Stijn Vanhoof

Ana Elisa Castro Sotos

Patrick Onghena

Lieven Verschaffel

Wim Van Dooren

Wim Van den Noortgate

Katholieke Universiteit Leuven

Journal of Statistics Education Volume 14, Number 3 (2006), ww2.amstat.org/publications/jse/v14n3/vanhoof.html

Copyright © 2006 by Stijn Vanhoof, Ana Elisa Castro Sotos, Patrick Onghena, Lieven Verschaffel, Wim Van Dooren, Wim Van den Noortgate all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor.

**Key Words:** Assessment; Attitudes Toward Statistics scale.

A widely used instrument is the Attitudes Toward Statistics (ATS) questionnaire (Wise
1985). The ATS is a 29-item, Likert-type scale with five response possibilities ranging from ‘strongly disagree’ to
‘strongly agree’. The ATS questionnaire includes both positively and negatively formulated items. The questionnaire
consists of two subscales – *Field* (20 items) and *Course* (9 items) – that respectively aim to measure
attitudes toward the use of statistics in the students’ fields of study and attitudes toward the particular statistics
course in which they are enrolled. Example items include:

*Field*

I feel that statistics will be useful to me in my profession.

Studying statistics is a waste of time.

*Course*

The thought of being enrolled in a statistics course makes me nervous.

I get upset at the thought of enrolling in another statistics course.

The ATS scales can be used to give a general overview of the attitudes toward statistics of a group of students. Most of the previous studies using ATS (e.g., Elmore and Lewis 1991, 1993; Waters et al. 1988; Wise 1985) include an evaluation of the internal consistency, a description of the attitudes students have toward statistics before and after taking the statistics course, and an analysis of how these attitudes are related to their first year statistics exam results (as an indication of their statistics performance). Most of these studies therefore involve two administrations, one before and one after the statistics course (but before the students know their exam results).

The present study aims at extending the existing evidence on the relationship between attitudes toward statistics and performance. This is done in three ways. First, the study provides new data and measures of reliability of the ATS by two administrations of the questionnaire in an introductory statistics course for Flemish undergraduate students in Educational Sciences. Second, while previous investigations are limited to the relationship between attitudes and first year exam results, this study examines the relationship between the attitudes students have and their exam results not only at the beginning of the curriculum, but also in later years. Third, while the previous research only addresses the relationship between students’ attitudes and their grades in a statistics course, the present study also investigates the relationship with their general exam results (short- and long-term). In this way, we examine whether the findings and trends of other studies are also valid for Flemish undergraduate students and, more importantly, we want to check whether the documented relationship between attitudes and statistics exam results also holds in the long term and for general exam results.

We are aware that some authors caution against the indiscriminate use of paper-and-pencil Likert-type scales, like the ATS, to study attitudes (Gal and Ginsburg 1994; Schau et al. 1995). For instance, it is difficult to imagine that students’ attitudes toward statistics could be captured by two global ATS scores ( Gal and Ginsburg 1994). Furthermore, we have to take into account that there may be cultural differences in responding to such questionnaires, even at the level of subtle nuances in the translation and interpretation of the items. Therefore, we acknowledge that our study will only be one step toward a deeper understanding of the complex relationship between attitudes and performance.

This paper is organized in five sections. Since we will compare our data with the findings reported in previous studies, in Section 2 we start with a summary of these earlier findings. Section 3 describes the methodology of this study. In Section 4, the results are presented, followed, in Section 5, by a discussion.

The Appendix provides an overview of these studies with some additional information concerning the number of samples, administrations, and participants. It also includes the level of the course that is involved (undergraduate or graduate), the field of study (e.g. psychology, education, engineering) and some remarks. Most authors do not provide information on the specific content of the course (probability, descriptive statistics or inferential statistics). We acknowledge that differences in courses, fields of study, and other characteristics of the population and the specific statistics courses in the different studies can complicate the comparison. Yet, because most studies include an introductory statistics course in the field of human sciences (education, psychology), a prudent comparison seems justified.

