Statistics as a Second Language? A Model for Predicting Performance in Psychology Students

The purpose of this study wns to test a model for predicting the performance of psychology students in statistics. Previous research in this area examined statistical performance in relation to three classes of variables: anxiety, attitudes, and ability. These variables are the essential components of an educational model developed by Gardner within the context of second language learning. It is argued that learning statistics is analogous to learning a second language, and that Gardner's model provides an integrative framework for understanding and predicting statistical performance. Measures assessing mathematical aptitude, math anxiety, and attitudinal and motivational variables were administered to volunteers from two introductory statistics courses in a psychology program. A causal model linking these variables was proposed and tested using a I.ISRKI. analysis. The results, which generally supported the model, are discussed in terms of their theoretical and practical implications. Resume I.c but de cette etude etait d'evaluer un modele pour la prediction dc la performance d'etudiants en statistiques. Les etudes anterieures ont examine trois types de variables en relation avec la performance en statistiques: l'anxiete, les attitudes et l'habiletc. Ccs memes variables sont a la base d'un modele d'apprentissage de langue scconde developpe par Gardner. II est possible que l'etude des statistiques soit analogue a I'apprenrissage d'unc langue seconde et que Ie modele de Gardner soit utile pour la comprehension et la prediction de la performance en statistiques. I/aptitude pour Ics math£matiques, 1'anxieK: envers les mathematiques, les attitudes et la motivation ont £t£ evaluecs chez des etudiants de psychologie qui prenaient un cours d'introduction aux statistiques. Un modele causal reliant ces variables fut eValue avec une analyse USRIIL. Les implications theoriques et pratiques des resultats de cette recherche sont discutees. One of the most prominent courses for many students of psychology is the introductory statistics course. While undergraduate programs differ in the Canadian Journal of Behavioural Science, 1993, 25:1, 108-125 Predicting Statistical Performance 109 number of methodological and statistical courses they require, virtually all of them have one course that involves basic descriptive and inferential statistics. The title of the course and its content may vary from program to program, but from the perspective of the student the course is commonly referred to by many as "stats" and by a significant minority as "sadistics". It is the latter perception that has led teachers to develop curricula designed to help students acquire an appreciation and understanding of the use of statistics in psychology (Dilbeck, 1983; Hastings, 1982; Greer & Semrau, 1984; Lovie & Lovie, 1973), and researchers to address the processes involved in learning statistics. In our experience, and that of other teachers (Hastings, 1982; Ray, 1962) it has been beneficial to conceptualize the learning of statistics as analogous to the learning of a language. In this paper the critical variables that have been examined by researchers studying the learning of statistics will be examined in a social psychological model of learning that has been developed within the context of second language learning. The research examining factors contributing to the successful acquisition of statistical knowledge mirrors much of the research addressing the learning of other subject matters such as mathematics and second languages. Most of the variables that have been examined fall within three broad categories: anxiety, attitudes, and ability. We will introduce these variables separately, since only a few studies have looked at all three classes of variables in relation to performance in statistics (Adams & Holcomb, 1986; Feinberg & Halperin, 1978). Anxiety Any teacher of statistics can attest to the significant number of students experiencing apprehension with regard to their ability to perform well in the course. This anxiety most likely stems from the individual's history of performance and affective reactions in learning mathematics, and is present when the individual enters a university program. In fact, Betz (1978) found that "math anxiety" is experienced by a significant number of college students. In the case of a psychology sample, Betz found that at least one quarter of the students expressed considerable math anxiety, and that this was more evident for female than male students. She also found a negative correlation between math anxiety and mathematics achievement for female psychology students. Math anxiety thus represents a potential stumbling block for many students enrolled in statistics courses, and a few studies have looked at the relationship between math anxiety and performance in statistics. Morris, Kellaway and Smith (1978) measured math anxiety using the Math Anxiety Rating