behavior research (3rd ed.). Thousand Oaks, CA: SAGE Inc.
6.
BergkviestL., & RossiterJ.R. (2007). The predictive validity of multiple-item versus single-item measures of the same constructs. Journal of Marketing Research, 44(2), 175–184.
7.
BrakusJ.J., SchmittB.H., & ZarantonelloL. (2009). Brand experience: What is it? How is it measured? Does it affect loyalty?Journal of Marketing, 73(3), 52–68.
8.
BrunerG.C., & HenselP.J. (1993). Multi-item scale usage in marketing journals: 1980 to 1989. Journal of the Academy of Marketing Science, 21(4), 339–344.
9.
BrunerG.C., HenselP.J., & JamesK.E. (2005). Marketing scales handbook: A compilation of multi-item measures (vol. 4). Chicago, IL: American Marketing Association.
10.
CharterR.A. (2003). A breakdown of reliability coefficients by test type and reliability method, and the clinical implications of low reliability. Journal of General Psychology, 130(3), 290–304.
11.
ChurchillG.A. (1979). A paradigm for developing better measures of marketing constructs. Journal of Marketing Research, 16(1), 64–73.
12.
ChurchillG.A. & PeterJ.P. (1984). Research design effects on the reliability of rating scales: A meta-analysis. Journal of Marketing Research, 21(4), 360–375.
13.
CortinaJ.M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78(1), 98–104.
14.
CronbachL.J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334.
15.
CronbachL.J., RajaratnamN., & GleserG.C. (1963). Theory of generalizability: A liberalization of reliability theory. British Journal of Statistical Psychology, 16(November), 137–163.
16.
CronbachL.J., SchönemannP., & McKie.D. (1965). Alpha coefficients for stratified-parallel tests. Educational and Psychological Measurement, 25(2), 291–312.
17.
D’AstousA., Hadj SaïdI., & LévesqueM. (2002). Conception et test d’une échelle de mesure de la personnalité des magasins. Paper presented at the 18th International Conference of the French Marketing Association, Lille, France. Retrieved 10June2009, from http://www.afm-marketing.org
18.
D’AstousA., & LévesqueM. (2003). A scale for measuring store personality. Psychology & Marketing, 20(5), 455–469.
19.
DasG. (2014). Store personality and consumer store choice behaviour: An empirical examination. Marketing Intelligence & Planning, 32(3), 375–394.
20.
DasG., GuinK.K., & DattaB. (2013). Impact of store personality antecedents on store personality dimensions: An empirical study of department retail brands. Global Business Review, 14(3), 471–486.
21.
DroletA.L., & MorrisonD.G. (2001). Do we really need multiple-item measures in service research?Journal of Service Research, 3(3), 196–204.
22.
DuhachekA., CoughlanA.T., & IacobucciD. (2005). Results on the standard error of the coefficient alpha index of reliability. Marketing Science, 24(2), 294–301.
23.
DuhachekA., & IacobucciD. (2004). Alpha’s standard error (ASE): An accurate and precise confidence interval estimate. Journal of Applied Psychology, 89(5), 792–808.
24.
FeldtL.S., & CharterR.A. (2003). Estimating the reliability of a test split into two parts of equal or unequal length. Psychological Methods, 8(1), 102–109.
25.
FeldtL.S., & QuallsA.L. (1996). Bias in coefficient alpha arising from heterogeneity of test content. Applied Measurement in Education, 9(3), 277–286.
FinnA., & Kayandé, U. (1997). Reliability assessment and optimization of marketing measurement. Journal of Marketing Research, 34(May), 262–275.
28.
FinnA., & Kayandé, U. (2004). Scale modification: Alternative approaches and their consequences. Journal of Retailing, 80(1), 37–52.
29.
GerbingD.W., & AndersonJ.C. (1988). An updated paradigm for scale development incorporating unidimensionality and its assessment. Journal of Marketing Research, 25(May), 186–192.
30.
GeuensM., WeijtersB., & De WulfK. (2009). A new measure of brand personality. International Journal of Research in Marketing, 32(1), 97–107.