In the following tables, we summarize the findings of these studies. Successively, we review (1) the internal consistency
and test-retest reliability, (2) mean data (and standard deviations) for the *Course* and *Field* subscales
(respectively for undergraduate and graduate students), and (3) the relationship with first year statistics exam results.
Since not all investigations mention all measures, some tables contain only a subset of the studies involved in our
comparative analysis.

Table 1 presents the observed internal consistency (Cronbach alphas). All studies
yield coefficient alpha reliability estimates that are high for both subscales and for both administrations. In general,
the estimates are between 0.77 and 0.93 for the *Course* subscale and between 0.83 and 0.96 for the *Field*
subscale. Some studies (Elmore and Lewis 1991;
Elmore et al. 1993; Roberts and Reese
1987) also mention the alpha estimate for the whole scale. Roberts and Reese
(1987) find a whole scale alpha estimate of 0.91, Elmore and Lewis (1991)
report for the first and the second administration an estimate of 0.92 and 0.93, respectively, and
Elmore et al. (1993) 0.92 and 0.94.

Study | Sample size | Course subscale |
Field subscale | ||
---|---|---|---|---|---|

Adm. 1 | Adm. 2 | Adm. 1 | Adm. 2 | ||

Aldogan and Aseeri, 2003 | 178 | 0.92 | 0.90 | ||

Elmore and Lewis, 19911 | 58 | 0.90 | 0.82 | 0.90 | 0.92 |

Elmore et al., 1993 | 289 | 0.90 | 0.90 | 0.90 | 0.93 |

Rhoads and Hubele, 2000 | 63 (Adm. 1) 61 (Adm. 2) |
0.77 | 0.85 | 0.89 | 0.90 |

Shultz and Koshino, 1998 (sample 1) | 36 | 0.85 | 0.92 | 0.96 | 0.96 |

Shultz and Koshino, 1998 (sample 2) | 38 | 0.93 | 0.89 | 0.90 | 0.92 |

Waters et al., 1998 | 302 | 0.90 | 0.90 | 0.83 | 0.86 |

Wise, 1985 | 92 | 0.90 | 0.92 | ||

Note 2: Shultz and Koshino (1998) include two samples. The first sample contains undergraduate students, the second sample graduate students (see the Appendix for more information).

Some authors also investigate the test-retest reliability for the *Course* and *Field* subscales. The reported
correlations are respectively 0.91 and 0.82 (Wise 1985), 0.59 and 0.72
(undergraduates, Shultz and Koshino 1998), and 0.71 and 0.76 (graduates,
Shultz and Koshino 1998). For Wise
(1985) there are only two weeks between the test and retest (as opposed to three months for
Shultz and Koshino 1998). Obviously, the time lapse between administrations can
affect the reliability.
Table 2 presents the mean scores (and standard deviations) for the different
studies. For all these data, if needed, item responses were reversed so that a higher score always refers to a more
positive attitude. A distinction is made between undergraduate and graduate courses, since
Shultz and Koshino (1998) predicted and found consistent differences in
attitudes between these two groups when discussing their own and previous study results.

Because the ATS-items are scored on a Likert-type scale with five response possibilities, ‘strongly disagree’ (score 1),
‘disagree’ (score 2), ‘neutral’ (score 3), ‘agree’ (score 4) and ‘strongly agree’ (score 5), 27 indicates an average
neutral position for the whole *Course* subscale, which contains 9 items. Similarly, because there are 20 *Field*
subscale items, with each time ‘neutral (score 3)’ as the neutral response possibility, 60 indicates an overall neutral
position for the whole *Field* subscale.

Study | Sample size | Course subscale |
Field subscale | ||
---|---|---|---|---|---|

Adm. 1 | Adm. 2 | Adm. 1 | Adm. 2 | ||

Undergraduate | |||||

Elmore et al., 1993 | 289 | 24.1 (7.8) | 22.1 (8.5) |
79.4 (9.5) | 80.2 (11.1) |

Mvududu, 2003(sample 1) | 120 | 34.9 (6.0) | 79.5 (8.9) | ||

Mvududu, 2003(sample 2) | 95 | 28.9 (8.0) | 74.0 (13.1) | ||

Shultz and Koshino, 1998 (sample 1) | 36 | 23.3 (6.5) | 24.0 (8.8) |
74.5 (11.8) | 74.3 (11.7) |