Scale (MARS; Suinn, Edie, Nicoletti & Spinelli, 1972) in mathematics students and introductory statistics students in psychology, and found higher levels of math anxiety for those in psychology compared to those in mathematics. Furthermore, a higher level of math anxiety was significantly n o Lalonde and Gardner related to poorer performance in statistics for the psychology students. Adams and Holcomb (1986) also present evidence of a relationship between math anxiety and performance in statistics for a group of graduate majors in education and psychology. They found no significant relationship, however, between performance in statistics and traditional measures of trait and state anxiety (Speilberger, Gorsuch, & Lushene, 1970). Feinberg and Halperin (1978), on the other hand, found a small but significant relationship between the same measure of state anxiety and performance in statistics for a group of students who were primarily enrolled in liberal arts programs. They found no relationship, however, between performance and trait anxiety. In summary, math anxiety seems to be prevalent among psychology students and is a consistent predictor of their performance in statistics. Math anxiety also seems to be different from and more specific than general anxiety (Adams & Holcomb, 1986; Morris et al., 1978) and a better predictor of success in learning statistics than trait or state anxiety. Attitudes Most of the research examining altitudes in relation to statistics has been directed at test construction and validation. Two scales, the Statistics Attitude Scale (SAS: Roberts & Bilderback, 1980) and the Attitude Towards Statistics scale (ATS: Wise, 1985) have been developed. In validating these scales, attitude toward statistics has usually been found to correlate positively with scores in statistics courses (Roberts & Bilderback, 1980; Roberts & Reese, 1987; Roberts & Saxe, 1982; Waters, Martelli, Zakrajsek & Popovich, 1988; Wise, 1985). In addition to these core findings, Roberts and Saxe (1982) reported that students who performed better on a basic mathematics test and who had taken a greater number of mathematics courses had more favourable attitudes towards statistics. While the scales specifically measuring attitudes towards statistics have been found to be related to performance in statistics, other more general attitude measures have not had the same success in prediction. Adams and Holcomb (1986) found no significant relationship between a mathematics attitude scale and achievement in statistics, while Feinberg and Halperin (1987) did. These mixed results suggest that a more specific measure of attitude may be a better predictor of behaviour, a result that is suggested by the work of Ajzen and Fishbein (1977) on the attitude-behaviour relationship. Of final note in the Adams and Holcomb (1986) and Feinberg and Halperin (1978) studies is that their anxiety measures, which were predictive of performance, correlated significantly and negatively with their attitude towards mathematics measures. These results suggest that both attitudes and anxiety are interrelated affective measures involved in learning statistics. Mathematical Ability Although it is our belief that an understanding of statistics and its applicaPredicting Statistical Performance 111 tions to psychological data does not require a sophisticated mathematical background, the relationship between mathematical ability and performance in statistics cannot be ignored. Both Adams and Holcomb (1986) and Feinberg and Halperin (1979) found significant positive relationships between performance in statistics and basic mathematical ability. In addition to the direct influence that mathematical ability can have on the acquisition of statistical skills, it should also share an important relationship with math anxiety. Past experience with mathematics should be a significant participant in the etiology of math anxiety. In fact, a number of studies report significant relationships between mathematical ability and math anxiety, where individuals who have weaker mathematical skills demonstrate greater math anxiety (Adams & Holcomb, 1986; Betz, 1978; Suinn et al., 1972). A model for predicting statistical performance: Thinking of statistics as a second language There are many theoretical models of educational achievement that offer general frameworks that can be applied to various educational subjects, including statistics (e.g. Bloom, 1976; Bruner, 1966; Carroll, 1963; Glaser, 1976). All of the variables deemed important by researchers addressing the learning of statistics (anxiety, attitudes, ability), however, are part of a more specialized socio-educational model that has been developed by Gardner (1979, 1981, 1985) in the area of second language learning. Gardner's model will be used as a basis for understanding the learning of statistics for two reasons. First, we believe that the conceptualization of statistics learning as language learning is both meaningful and fruitful. Furthermore, many of the