Gender differences in perception of effectiveness of using statistical software in learning statistics.

Freeman, Gordon ; Wyatt, Jacqueline ; Adams, C. Nathan 等

INTRODUCTION

In 1973, Lucy W. Sells identified mathematics as the "critical filter" that prohibits many women from entering the ranks of higher paying, prestigious occupations, and since the publication of that seminal work there has been a great emphasis upon gender differences in mathematical performance.

Studies of gender differences in mathematics performance indicate that females "showed a slight superiority in computation in elementary school and middle school. There were no gender differences in problem solving in elementary or middle school; differences favoring men emerge in high school and college" (Hyde, Fennama & Lamon, 1990). Leo (1999) states that females lag behind males in math and science test scores. Enzensberger (1999) goes so far as to state "...[mathematical ability] is established genetically in the human brain." These conflicting data are rather typical of the disagreement in literature regarding the evidence for a male advantage in math performance (Casey, Nuttall & Pezaris, 1997). They do state that there is a gender difference favoring males among high-ability students at measured by the Mathematics Scholastic Aptitude Test (SAT-M), and this has major implications for women's entrance into math-science fields.

There have been fewer studies concerning gender difference in the use and acceptance of computers. Dambrot, et al (1985) states that "there is every reason to believe that people in general and women in particular who have had problems with mathematics will find working with computers even more difficult and threatening". A study by Igbaria and Parasuraman (1989) indicates that there is a moderate connection between math anxiety and computer anxiety with managers

OVERVIEW OF CURRICULUM CONSIDERATIONS

Virtually all universities and colleges require students to take one or more statistics courses in many different majors, e.g., education, psychology, business, etc., for the non-specialist, and most Schools of Business require one or more courses in computer literacy. This paper focuses on whether there are gender differences in the perception of how helpful a statistical software package (MINITAB) is in learning statistical procedures for those non-specialists who are majoring in a field within business. The traditional method currently used in teaching statistics is widely viewed as being ineffective (Cobb, 1993; Mosteller, 1988).

The recommendations of the American Statistical Association and the Mathematical Association of America (ASA/MAA, 1996) Committee on Undergraduate Statistics should be integrated into the methodology utilized for teaching statistical courses. These recommendations are to teach statistical thinking; to emphasize more data and concepts, less theory and fewer recipes; and, to foster active learning. There are several approaches for teaching statistics to the non-specialists: (1) the use of manual calculations by using a hand-held calculator, (2) the use of a computer software package, and (3) a combination using both the manual and computer software package. A computer software package, such as MINITAB, could be selected which would enhance the student's ability to visualize and explore basic statistical concepts. MINITAB provides the means to generate the output and then allows the student to become statistical thinkers.

Many students who enroll in the statistics courses do so without sufficient computer literacy skills, and, therefore, spend their time attempting to master those requisite computer skills, ultimately neglecting the in-dept understanding of the statistics which was the objective of the course. Students appear to be more interested in acquiring computer skills than mathematical skills, probably because it is much more fashionable to discuss computers than statistics, and, very importantly, students are aware that computer literacy skills are advertised as a prerequisite for most jobs whereas they seldom find mathematical competencies advertised as a prerequisite for jobs.

A study of undergraduates by Dambrot, et al (1985) indicates that computer aptitude was strongly related to mathematics ability and experience. The results show that females held more negative attitudes toward computers, scored lower in computer aptitude, and had less prerequisite mathematics ability and course work.

OVERVIEW OF PRESENT STUDY

Middle Tennessee State University (MTSU) students must take advanced business statistics (Statistical Methods II) which covers topics in hypothesis testing and regression analysis after taking the introductory statistics course. While each faculty member teaching these courses must cover specific core topics, the method of presentation is an individual decision. Teaching techniques range from those faculty members who make minimal use of a statistical software package (MINITAB) to those who make minimal use of manual calculations (hand-held calculators).

The MTSU statistics faculty have had considerable discussions on teaching methodologies and outcomes, particularly with regard to the emphasis placed upon statistical software in teaching statistical procedures. In an attempt to satisfy faculty at both ends of the continuum, many statistics faculty members introduce new topics to students with manual methods (hand-held calculators) then reinforce the topic with the use of a computer statistical package (MINITAB).

The College of Business at MTSU is AACSB accredited and has a state-of-the-art new building with computer labs and networked telecommunication facilities. Each classroom has multimedia, a projector, and is networked so that computer software is immediately available to the instructor and students alike. MINITAB for Windows is used in the classrooms and in the computer laboratory, making MINITAB available both in class and for out-of class assignments. In addition to the computer lab, there is a separate business statistics lab in the same locale as the offices of the faculty members who teach the statistical courses. The business statistics lab is staffed by graduate assistants whose job it is to assist students who require additional information, as well as help them utilize computer statistical packages.