31.
GrahamJ.M. (2006). Congeneric and (essentially) tau-equivalent estimates of score reliability: What they are and how to use them?Educational and Psychological Measurement, 66(6), 930–944.
32.
GreenS.B., LissitzR.W., & MulaikS.A. (1977). Limitations of coefficient alpha as an index of test unidimensionality. Educational and Psychological Measurement, 37(4), 827–838.
33.
HardestyD.M., & BeardenW.O. (2004). The use of expert judges in scale development: Implications for improving face validity of measures of unobservable constructs. Journal of Business Research, 57(2), 98–107.
34.
HeiseD.R., & BohrnstedtG.W. (1970). Validity, invalidity and reliability. In BorgattaE.F. & BohrnstedtG.W. (Eds), Sociological methodology (pp. 104–129). San Francisco, CA: Jossey-Bass.
35.
HelmsJ.E., HenzeK.T., SassT.L., & MifsudV.A. (2006). Treating Cronbach’s alpha reliability coefficients as data in counseling research. The Counseling Psychologist, 34(5), 630–660.
36.
HoganT.P., BenjaminA., & BrezinskiK.L. (2000). Reliability methods: A note on the frequency of use of various types. Educational and Psychological Measurement, 60(4), 523–531.
37.
HornJ.L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(June), 179–185.
38.
IacobucciD. (1994). Classic factor analysis. In BagozziR.P. (Ed.), Principles of marketing research (pp. 279–316). Cambridge, MA: Blackwell.
39.
IacobucciD. (2001). Factor analysis. Journal of Consumer Psychology, 10(1/2), 75–76.
40.
JarvisC., MacKenzieS.B., & PodsakoffP.M. (2003). A critical review of construct indicators and measurement model misspecification in marketing and consumer research. Journal of Consumer Research, 30(September), 199–218.
41.
JhaS., & BhattacharyyaS.K. (2013). Learning orientation and performance orientation: Scale development and its relationship with performance. Global Business Review, 14(1), 43–54.
42.
JöreskogK.G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36(2), 109–133.
43.
KamataA., TurhanA., & DarandariE. (2003). Estimating reliability for multidimensional composite scale scores. Paper presented at the annual meeting of the American Educational Research Association, April, Chicago, IL. Retrieved 3January2010, from http://www.coe.fsu.edu/AERA/Kamata2.pdf
44.
KoçakA., AbimbolaT., & ÖzerA. (2007). Consumer brand equity in a cross-cultural replication: An evaluation of a scale. Journal of Marketing Management, 23(1/2), 157–173.
45.
KomaroffE. (1997). Effect of simultaneous violations of essential tau–equivalence and uncorrelated error on coefficient alpha. Applied Psychological Measurement, 21(4), 337–348.
46.
LeeN., & HooleyG. (2005). The evolution of ‘classical mythology’ within marketing measure development. European Journal of Marketing, 39(3/4), 365–385.
47.
LiH., RosenthalR., & RubinD.B. (1996). Reliability of measurement in psychology: From Spearman–Brown to maximal reliability. Psychological Methods, 1(1), 98–107.
48.
LordF.M., & NovickM.R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
49.
LuckeJ.F. (2005). ‘Rassling the hog’: The influence of correlated item error on internal consistency, classical reliability, and congeneric reliability. Applied Psychological Measurement, 29(2), 106–125.
50.
LumsdenJ. (1976). Test theory. Annual Review of Psychology, 27(1), 251–280.
51.
McDonaldR.P. (1970). The theoretical foundations of common factor analysis, principal factor analysis and alpha factor analysis. British Journal of Mathematical Psychology, 23(1), 1–21.
52.
McDonaldR.P. (1985). Factor analysis and related methods. Hillsdale, NJ: Erlbaum.
53.
McDonaldR.P. (1999). Test theory: A unified treatment. Mahwah, NJ: Erlbaum.
NovickM.R., & LewisC. (1967). Coefficient alpha and the reliability of composite measurements. Psychometrika, 32(1), 1–13.
56.
