Orientation: The attitude of students toward statistics may influence their enrolment, achievement and motivation in the subject of research and Industrial Psychology.

Research purpose: The aims of this study were to determine the reliability and validity of the survey of attitudes toward statistics (SATS-36) for a South African sample and to determine whether biographical variables influence students’ attitudes.

Motivation for study: Students could be better prepared for, and guided through, a course in statistics if more is known about their attitudes towards statistics.

Research design, approach and method: A cross-sectional survey design was used and the SATS-36 was administered to a sample of convenience consisting of 235 students enrolled in Industrial and Organisational Psychology at a large tertiary institution in South Africa.

Main findings: Results revealed that even though students perceive statistics to be technical, complicated and difficult to master, they are interested in the subject and believe statistics to be of value. The degree to which students perceived themselves to be competent in mathematics was related to the degree to which they felt confident in their own ability to master statistics. Males displayed slightly more positive feelings toward statistics than females. Older students perceived statistics to be less difficult than younger students and also displayed slightly more positive feelings concerning statistics.

Practical implications: It seems that in preparing students for statistics, their perception regarding their mathematical competence could be managed as well.

Contribution: This study provides the first preliminary evidence for the reliability and validity of the SATS-36 for a sample of South African students.

Statistics is a methodological discipline that offers other fields of study a coherent set of ideas and tools for dealing with data. The discipline does not exist for itself, but rather provides means for dealing with data that take into account the omnipresence of variability (Cobb & Moore, 1997). Florence Nightingale went so far as to say that statistics can be viewed as the most important science in the whole world (Ridgway, Nicholson & McCusker, 2007), the reason being that the practical application of every other science depends on statistics and it is therefore the one science essential to all political and social administration as well as education (Ridgway, Nicholson & McCusker, 2007). Consequently, statistics is near-universally recognised as an important component of almost all studies at tertiary level.

The objective of a statistics course is to equip students with basic statistical skills in order to appreciate the value of statistics in their professional and personal lives (North & Zewotir, 2006). A baseline comprehension of statistics equips students to understand previous and current research, generate some of their own research, evaluate practices and draw informed conclusions regarding studies that were undertaken (Quinn, 2006). At undergraduate level, the ability to evaluate empirical evidence in published material (Mulhern & Wylie, 2004) and at postgraduate level, the ability to undertake empirical work, is central to any professional training.

However, for most students, statistics is seen only as a professional tool rather than a central skill (Petocz & Reid, 2005) and their statistics education as part of their degree does not set out to prepare them as statistics consultants. It rather prepares them to recognise when a statistician is needed and to be able to better use a statisticians’ consultancy services in their profession (North & Zewotir, 2006). As a result of this, statistics represents a new way of thinking for most students and is also seen as a somewhat unexpected component of their studies and future professions (Petocz & Reid, 2005). Most students find the completion of statistics as part of their education quite daunting (Laher, Israel & Pitman, 2007).

The perceptions and attitudes of students regarding statistics might therefore pose some challenges for everyone teaching statistics, also in the field of Industrial Psychology in South Africa. Investigating students’ attitudes towards statistics might aid those teaching statistics to better prepare and guide students through this compulsory statistical education. It can also equip teachers to influence students’ perceptions of the role of statistics in their future careers.

Students’ attitudes toward statistics

Students often view statistics as one of the biggest hurdles they face as graduate students. In this regard, Birenbaum and Eylath (1994) are of the opinion that statistics-related courses are considered by many students as the most dreadful courses in the curriculum and their experience of these courses can be rather onerous and anxiety-laden (Piotrowski, Bagui & Hemasinha, 2002). Evidence of this can also be traced to the titles of some statistics references such as ‘Statistics anxiety over learning statistics.