RESEARCH METHODOLOGY

A questionnaire was created and administered to seven sections of the advanced statistics course (Statistical Methods II) during the last scheduled class day in the fall semester of 1998, and another seven sections during the last class day in the spring semester of 1999. The students were asked to relate their views on the effectiveness of the dual method of presentation, i.e., utilizing both the manual (hand-held calculators) and a computer software package, as well as their evaluation of the effectiveness of more or less presentation with either of the methods. Various demographic data were also collected, including gender (See Appendix for Questionnaire). A Likert-type scale from 1 (strongly disagree) to 7 (strongly agree) was utilized in an effort to determine the student's perceptions of the benefits of one teaching methodology over the others, and whether these results would differ by gender.

DATA ANALYSIS

All statements in which the male and female responses differed significantly were identified ([alpha] = 0.05). The responses of both genders to each of the twenty-six statements were tested using an Anderson-Darling test for normality, and all twenty-six statements were found to have responses that were not normally distributed at the 0.000 level of significance. Even the robustness of the normality assumption in ANOVA tests was not expected to compensate for that lack of normality, so the Mann-Whitney-Wilcoxon test was used to check for gender differences. The results for the nine statements showing significant ([alpha] = 0.05) gender differences are presented in Table 1.

To rank these nine statements by the degree of gender difference (with 1 being the rank of the statement having the largest degree of gender difference) Z-values for the normal approximation to the Mann-Whitney-Wilcoxon test were calculated. For the Mann-Whitney-Wilcoxon test, the normal approximation formula used was:

Z = [M--([n.sub.1])([n.sub.T] + 1)/2]/sqrt[([n.sub.1])([n.sub.2])([n.sub.T] + 1)/12],

where M was the computed value of the Mann-Whitney-Wilcoxon test;

[n.sub.1] was the number of female responses;

[n.sub.2] was the number of male responses; and

[n.sub.T] was the sum of [n.sub.1] and [n.sub.2].

These Z-values and their ranks are shown in Table 1. Note that all the Z-values are negative. A negative Z-value indicates that the typical female response to each of these nine statements was lower than the typical male response.

Of the nine statements in Table 1, eight (18--25) dealt with the helpfulness of MINITAB with respect to a particular subset of statistical procedures. The other statement, (17), " It is easier to learn how to use MINITAB to perform a hypothesis test than it is to learn how to perform the hypothesis test manually" while more general, showed the least amount of gender difference in the group.

With regard to statements 18--25, two observations deserve special mention. The two statements that show the highest degree of gender difference are {23 and 22}. These two state that MINITAB was particularly helpful in understanding multiple-sample parametric and multiple-sample non-parametric tests. The four statements showing the highest degree of gender difference are {23, 22, 19 and 21}. This set of four statements includes all the types of non-parametric tests covered in the QM 362 course.

The results shown in Table 1 illustrate which statements in the survey have the largest amount of gender difference, but does not illustrate the type of gender difference. The negative Z-values show that the typical female response to a statement is significantly less than the typical male response for each of the nine statements in Table 1. However, it cannot be determined if both genders agreed, both genders disagreed, or the males agreed and the females disagreed. Quantification requires the use of additional hypothesis tests. The information provided by these tests allows the determination of the types of the nine gender differences shown in the responses to the statements in Table 1.

The Likert-type scale used to measure the degree of agreement (disagreement) had a midpoint of 4, so a null hypothesis that the midpoint of responses = 4 for the female responses and the male responses was tested for each of these nine statements. What test statistic should be used for these tests?

Since the Anderson-Darling tests indicated that the statement responses for each gender were not normally distributed, a t-test was not appropriate. The nagging question that remained was whether the responses constituted at least an interval level of measurement and justified the use of the Wilcoxon Signed-Rank test. The use of the Sign test for such responses is clearly justified, but is it the best test? It was decided to perform both the Wilcoxon Signed-Rank test and the Sign test on the female and male responses to each of these nine statements and be conservative in the interpretation of the results. Both tests had to show a significant effect or it would not be reported as significant. See Table 2.

Since two-tailed hypothesis tests were being used, the p-values of the tests show evidence of significant agreement or disagreement, but the p-value by itself does not indicate which one. It could mean significant agreement in one case and significant disagreement in another case. Again we used the Z approximations to the two test statistics to tell if there was agreement (positive Z-value) or disagreement (negative Z-value) and to make it easy to rank the degree of the agreement or the degree of disagreement.

For the Wilcoxon Signed-Rank test, the normal approximation formula is:

Z = [W--(n')(n' + 1)/4]/sqrt[(n')(n' + 1)(2n' + 1)/24], where n' is the number of responses that differ from the hypothesized median. These Z-values and their ranks and are shown in Table 3.

For the Sign test, the normal approximation formula is:

Z = [Above--(n')/2]/sqrt[(n')/4], where n' is the number of responses that differ from the hypothesized median. These Z-values and their ranks and are shown in Table 3.