Waters et al., 1988 | 212 | 28.3 | 30.2 | ||

Graduate | |||||

Elmore and Lewis, 1991 | 58 | 30.5 (7.4) | 33.1 (6.3) |
79.0 (9.8) | 80.5 (10.9) |

DAndrea and Waters, 2002 | 17 | 29.1 (9.0) | 35.2 (5.7) |
84.9 (9.2) | 86.6 (6.7) |

Shultz and Koshino, 1998 (sample 2) | 38 | 29.8 (8.9) | 32.5 (7.1) |
81.1 (9.2) | 81.3 (9.6) |

Note: Waters et al. (1988) do not provide standard deviations.

A comparison of the mean results for the undergraduate and graduate courses is in line with the conclusion of
Shultz and Koshino (1998) that, in general, graduate students have higher
scores than undergraduate students, for both the *Course* and *Field* subscale.

Table 3 shows the correlations between the attitude scores and the first year
statistics exam results. In addition to the statistical significance of the correlations (which is discussed in all
articles), we report effect sizes. Cohen (1988, 1992) provides a classification
of effect sizes for correlations in terms of small (*r* = 0.1), medium (*r* = 0.3), and large (*r* = 0.5)
effects as compared to the effects typically found in the social, educational and behavioral sciences. Except for
Shultz and Koshino (1998), all studies demonstrate a statistically significant
positive correlation between the first administration of the *Course* subscale scores and the exam results (first
column). According to the guidelines of Cohen (1988, 1992), the corresponding
correlations are small to medium. The correlations of the second administration (second column) are higher (effect sizes
ranging from medium to large), and statistically significant for all studies. None of the studies shows a statistically
significant correlation between the *Field* subscale scores and
the exam results for the first administration (third column). Two studies
(Shultz and Koshino 1998, first sample;
Waters et al. 1988) show a statistically significant correlation for the second
administration (fourth and sixth column), but for all studies in the table, the correlation at the second administration is
smaller for the *Field* subscale as compared to the *Course* subscale.

Study | Sample size | Course subscale |
Field subscale | ||
---|---|---|---|---|---|

Adm. 1 | Adm. 2 | Adm. 1 | Adm. 2 | ||

Shultz and Koshino, 1998 (sample 1) | 36 | 0.06 (ns) | 0.45(p < 0.05) |
0.16 (ns) | 0.43(p < 0.05) |

Shultz and Koshino, 1998 (sample 2) | 38 | 0.13 (ns) | 0.34(p < 0.05) |
0.13 (ns) | 0.08 (ns) |

Rhoads and Hubele, 2000 | 63 (Adm. 1) 61 (Adm. 2) |
0.29(p < 0.05) | 0.29(p < 0.05) |
ns | ns |

Waters et al., 1988 | 302 | 0.20(p < 0.05) | 0.42(p < 0.05) |
0.07 (ns) | 0.17(p < 0.05) |

Wise 1985 | 70 | 0.27(p < 0.05) | -0.04 (ns) | ||

Note1: None of the authors report exact *p*-values. (‘ns’ stands for ‘not significant’)

Note2: Rhoads and Hubele (2000) do not provide exact correlation values
for the *Field* subscale.

These data are in line with the conclusion of Waters et al. (1988) that there
exists a consistent positive relationship between students’ attitudes toward statistics and their first year statistics
exam results. They notice that especially the *Course* subscale scores are related to the statistics exam results, as
also reported by Harvey et al. (1985, in Mvududu 2003). The latter authors
suggested that a supportive atmosphere in the course can positively affect performance, regardless of the attitudes toward
the field of statistics.

The curriculum of Educational Sciences takes five years to complete. The introductory statistics course takes place in the first semester of the first year. In general, the course deals with some introductory methodology and statistical concepts (tables, figures, and descriptive statistics), but no formal probability or statistical inference. The mathematical background required for this course is limited.