Students’ attitudes toward statistics may create a major obstacle for effective learning (Mills, 2004; Onwuegbuzie & Seaman, 1995) and as a result, teaching statistics and even research methods can become a major pedagogic challenge (Mulhern & Wylie, 2004). Onwuegbuzie (2000) also expressed the concern that non-cognitive issues like students’ attitudes, feelings, beliefs and perceptions may counteract the learning environment which statistics instructors are attempting to create. Earlier authors have even gone so far as to suggest that the first goal in teaching statistics should be to reduce the fear of statistics (Blalock, 1987). Garfield and Ben-Zvi (2007), in a review of a number of studies regarding how students learn statistics, suggested that teachers need to cultivate more positive beliefs about the value of statistics and statistical literacy. Teachers should also be aware that students come to statistics courses with a variety of perspectives regarding their own ability or lack of ability to succeed in the course (Garfield & Ben-Zvi, 2007). Schau (2003) found that students’ attitude toward statistics were positively related to their achievement in statistics. Hilton, Schau and Olsen (2004) believed that evidence is slowly growing to support the belief that students’ attitudes toward statistics affects their course enrolment, persistence, achievement and the general climate in the class. Since students’ attitudes toward statistics are important, we must be able to assess them.

The assessment of attitude toward statistics

Schau et al. (1995) developed an instrument, the Survey of Attitude Toward Statistics (SATS-28 item version), designed to measure attitudes toward statistics based on four facets – namely, affect (positive and negative feelings concerning statistics), cognitive competence (students’ attitudes about their own intellectual knowledge and skills when applied to statistics), value (attitudes about the usefulness, relevance and worth of statistics in one’s personal and professional life) and difficulty (attitudes about the difficulty of statistics as a subject). The SATS-28 item version has been proven to be valid and reliable for American (Mills, 2004; Schau et al., 1995) and Italian samples (Chiesi & Primi, 2009). The 28-item version was extended to a 36-item version to include two additional components – namely, interest (level of individual interest in the topic of statistics) and effort (amount of work needed to learn statistics) (Schau 2003). The SATS-36 item version has been used with a European sample (Tempelaar, Gijselaers & Van der Loeff, 2006). No records could, however, be found of this measurement being used in a South African sample.

Variables related to attitude toward statistics

Age appeared to be an influencing factor based on the time that had elapsed since previous mathematical or statistical experience (Onwuegbuzie, DaRos & Ryan, 1997; Onwuegbuzie, 2000). Baloglu (2003) also found that although older students showed more positive attitudes towards the usefulness of statistics, they tended to have higher levels of statistics anxiety.

The aim of this paper is to (1) determine the validity and reliability of the SATS-36 item version as an instrument to measure attitude toward statistics in a South African sample, (2) determine the general attitude of students towards statistics and (3) determine whether the variables of prior math experience, level of statistics course (academic year), gender and age influence students’ attitudes towards statistics.

Research approach

Research method

Participants
The characteristics of the participants are described in Table 1. The participants were 235 undergraduate (n = 111), honours (n = 107) and masters (n = 17) students enrolled in Industrial and Organisational Psychology at a large tertiary institution in South Africa. Females comprised 72.8% of the sample. More than half of the participants (52.8%) were black, whereas the remaining participants were white (30.2%), asian (10.6%) or coloured (5.1%). The average age of the sample was 31 years and the ages ranged from 19 to 58 years.

Measuring instruments
The SATS-36 (Schau, 2003) was used to measure students' attitudes toward statistics. The SATS-36 uses a 7-point Likert scale (1 = strongly disagree, 4 = neither disagree nor agree, 7 = strongly agree) and contains six subscales. Affect measures students’ feeling concerning statistics (e.g. ‘I am scared by statistics’). This subscale consists of six items and internal reliability (alpha coefficient) has been shown to range between 0.80 and 0.89. Cognitive competence investigates students’ attitudes about their intellectual knowledge and skills when applied to statistics (e.g. ‘I can learn statistics’). The subscale has six items and reliability ranged between 0.77 and 0.88. Value is a measurement of students’ attitudes about the usefulness, relevance, and worth of statistics in their personal and professional life (e.g. ‘Statistics is irrelevant in my life’). This is measured by nine items and Cronbach alpha coefficients ranged between 0.74 and 0.90. Difficulty relates to students’ attitudes about the difficulty of statistics as a subject (e.g. ‘Statistics is highly technical’). Seven items are included in this subscale and reliability coefficients ranged between 0.64 and 0.81. Four new items measure students’ level of individual interest in statistics (interest) (e.g. ‘I am interested in using statistics’) and another four items measures effort (the amount of work the student expends to learn statistics) (e.g. ‘I plan to work hard in my statistics course) (Dauphinee, Schau & Stevens, 1997; Hilton et al., 2004; Schau et al., 1995). The SATS therefore yielded good internal consistency. Schau et al. (1995) confirmed the four-factor structure of the 28-item version through confirmatory factor analysis. The estimated correlations among the four factors of the 28-item version were significant, except for the correlation between value and difficulty (Schau et al., 1995). Convergent validity was proven with the attitude towards statistics (ATS) scale of Wise (1985).

