University of Florence, Italy



University of Florence, Italy




The aim of this study was to investigate students’ achievement in introductory statistics courses taking into account the relationships between cognitive and non-cognitive factors. It was hypothesised that achievement was related to background in mathematics (a cognitive variable), as well as to attitudes toward statistics and anxiety (non-cognitive variables). Students were presented with measures assessing their attitudes, mathematical competence, and anxiety toward courses and examinations at the beginning and at the end of their statistics course. Achievement was assessed by tasks assigned during the course, as well as by students’ final grades and the number of exam failures. The results reveal the relationships between cognitive and non-cognitive factors, their changes during the course, and how both interact in predicting achievement.


Keywords: Statistics education research; Statistics attitudes; Statistics anxiety; Mathematical competence; Structural equation modelling



Statistics Education Research Journal, 9(1), 6-26,

Ó International Association for Statistical Education (IASE/ISI), May, 2010




Arbuckle, J. L. (2003). Amos 5.0 [Computer software]. Chicago: Smallwaters.

Auzmendi, E. (1991, April). Factors related to attitude toward statistics: A study with a Spanish sample. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

Baloglu, M. (2002). Psychometric properties of the statistics anxiety scale. Psychological Reports, 90(11), 315-125.

Bandalos, D. L., Finney, S. J., & Geske, J. A. (2003). A model of statistics performance based on achievement goal theory. Journal of Educational Psychology, 95(3), 604-616.

Bell, J. A. (1998). International students have statistics anxiety too! Education, 118(4), 634-636.

Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238–246.

Bentler, P. M. (1995). EQS: Structural equations program manual. Encino, CA: Multivariate Software, Inc.

Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88(3), 588–606.

Bollen, K. A. (1986). Sample size and Bentler and Bonett’s nonnormed fit index. Psychometrika, 51(3), 375–377.

Bollen, K. A. (1989a). Structural equations with latent variables. New York: Wiley.

Bollen, K. A. (1989b). A new incremental fit index for general structural equation models. Sociological Methods and Research, 17(3), 303–316.

Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen, & J. S. Long (Eds.) Testing structural equation models (pp. 136–162). Newbury Park, CA: Sage.

Budé, L., Van De Wiel, M. W. J., Imbos, T., Candel, M. J. J. M., Broers, N. J., & Berger, M. P. F. (2007). Students’ achievements in a statistics course in relation to motivational aspects and study behaviour. Statistics Education Research Journal, 6(1), 5-21.


Carmona, M. J. (2004a, July). Mathematical background and attitudes toward statistics in a sample of undergraduate students. Paper presented at the 10th International Congress on Mathematics Education, Copenhagen, Denmark.


Carmona, M. J. (2004b). Una revisión de las evidencias de fiabilidad y validez de los cuestionarios de actitudes y ansiedad hacia la estadística [A review of the evidence of reliability and validity of questionnaires of attitudes and anxiety towards statistics]. Statistics Education Research Journal, 3(1), 5-28.

Carmona J., Primi, C., & Chiesi, F. (2008, July). Testing for measurement invariance of the Survey of Attitudes Toward Statistics: A comparison of Italian and Spanish students. III European Congress of Methodology, Oviedo, Spain.

Cashin, S. E., & Elmore, P. B. (2005). The Survey of Attitudes Toward Statistics scale: A construct validity study. Educational and Psychological Measurement, 65(3), 1-16.

Chiesi, F,. & Primi, C. (2009). Assessing statistics attitudes among college students: Psychometric properties of the Italian version of the Survey of Attitudes Toward Statistics (SATS). Learning and Individual Differences, 19(2), 309-313.

Chiesi, F., Primi, C., & Ciancaleoni, M. (2008). Le proprietà psicometriche della Statistics Anxiety Rating Scale [The psychometric properties of STARS]. Psicologia dell’Educazione, 3(2), 48-58.

Chiorri C., Chiesi F., Piattino S., Primi C., & Vannucci M. (2009). Ansia nei confronti della statistica e stile cognitivo: Un'indagine sugli studenti di psicologia [Anxiety about statistics and cognitive style: A survey of psychology students]. Proceedings of the III Congress “Verso una nuova qualità dell'insegnamento e apprendimento della Psicologia.” [Online:]

Ciancaleoni, M., Galli, S., Chiesi, F., & Primi, C. (2008, July). Assessing the predictive validity of the mathematical ability scale constructed applying the Rasch model. Paper presented at III European Congress of Methodology, Spagna, Oviedo.