To relate the attitude scores to statistics performance, we record students’ statistics exam results and their dissertation grades at the end of the five year program. Again, this is only done for the students who completed the ATS and who completed the program successfully (see Table 4 for an overview of the sample sizes). For the statistics exam results, there are three results from obligatory statistics courses that students have to follow during their curriculum, namely in the first, the second, and the third year. For the first and the second statistics courses, the instructor is the same. For the third year’s statistics course, the same teacher as in the two previous years teaches half of the course, and another teacher teaches half of it. It is important to notice that the third year results are somewhat atypical and more difficult to interpret, because the course is evaluated through group assessment. Students do not follow any statistics courses in the fourth and fifth year, but because of the major role of methodology and statistics in a student’s dissertation, we consider this as a partial indication of long-term statistics performance.

To relate the attitude scores to general performance, we record students’ general exam results for the five years of the curriculum. For the present study, we excluded the dissertation grade from the variable ‘general exam result’, as it contributes 50% to that result.

All these measures together make it possible to relate the attitude scores of the two administrations at the beginning of the curriculum with (1) short- and long-term and (2) statistics and general exam results. As mentioned before, the conclusions of the relationship between the attitudes and long-term exam results only pertain to the students who actually pass the exams. Table 4 provides an overview of the different measures and of the sample sizes at each moment of data collection.

Year | ATS | Statistics exam result | General exam result | ||
---|---|---|---|---|---|

96 - 97 | 1^{st} administration(October 1996) ( n = 264) |
1^{st} year( n = 234) |
1^{st} year( n = 234) | ||

97 - 98 | 2^{nd} administration(October 1997) ( n = 127) |
2^{nd} year( n = 102) |
2^{nd} year( n = 102) | ||

99 - 00 | 3^{rd} year(group work) ( n = 78) |
3^{rd} year( n = 78) | |||

00 - 01 | (no statistics course) | 4^{th} year( n = 74) | |||

01 - 02 | 5^{th} year(Dissertation grade) ( n = 72) |
5^{th} year(Courses grade) ( n = 72) | |||

Note: The number of participants mentioned for the exam results refers to the participants who have a score on the first administration of the ATS as well as on the exams.

The relationships of the attitude scores with the short- and long-term exam results are examined by Pearson product-moment correlation coefficients, separately for statistics and general exam results. The relationships of the attitude scores with all these exam results are compared with the relationships of first year exam results with later exam results. In other words, cognitive and affective predictors of exam results are compared, again separately for statistics and general exam results.

The average *Course* subscale scores for the two administrations are respectively 28.5 (*s* = 6.4) and 30.7
(*s* = 6.5), indicating a rather positive attitude toward the statistics course (given that the neutral score is 27).
Concerning the attitudes toward the course, our sample of undergraduate Flemish students is comparable with the (higher)
graduate student scores observed in other studies. The average *Field* subscale scores, 66.9 (*s* = 7.6) and 68.0
(*s* = 6.7), respectively, are also positive (above the neutral score of 60), but compared to the other studies, these
scores are low. Finally, the standard deviations of the *Field* and the *Course* subscale scores in our study are
lower than in the other studies.

Statistics exam | 1^{st} administration |
2^{nd} administration |
Statistics exam | |||||
---|---|---|---|---|---|---|---|---|

N | Course | Field |
N | Course | Field |
N | 1^{st} year | |

1^{st} year | 234 | 0.33(p < 0.001) | 0.15 (p = 0.02) |
127 | 0.47(p < 0.001) | 0.20 (p = 0.03) |
127 | 1 |

2^{nd} year | 102 | 0.23 (p = 0.02) | 0.14 (p = 0.17) |
115 | 0.31(p < 0.001) | 0.20 (p = 0.04) |
115 | 0.45(p < 0.001) |

3^{rd} year | 78 | -0.03 (p = 0.79) | -0.01 (p = 0.94) |
88 | 0.22 (p = 0.04) | 0.07 (p = 0.53) |
88 | 0.26 (p = 0.01) |

5^{th} year | 72 | 0.09 (p = 0.44) | 0.04 (p = 0.75) |
83 | 0.03 (p = 0.78) | 0.23 (p = 0.04) |
83 | 0.19 (p = 0.08) |

Note: Numbers in bold indicate significant values at the 0.001 level.