Statistical analysis
Confirmatory factor analysis was used to determine the validity of the SATS-36 for the specific sample of this study. Cronbach alpha coefficients were determined to indicate the reliability of the sub-factors of the survey. Descriptive statistics were calculated to determine the students’ attitudes towards statistics. Skewness and kurtosis were used to determine if the data are normally distributed (zskewness = S-0/SEskewness < 1.96 = normally distributed; zkurtosis = K-0/SEkurtosis < 1.96 = normally distributed). Based on the values of skewness and kurtosis displayed in Table 4, it could be seen that only cognitive competence and difficulty are normally distributed. Therefore, since most of the data are not normally distributed, non-parametric statistics were used for the rest of the analyses. Spearman correlations were used to test for the relationships between attitudes and prior math experience. Effect sizes were used to decide on the practical significance of the findings, where 0.10 was regarded as a small effect, 0.30 as a medium effect and 0.50 as a large effect (Cohen, 1988). The Mann–Whitney non-parametric t-test was used to determine the significance of difference between the level of statistics course (academic year), gender and age. Effect sizes were determined for the Mann–Whitney test by calculating r = Z/√N. This is a standardised measure of the size of the effect that is observed, where r = 0.00 – 0.29 denotes a small effect; r = 0.30 – 0.49 denotes a medium effect; and r = > 0.50 denotes a large effect (Field, 2005).

Reliability and validity of the measuring instrument

The first step in the confirmatory factor analysis was to determine whether a single factor model could possibly fit the data satisfactorily. The fit indices, as shown in Table 2, indicated that a single latent factor model could not describe the data adequately.

Secondly, the basic six-factor model was fitted which resulted in an improvement of all the fit indices considered. The Normed chi-square was acceptable, but none of the other indices conformed to the generally prescribed limits. All possible covariances between the six latent factors were introduced and used in all subsequent analyses.

Thirdly, a series of steps were followed for improving the overall fit of the model as portrayed by the indices listed in Table 2. At each possible alteration to the model, only a single change was made, the model was rerun and again inspected for possible changes. Some of the steps used included the following:

The use of Wald indices for reducing the number of non significant parameters in a given model.

La Grange multipliers were calculated for the purpose of adding new paths between latent factors and items, such as moving an item from one factor to another or for the introduction of covariance terms between the error terms of items which may indicate a common cause.

Steps 1 and 2 were reiterated until a satisfactory model was obtained. Values of 0.90 and higher signify acceptable fit for GFI, TLI and CFI, whereas values of 0.08 and lower indicate acceptable fit for RMSEA (Byrne, 2001). From Table 3 it can also be seen that items 21, 24, 27, 30 and 36 were deleted. These items had lower R²-values compared to other items and deleting them improved the model significantly.

The suggested (basic) and developed (final) measurement models are given in Table 3. All six factors had acceptable Cronbach alpha levels above 0.70, except for Difficulty (0.66).