NunnallyJ.C. (1967). Psychometric theory. New York, NY: McGraw-Hill.
57.
O’connorB.P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test. Behavior Research Methods, Instruments, & Computers, 32(3), 396–402.
58.
OsburnH.G. (2000). Coefficient alpha and related internal consistency reliability coefficients. Psychological Methods, 5(3), 343–355.
59.
PatilV.H., SinghS.N., MishraS., & DonavanT.D. (2008). Efficient theory development and factor retention criteria: Abandon the ‘eigenvalue greater than one’ criterion. Journal of Business Research, 61(2), 162–170.
60.
PeterJ.P. (1979). Reliability: A review of psychometric basics and recent marketing practices. Journal of Marketing Research, 16(1), 6–17.
61.
PeterJ.P. (1981). Construct validity: A review of basic issues and marketing practices. Journal of Marketing Research, 18(2), 133–145.
62.
PetersonR.A. (1994). A meta-analysis of Cronbach’s coefficient alpha. Journal of Consumer Research, 21(September), 381–391.
63.
PreacherK.J., & MacCallumR.C. (2003). Repairing Tom Swift’s electric factor analysis machine. Understanding Statistics, 2(1), 13–43.
64.
RaeG. (2007). A note on using stratified alpha to estimate the composite reliability of a test composed of interrelated nonhomogeneous items. Psychological Methods, 12(2), 177–184.
65.
RaeG. (2008). A note on using alpha and stratified alpha to estimate the reliability of a test composed of item parcels. British Journal of Mathematical and Statistical Psychology, 61(2), 515–525.
RaykovT. (1997). Estimation of composite reliability for congeneric measures. Applied Psychological Measurement, 21(2), 173–184.
68.
RaykovT. (1998). Coefficient alpha and composite reliability with interrelated non homogeneous items. Applied Psychological Measurement, 22(4), 375–385.
69.
RevelleW. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14(1), 57–74.
70.
RichinsM.L. (2004). The material values scale: Measurement proprieties and the development of a short form. Journal of Consumer Research, 31(June), 209–219.
71.
RossiterJ.R. (2002). The C-OAR-SE procedure for scale development in marketing. International Journal of Research in Marketing, 19(4), 305–335.
72.
RossiterJ.R. (2011). Marketing measurement revolution: The C-OAR-SE method and why it must replace psychometrics. European Journal of Marketing, 45(11), 1561–1588.
73.
SijtsmaK. (2009). On the use, the misuse, and the very limited usefulness of Cronbach’s alpha. Psychometrika, 74(1), 107–120.
74.
SmithR.E., MacKenzieS.B., YangX., BuchholzL.M., & DarleyW.K. (2007). Modeling the determinants and effects of creativity in advertising. Marketing Science, 26(6), 819–833.
75.
StreinerD.L. (2003). Starting at the beginning: An introduction to coefficient alpha and internal consistency. Journal of Personality Assessment, 80(1), 99–103.
76.
SungY., ChoiS.M., AhnH., & SongY.-A. (2015). Dimensions of luxury brand personality: Scale development and validation. Psychology & Marketing, 32(1), 121–132.
77.
VelicerW.F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321–327.
78.
VossK.E., StemD.E., & FotopoulosS. (2000). A comment on the relationship between coefficient alpha and scale characteristics. Marketing Letters, 11(2), 177–191.
79.
WertsC.E., RockD.R., LinnR.L., & JöreskogK.G. (1978). A general method of estimating the reliability of a composite. Educational and Psychological Measurement, 38(4), 933–938.
80.
WillemsK., & SwinnenG. (2011). Am I cheap? Testing the role of store personality and self-congruity in discount retailing. The International Review of Retail, Distribution and Consumer Research, 21(5), 513–539.
81.
ZinbargR.E., RevelleW., YovelI., & LiW. (2005). Cronbach’s α, Revelle’s β, and McDonald’s ωh: Their relation with each other and two alternative conceptualizations of reliability. Psychometrika, 70(1), 1–11.
82.
ZwickW.R., & VelicerW.F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletins, 99(3), 432–442.