Because we are carrying out a large number of statistical tests on the same data, we have to take into account that the
probability of committing at least one Type I error is substantially larger than the significance level set for each
individual test. Multiple correlations are calculated and tested, the ones in Table 5
and Table 6, and additional tests are performed to compare correlated correlation
coefficients. To avoid potentially spurious results, we perform a Bonferroni correction on the overall significance level
(0.05). The resulting significance level for an individual test is 0.001, which means that a *p*-value must be smaller
than 0.001 in order to conclude that the correlation differs from zero.

For the first year, the results show statistically significant (*p*-values < 0.001) positive correlations between the
attitudes toward the course and the statistics exam results. Although the correlations for the *Field* subscale are
not statistically significant after the Bonferroni correction, all effect sizes
(Cohen 1988, 1992) range between small and medium. The *Course* subscale
scores show the highest correlations for both administrations, meaning that for the included sample the attitudes toward
the course are a slightly better predictor of the first year exam results than attitudes toward the field. The
test for comparing correlated correlation coefficients provided by Meng, Rosenthal,
and Rubin (1992) shows that the difference between the correlations (*Course* versus *Field*) is
statistically significant for the second administration (*Z* = 2.46, *p* = 0.01 for the first administration and
*Z* = 3.39, *p* < 0.001 for the second administration). These results are a compelling replication of the
findings from the earlier studies summarized in Table 3. However, recall that the
students in our study already knew their exam results during the second administration of the ATS.

For the second year, the trends are similar, but differ in terms of statistical significance. The *Course* subscale
scores are the most highly related to the second year statistics exams scores. However, only for the second administration
is the correlation between *Course* and exam results statistically significant. The test for comparing correlated
correlation coefficients shows that the difference between the correlations (*Course* versus *Field*) is not
statistically significant for the second year (*Z* = 1.02, *p* = 0.31 for the first administration and
*Z* = 1.27, *p* = 0.20 for the second administration). The effect sizes
(Cohen 1988, 1992) of the correlations still range between small and medium.

For the third year, the attitude scores do not show statistically significant correlations with the statistics exam results. However, recall that we have to be careful with the interpretation of the data from the third year statistics exam results, because they are based on group assessment (see Section 3.2).

In the fifth year, the attitudes scores do not correlate significantly with the dissertation grade, but when we take a
closer look at the results, we see that the *Field* subscale scores for the second administration show a substantive
correlation with the dissertation grades in the fifth year (*r* = 0.23, *p* = 0.04).

Furthermore, in contrast to the correlation of the second administration with the first year statistics exam results, where
Course was related highest to statistics exam results, in the long term, *Field* is more highly related to the
dissertation grade than *Course* (test for comparing correlated correlation coefficients: *Z* = -1.93, *p*
= 0.05).

Because this study is one of the first to explore the relation between attitudes toward statistics and long-term results,
and because of the negative impact that Bonferroni corrections can have on the power of the tests, this correlation between
the *Field* subscale and the dissertation grade – although no longer statistically significant after the Bonferroni
correction – is worth mentioning.

The last column of Table 5 shows the correlations between the first year statistics exam results and all following statistics exam results (including the dissertation grade). Since these data relate to the same students as those who participated in the second administration of the ATS, the relative predictive values of affective (ATS) and cognitive (first year statistics results) characteristics in predicting later exam results can be compared for that administration.

Not surprisingly, the second year statistics exam results are more highly correlated with the first year exam scores
(*r* = 0.45, *p* < 0.001) than with the ATS scores (*r* = 0.31, *p* < 0.001 and *r* = 0.20,
*p* = 0.04 respectively). The test for comparing correlated correlation coefficients shows that this difference
between the correlations is most convincing (although not statistically significant after Bonferroni correction) for the
*Field* subscale (*Z* = -2.28, *p* = 0.02).

In the long term, the observed correlation for *Field* (*r* = 0.23, *p* = 0.04) is higher than the
correlation between the first year exam results and the dissertation grade (*r* = 0.19, *p* = 0.08). Thus for our
sample, in the long-term, the *Field* score of the second administration is a better predictor of the dissertation
grade than the first year statistics exam result. In other words, the observed affective measure shows a higher correlation
with the dissertation grade than the cognitive measure, although the test for comparing correlated correlation coefficients
provided by Meng et al. (1992) shows that this difference between the
correlations is not statistically significant (*Z* = 0.31, *p* = 0.76).