Attitudes towards statistics

Students displayed a high level of interest in statistics (the modal score for the sub-factor of interest is 7.00, indicating that most students strongly agreed with statements like ‘I am interested in learning statistics’ or ‘I am interested in using statistics’). Students acknowledged that they were prepared to expend a high amount of work in order to learn statistics (the modal score for the subfactor of effort is 7.00, indicating that most students strongly agreed with statements like ‘I plan to work hard in my statistics course’ or ‘I plan to complete all of my statistics assignments’). Students were slightly more positive in rating their confidence in their own intellectual knowledge and skills when applied to statistics (the modal score for the subfactor cognitive competence is 5.33, indicating that most students agree with statements like ‘I can learn statistics’ or ‘I will understand statistics equations’). They tended to be somewhat neutral in their response when rating the feelings they harbour regarding statistics (the modal score for affect is 4.6, indicating that students neither disagreed, nor agreed, or slightly agreed with statements like ‘I will like statistics’ or ‘I will enjoy taking statistics courses’), as well as rating statements about the usefulness, relevance and worth of statistics in their personal and professional life (the modal score for value is 4.88, indicating that most students neither agreed nor disagreed or slightly disagreed with statements like ‘Statistics is not useful to the typical professional’ or ‘Statistics is irrelevant in my life’). They were, however, in agreement that statistics could be viewed as difficult and were slightly more negative when rating the difficulty of statistics as a subject (the modal score for difficulty is 3.40, indicating that students slightly disagreed with statements like ‘Statistics formulas are easy to understand’ or slightly agreed with statements like ‘Statistics is a complicated subject’).

Variables that influence students’ attitudes toward statistics

Students were asked the number of years they had studied mathematics at high school and how many previous mathematics or statistics courses they had completed at university. The correlations between these questions and student’s attitudes toward statistics are shown in Table 5.

From Table 5 it can be seen that no significant correlations were obtained between attitudes toward statistics and the number of years that students had studied mathematics at high school or the number of previous mathematics or statistics courses they had taken at university. An exception was a practically significant relationship of small effect between the number of years high school mathematics taken and the degree to which students believed that they had the knowledge and skills required to succeed at statistics (cognitive competence).

Students were also asked how well they did at mathematics in high school and how good they believed they were at mathematics. Correlations between these questions and students’ attitudes are displayed in Table 6.

Table 6 indicates that the proficiency of students at mathematics in high school had a practically significant relationship of small effect with affect, value and difficulty and a practically significant relationship of medium effect with cognitive competence. No statistically significant correlations were found between how well students did at mathematics in high school and their interest in statistics or the effort they were planning to extend to master statistics. In addition, there was a practically significant correlation of small effect between students’ perception of their competence regarding mathematics on the one hand, and affect, value, difficulty, interest and effort on the other hand. There was also a practically significant correlation of medium effect between students’ perception of their mathematic competence and their perception of their statistics competence (cognitive competence).

Differences between the levels of statistics course (academic year) and students’ attitudes regarding statistics were calculated by means of the Mann–Whitney test. Results revealed that there were no significant difference between the attitudes of postgraduate students (honours and masters’) and undergraduate students toward statistics. Results are presented in Table 7.

Gender and age differences with regard to attitude toward statistics are given in Table 8.

No significant differences were found between males and females regarding their attitudes towards statistics, except for their feelings concerning statistics (affect). Males displayed somewhat more positive feelings towards statistics, but the difference is of small effect (r = 0.10). The youngest 15.5% of students (19–22 years of age) differed significantly with regard to their feelings toward statistics from the oldest 15.5% of students (41–58 years of age). They felt less positive regarding statistics, but the difference was of small effect (r = -0.26). The younger students also regarded statistics to be somewhat more difficult (r = -0.34) than the older students. The difference is of medium effect.

The aim of this paper were to determine the validity and reliability of the SATS-36 item version as an instrument to measure attitude toward statistics in a South African sample, to determine the general attitude of students towards statistics and to determine whether the variables of prior math experience, level of statistics course (academic year), gender and age influence students’ attitudes towards statistics.

The overall findings of the present study provide evidence for the validity and reliability of the SATS-36 item version for a South African sample. A one-factor structure model did not fit the data well. This is in line with suggestions from the developer of the survey (Schau, 2008). The six-factor structure was confirmed and all the sub-factors, except for difficulty, displayed acceptable levels of internal consistency. This result is in accordance with previous results which also showed the reliability coefficients of difficulty ranging between 0.64 and 0.81 (Dauphinee et al., 1997; Hilton et al., 2004; Schau et al., 1995). It therefore seems that presenters of statistics courses in South Africa can use the SATS-36 as a measure of students’ attitude toward statistics in future.