Cruise, J. R., Cash, R. W., & Bolton, L. D. (1985). Development and validation of an instrument to measure statistical anxiety. In American Statistical Association Proceedings of the Section on Statistical Education (pp. 92-97). Alexandria, VA: American Statistical Association.

D’Andrea, L., & Waters, C. (2002). Teaching statistics using short stories: Reducing anxiety and changing attitudes. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a statistically literate society, Cape Town, South Africa. [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.

[Online: ]

Dauphinee, T. L., Schau, C., & Stevens, J. J. (1997). Survey of Attitudes Toward Statistics: Factor structure and factorial invariance for female and males. Structural Equation Modeling, 4(2), 129-141.

Eccles, J., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., et al. (1983). Expectations, values, and academic behaviors. In J. T. Spence (Ed.), Achievement and Achievement Motivation (pp. 75-146). W. H. Freeman: San Francisco.

Elmore, P. B., & Lewis, E. L. (1991, April). Statistics and computer attitudes and achievement of students enrolled in Applied Statistics: Effect of a computer laboratory. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL.

Feldt, L. B., Woodruff, D. J., Salih, F. A., & Srichai, M. (1986). Statistical tests and confidence intervals for Cronbach’s coefficient alpha (Iowa Testing Programs Occasional Papers No. 33). (ERIC Document Reproduction Service No. ED291755)

Finney, S. J., & Schraw, G. (2003). Self-efficacy beliefs in college statistics courses. Contemporary Educational Psychology, 28(2), 161-186.

Fitzgerald, S. M., Jurs, S., & Hudson, L. M. (1996). A model predicting statistics achievement among graduate students. College Student Journal, 30, 361-366.

Franklin, C. A., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., et al. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K–12 curriculum framework. Alexandria, VA: American Statistical Association.


Gal, I., Ginsburg, L., & Schau, C. (1997). Monitoring attitudes and beliefs in statistics education. In I. Gal & J. B. Garfield (Eds.), The assessment challenge in statistics education (pp. 37-51). Amsterdam: IOS Press.

Galli, S., Chiesi, F., & Primi, C. (2008). The construction of a scale to measure mathematical ability in psychology students: An application of the Rasch Model. TPM (Testing Psicometria Metodologia), 15(1), 1-16.

Garfield, J. (2003). Assessing statistical reasoning. Statistics Education Research Journal, 2(1), 22-38.


Gravetter, F. J., & Wallnau, L. B. (1996). Statistics for the behavioural sciences: A first course for students of psychology and education. St. Paul, MN: West.

Harlow, L. L., Burkholder, G. J., & Morrow, J. A. (2002). Evaluating attitudes, skill, and performance in a learning-enhanced quantitative methods course: A structural modelling approach. Structural Equation Modeling, 9(3), 413-430.

Hilton, S. C., Schau, C., & Olsen, J. A. (2004). Survey Attitudes Toward Statistics: Factor structure invariance by gender and by administration time. Structural Equation Modeling, 11(1), 92-109.

Keeley, J., Zayac, R. M., & Correia, C. (2008). Curvilinear relationships between statistics anxiety and performance among undergraduate students: Evidence for optimal anxiety. Statistics Education Research Journal, 7(1), 4-15.


Kline, R. B. (1998). Principles and practice of Structural Equation Modeling. New York: Guilford Press.

Lalonde, R. N., & Gardner, R. C. (1993). Statistics as a second language? A model for predicting performance in psychology students. Canadian Journal of Behavioural Science, 25(1), 108-125.

Marcoulides, G. A., & Hershberger, S. L. (1997). Multivariate statistical methods. A first course. Mahwah, NJ: Lawrence Erlbaum Associates.

Marsh, H. W., & Hocevar, D. (1985). Application of confirmatory factor analysis to the study of self-concept: First- and higher-order factor models and their invariance across groups. Psychological Bulletin, 97(3), 562-582.

McCall, C. H., Belli, G., & Madjidi, F. (1991). The complexities of teaching graduate students in educational administration introductory statistical concepts. PICTeachSt, 3, 495-497.

Muthén, B., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38(1), 171-189.

Nasser, F. (2004). Structural model of the effects of cognitive and affective factors on the achievement of Arabic-speaking pre-service teachers in introductory statistics. Journal of Statistics Education, 12(1).