General exam | 1^{st} administration |
2^{nd} administration |
General exam | |||||
---|---|---|---|---|---|---|---|---|

N | Course | Field |
N | Course | Field |
N | 1^{st} year | |

1^{st} year | 234 | 0.16 (p = 0.02) | 0.07 (p = 0.26) |
127 | 0.17 (p = 0.06) | 0.12 (p = 0.20) |
127 | 1 |

2^{nd} year | 102 | 0.01 (p = 0.91) | -0.03 (p = 0.79) |
115 | 0.09 (p = 0.32) | 0.03 (p = 0.76) |
115 | 0.42(p < 0.001) |

3^{rd} year | 78 | -0.01 (p = 0.92) | 0.07 (p = 0.57) |
88 | 0.08 (p = 0.44) | 0.16 (p = 0.14) |
88 | 0.48(p < 0.001) |

4^{th} year | 74 | 0.13 (p = 0.28) | 0.17 (p = 0.15) |
84 | 0.04 (p = 0.75) | 0.13 (p = 0.23) |
84 | -0.01 (p = 0.96) |

5^{th} year (courses) | 72 | -0.01 (p = 0.95) | 0.01 (p = 0.95) |
83 | -0.04 (p = 0.75) | 0.14 (p = 0.23) |
83 | 0.46(p < 0.001) |

Note: Numbers in bold indicate significant values at the .001 level.

First, as in previous studies reported in the first part of this article (see Table 1), we find a high internal
consistency for the Attitude Toward Statistics (ATS) scale (Wise 1985). The
test-retest reliabilities are fairly high (0.62 for the *Field* subscale and 0.76 for the *Course* subscale) and
within the range of the reliabilities reported by previous studies.

Second, this study provides new descriptive data concerning students’ attitudes toward statistics. These data are somewhat
different from the trends mentioned in the literature. More specifically, the results on the *Course* subscale indicate that
Flemish __undergraduate__ students in Educational Sciences have an attitude toward the particular course in which they
are enrolled that is more positive than the attitudes of undergraduate students elsewhere, but comparable to the attitudes
of __graduate__ students in other studies. However, the analysis of the *Field* subscale scores reveals a
relatively negative attitude toward the use of statistics in the students’ field of study as compared to the scores from
graduate and undergraduate students from the ‘bench-mark’ studies.

Third, the analysis of the relationship between the ATS scores and short-term statistics exam results complemented findings obtained by other authors, namely that especially attitudes toward the course are related to short-term exam results.

Fourth, an innovative element in our study is that it also yields findings concerning the analysis of the relationship between attitudes in the beginning of the curriculum and the dissertation grade. While for short-term exam results, attitudes toward the course are more highly related to statistics exam results than the attitudes toward the field, the latter are more highly related to the fifth year dissertation grade than the attitudes toward the course. Our results suggest that students who recognize the importance of statistics for their field of study (in the case of the present study: educational sciences) will tend to obtain a better dissertation grade.

Fifth, this study also investigates the relative predictive value of affective (ATS) and cognitive (exam results) measures in predicting later exam results. The data show that the relationship between the attitudes toward the field after experiencing a statistics course (affective measure) and second year statistics exam results were smaller than between first year exam results (cognitive measure) and those second year exam results. This finding is similar to the findings of Fienberg and Halperin (in Roberts and Bilderback 1980), namely that a cognitive measure predicted statistics performance with slightly higher accuracy than the measure of attitudes toward quantitative concepts. However, this difference between the affective and the cognitive measure as predictors is smaller for the relation with the long-term dissertation grade. In fact, the relationship for the affective measure is even slightly (but not significantly) higher than the relationship for the cognitive measure. These results are an important indicator of the essential role attitudes toward statistics (besides cognitive characteristics) play for the development of statistical competence.

Obviously, replications of this research on the relationship between attitudes toward statistics and long-term statistics exam results are needed. For instance, a comparison of dissertation scores and other measures that can be used as indications of long-term statistics performance, such as exam scores and/or scores on more traditional or performance-based statistical tests problems, can provide a deeper insight into this relationship. Furthermore, it would be very interesting to follow up the non-successful students, under more to compare the attitudes and statistics performance of these students with the students who did pass the exams.