Results from this study indicated that students have more positive attitudes about statistics than negative attitudes – a finding that coincides with research by Mills (2004) (in a sample of 203 undergraduate students enrolled for an introductory statistics course in the College of Business of which 89.1% participants students in the educational sciences) and Onwuegbuzie (2004) (in a sample of 135 graduate students enrolled in three sections of a required introductory-level educational research course at a university in the south-eastern part of the USA) in which students displayed much more negative attitudes towards statistics. It seems that further research is required regarding the external factors that influences students’ attitudes in order to shed more light on these inconsistent results.

The students in the current study displayed a high level of interest in statistics (this is in line with research by Tempelaar et al. (2006) in a sample of European first year students enrolled for a course in Quantitative Methods (QM) that forms part of both Economics and Business first-year programs). They displayed an interest in learning, understanding and using statistics, as well as being able to communicate statistical information. Students were somewhat neutral with regard to statistics being of value in their personal and professional life. Nevertheless, they agreed that statistics should be a required part of their professional training, that statistics will have some application in their profession and also that statistical skills will make them more employable. They even agreed to some extent that they can use statistics in their everyday life. Similar results regarding the value students attach to statistics were found by Schau (2003) in a sample of undergraduate students enrolled for an introductory statistics course offered by the Mathematics and Statistics Department at a major south-western research university in the USA, as well as by Mills (2004). In accordance with the students assessed by Tempelaar et al. (2006) students in this study were also prepared to put in a high level of effort in order to learn statistics. Most students agreed that they planned to work hard, study hard and complete all of their assignments for statistics.

Although students agreed that they liked and enjoyed statistics, they were somewhat more neutral in rating their feelings of insecurity, frustration and stress when it came to statistics. As a result students were somewhat more neutral in their response to affect. Schau (2003) indicated that statistical anxiety can be understood as a part of the affect measurement. These results suggest that even though students are interested in statistics and value the worth of statistics, they might still feel somewhat anxious regarding the subject matter. This may also relate to the fact that most students were in agreement that statistics as a subject is complicated, highly technical and difficult to master. Nevertheless, students were slightly more positive in rating their own levels of confidence to master statistics. It is noted that students in this study and that of Tempelaar et al. (2006) displayed somewhat lower levels of confidence in their own ability to master statistics than students in the studies of Schau (2003) and Mills (2004). Students’ rating of their confidence to master statistics (cognitive competence) was not related to how many prior mathematics courses or statistics courses they had completed, but rather to how well they performed at mathematics in high school, and even more so to how good they believed they were at mathematics. This is in accordance with results from Latief and Blignaut (2008) who also found that throughput in an undergraduate statistics course at a South African university was related to students’ Grade 12 Mathematics results. Schau (2003) noted that many students think that statistics is mathematics, especially at the beginning of an introductory course to statistics. North and Zewotir (2006) also warn that emphasising mathematical skills in a statistics course leads to the failure of emphasising what is important – namely, the role of statistics in students’ professional careers. It therefore appears that students’ own concept of mathematics influences their attitudes toward statistics, especially regarding their perception of how well they will be able to succeed in statistics.

Regarding other biographical variables that might influence attitude toward statistics, results in this study is in line with that of Schau (2003), Tempelaar et al. (2006), and Waters et al. (1989) which showed that males have a somewhat stronger affect (positive feelings) for statistics than females. Older students also revealed a more positive affect and regarded statistics to be less difficult than younger students. This might be somewhat contradictory to the research of Baloglu (2003) which indicated that older students (albeit older than 27 years of age and seen to be seniors) experience more statistics anxiety.

Recommendations

In conclusion, the objectives of this study were achieved in that the results provide preliminary evidence for the validity and reliability of the SATS-36 item version as an instrument to measure attitude toward statistics in a South African sample of students; the general attitude of students towards statistics were explored and the influence of some biographical variables like prior mathematics experience, gender and age on students’ attitudes towards statistics were confirmed to some extent.

Possible limitations

Suggestions for future research

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