[Online: jse/v12n1/nasser.html]

Onwuegbuzie, A. J. (1998). Statistics anxiety: A function of learning style? Research in School, 5(1), 43-52.

Onwuegbuzie, A. J. (2000). Statistics anxiety and the role of self-perceptions. Journal of Educational Research, 93(5), 323-335.

Onwuegbuzie, A. J. (2003). Modeling statistics achievement among graduate students. Educational and Psychological Measurement, 63(6), 1020-1038.

Onwuegbuzie, A. J., & Seaman, M. (1995). The effect of time constraints and statistics test anxiety on test performance in a statistics course. Journal of Experimental Education, 63(2), 115-124.

Onwuegbuzie, A. J., & Wilson, V. A. (2000, November). Statistics anxiety: Nature, etiology, antecedents, effects, and treatments: A comprensive review of the literature. Paper presented at the Annual Meeting of the Mid-South Educational Research Association, Lexington, KY.

Onwuegbuzie, J. A., Bailey, P., & Daley, C. E. (2002). The role of foreign language anxiety and students’ expectations in foreign language learning. Research in the Schools, 9(1), 33-50.

Perney, J., & Ravid, R. (1990, April). The relationship between attitudes toward statistics, math self-concepts, test anxiety and graduate students’ achievement in an introductory statistics course. Paper presented at the Annual Meeting of the American Educational Research Association, Boston.

Primi, C., & Chiesi, F. (2007). Come promuovere il rendimento all’esame di Psicometria: un modello per identificare i predittori sui quali intervenire [How to promote the efficiency of psychometrics under consideration: A model to identify the influential predictors]. Proceedings of the II° Convegno“Verso una nuova qualità dell'insegnamento e apprendimento della Psicologia” (pp. 624-637).


Roberts, D. M., & Bilderback, E. W. (1980). Reliability and validity of statistics attitudes survey. Educational and Psychological Measurement, 40(1), 235-238.

Schau, C. (2003, August). Students’ attitudes: The “other” important outcome in statistics education. Paper presented at the Joint Statistical Meetings, San Francisco, CA.

Schau, C., Stevens, J. J., Dauphinee, T. L., & Del Vecchio, A. (1995). The development and validation of the survey of attitudes toward statistics. Educational and Psychological Measurement, 55(5), 868-875.

Schumaker, R. E., & Lomax, R. G. (1996). A beginner’s guide to structural equation modeling. Mahwah, NJ: Lawrence Erlbaum.

Schutz, P. A., Drogosz, L. M., White, V. E., & Distefano, C. (1998). Prior knowledge, attitude, and strategy use in an introduction to statistics course. Learning and Individual Differences, 10(4), 291-308.

Sorge, C., & Schau, C. (2002, April). Impact of engineering students’ attitudes on achievement in statistics: A structural model. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans.

Steiger, J. H., & Lind, J. C. (1980, May). Statistically-based tests for the number of common factors. Paper presented at the Annual Spring Meeting of the Psychometric Society, Iowa City.

Tempelaar, D. T., van Der Loeff, S. S., & Gijselaers, W. H. (2007). A structural equation model analyzing the relationship of students’ attitudes toward statistics, prior reasoning abilities and course performance. Statistics Education Journal, 6(2), 78- 102.


Tremblay, P.F., Gardner, R. C., & Heipel, G. (2000). A model of the relationships among measures of affect, aptitude, and performance in introductory statistics. Canadian Journal of Behavioral Science, 32(1), 40-48.

Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38(1), 1–10.

Wheaton, B., Muthén, B., Alwin, D. F., & Summers, G. F. (1977). Assessing reliability and stability in panel models. In D. R. Heise (Ed.), Sociological methodology (pp. 84–136). San Francisco, CA: Jossey-Bass.

Wise, S. L. (1985). The development and validation of a scale measuring attitudes toward statistics. Educational and Psychological Measurement, 45(2), 401-405.

Wisenbaker, J. M., Scott, J. S., & Nasser, F. (2000, July/August). Structural equation models relating attitudes about and achievement in introductory statistics courses: A comparison of results from the U.S. and Israel. Paper presented at the 9th International Congress on Mathematics Education, Tokyo, Japan.

Zeidner, M. (1991). Statistics and mathematics anxiety in social science students: Some interesting parallels. British Journal of Educational Psychology, 61(3), 319-328.



Department of Psychology, University of Florence

via di San Salvi 12, Complesso di San Salvi, Padiglione 26

50135 Florence ITALY