Finally, results from this study reveal that the important relationship between attitudes toward statistics and statistics performance is content-specific. Indeed, we found no relationship between the attitudes toward statistics and general exam results. Further research should investigate how the attitudes measured by the ATS differ from ‘general academic attitudes’ and how different attitude scales are related to different kinds of performance. Such research might reveal the importance of a separate assessment of attitudes toward studying specific fields of study, besides the assessment of ‘general academic attitudes’.

Study | Sample | # Admin | n | (Under)graduate | Field of Study | Remarks |
---|---|---|---|---|---|---|

Wise 1985 | 1 | 1 | 92 | Education | Original article ATS | |

2 | 2 | 70 70 | Education | |||

Roberts and Reese 1987 | 1 | 1 | 280 | Undergraduate | Also administration of another scale to measure attitudes toward statistics, the Statistics Attitutde Survey (SAS; Roberts and Bilderback 1980. ATS is treated as one scale in this study. | |

Waters et al. 1988 | 1 | 2 | 302 | Undergraduate | Variety of majors (mainly psychology) | Also administration of SAS. Only 212 respondents were measured on both occasions. |

Elmore and Lewis 1991 | 1 | 2 | 58 | Graduate | Variety of majors | |

Elmore et al. 1993 | 1 | 2 | 289 | Undergraduate | Variety of majors | |

Shultz and Koshino 1998 | 1 2 | 2 2 |
36 38 |
Undergraduate Graduate | Psychology Psychology | |

Rhoads and Hubele 2000 | 1 | 2 | 63 61 |
Undergraduate | Engineering | Used to measure change in attitudes before and after a computer-integrated statistics course. |

D’Andrea and Waters 2002 | 1 | 2 | 32 17 |
Graduate | Education | Used to measure change in attitudes before and after a statistics course using ‘short stories’. |

Aldogan and Aseeri 2003 | 1 | 1 | 178 | Graduate | Variety of majors | Arabic version. |

Mvududu 2003 | 1 2 | 1 1 | 95 120 |
Undergraduate Undergraduate | Variety of majors (USA) Business, Accounting and Economics (Zimbabwe) |
Cross-cultural study (USA and Zimbabwe). Used to measure the relationship between attitudes toward statistics and the use of constructivist strategies. |

Note 1: As can be seen from the table (column **Sample**), some authors use two different samples.

Note 2: **# Adm.** stands for the number of administrations for a particular sample.

We want to thank Brian Greer for his comments and Tine Gheysen for her assistance in data collection and initial statistical analyses.

This research was partially supported by Grant GOA 2006/01 “Developing adaptive expertise in mathematics education” from the Research Fund Katholieke Universiteit Leuven, Belgium.

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Stijn Vanhoof

Department of Educational Sciences

Centre for Methodology of Educational Research

Katholieke Universiteit Leuven

Leuven

Belgium
*stijn.vanhoof@ped.kuleuven.be*

Ana Elisa Castro Sotos

Department of Educational Sciences

Centre for Methodology of Educational Research

Katholieke Universiteit Leuven

Leuven

Belgium
*anaelisa.castrosotos@ped.kuleuven.be*

Patrick Onghena

Department of Educational Sciences

Centre for Methodology of Educational Research

Katholieke Universiteit Leuven

Leuven

Belgium
*patrick.onghena@ped.kuleuven.be*

Lieven Verschaffel

Department of Educational Sciences

Centre for Instructional Psychology and Technology

Katholieke Universiteit Leuven

Leuven

Belgium
*lieven.verschaffel@ped.kuleuven.be*

Wim Van Dooren

Department of Educational Sciences

Centre for Instructional Psychology and Technology

Katholieke Universiteit Leuven

Leuven

Belgium
*wim.vandooren@ped.kuleuven.be*

Wim Van den Noortgate

Department of Educational Sciences

Centre for Methodology of Educational Research

Katholieke Universiteit Leuven

Leuven

Belgium
*wim.vandennoortgate@ped.kuleuven.be*

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