The ranks in Table 3 represent the level of disagreement with the corresponding statement. The statement disagreed with at the highest level (most negative Z-value) received a rank of 1 and so on. Positive Z-values indicated agreement. Using the p-values in Table 2 and the sign of the Zvalues in Table 3, Table 4 was constructed. It shows the types of the gender differences for the nine statements that showed a significant gender difference.

In seven out of the nine statements showing significant gender differences (17--23), both genders disagreed with the statements with the females disagreeing more strongly. In statement 24, the females significantly disagreed, while the males insignificantly agreed. In statement 25 the females insignificantly disagreed, while the males insignificantly agreed. In all nine statements showing significant gender differences, the female responses showed more disagreement that the male responses did.

Eight of the nine statements showing significant gender differences (18--25) dealt with the helpfulness of MINITAB with respect to a particular subset of statistical procedures. The statistical procedures mentioned in these eight statements were broken down into two groups: the parametric statistical procedures {18, 20, 22, 24 and 25} and the non-parametric statistical procedures {19, 21 and 23}. The list {18, 20, 22, 24 and 25} orders the parametric statistical procedures by increasing complexity. Likewise, the list {19, 21 and 23} orders the non-parametric statistical procedures by increasing complexity. Table 5 was created to show each of the two groups of statistical procedures with the corresponding survey statements ordered by increasing complexity of the tests. The level-of disagreement ranks from Table 3 were inserted in the same row with the corresponding statement. The purpose was to see how the level of difficulty of the test correlated with the level of disagreement with the statement shown by each gender. Regardless of the test used to obtain the level-of-disagreement ranks or the gender, the ranks were perfectly correlated with the level of difficulty in the parametric statistical procedures. As the level of difficulty of the parametric statistical procedure increased, the level of disagreement with the associated survey statement decreased. Regardless of the test used to obtain the level-of-disagreement ranks for the female responses, the ranks were perfectly correlated with the level of difficulty in the non-parametric statistical procedures. Using the Wilcoxon Signed-Rank test to obtain the level-of-disagreement ranks for the male responses, the ranks were perfectly correlated with the level of difficulty in the non-parametric statistical procedures. The only case where the correlation was not perfect (R = 0.5 if least complex gets a rank of 1) was when the Sign Test was used to obtain the level-of-disagreement ranks for the male responses.

DISCUSSION OF RESULTS

Only nine statements showed a significant difference at the .05 level of significance. In all statements where there was a clear gender difference in the responses, the females had a higher level of disagreement with the statement than the males. If these nine statements are ordered by the degree of significance with the statements having the most significant gender differences being listed first, the order of the statements is: {23, 22, 19, 21, 20, 24, 25, 18 and 17}. In statements 23 and 22 both genders tended to disagree with these two statements, but the level of the female disagreement was significant ([alpha] = 0.05). This result suggests the conclusion that females find MINITAB to be of less help than males in understanding multiple-sample statistical tests.

All three of the survey statements that mention non-parametric tests {19, 21 and 23} are in the "top four" of the nine statements with significant gender differences. Both genders tended to disagree with these three statements, but the level of the female disagreement was significantly more than that of the males. This result suggests the conclusion that females find MINITAB to be of less help than males in understanding non-parametric statistical tests.

In seven out of the nine statements showing significant gender differences (17--23), both genders were disagreeing with the statements with the females disagreeing more strongly. Of these seven statements, 19, 21, and 23 were addressed as a group above. A similar group is the group of the only three survey statements that specifically refer to parametric tests. Both genders tended to disagree with these three statements, but the level of the female disagreement was significantly more than that of the males. This result suggests the conclusion that females find MINITAB to be of less help than males in understanding one-sample, two-sample and multiple-sample parametric tests.

The other two statements dealt with regression. In statement 24, the females significantly disagreed, while the males insignificantly agreed. This result suggests the conclusion that males see some benefit in using MINITAB to help them understand simple linear correlation and regression, but the females do not. In statement 25 the females insignificantly disagreed, while the males insignificantly agreed. This result suggests the conclusion that the females do not see as much benefit in using MINITAB to help them understand multiple regression analysis as the males do.

In both parametric tests and non-parametric tests, the females tend to see MINITAB of being less helpful in their understanding of those statistical procedures than the males do. However, as the tests get more complex, both genders tend to disagree less with the statement that MINITAB aids understanding.

The females continue to disagree that MINITAB aids their understanding even up to the complexity of regression analysis, while the males start to agree that MINITAB is helpful when the complexity of regression analysis is reached.

SUMMARY AND CONCLUSIONS

A questionnaire was administered to students at MTSU who were enrolled in advanced statistics in the fall of 1998 and the spring of 1999 in an effort to investigate if there were gender differences in the perception of effectiveness of various methodologies of teaching advanced business statistics. Statistical analysis of the results indicates that there are differences in gender acceptance and opinion regarding the understanding of statistics when using statistical software (MINITAB).

In both parametric tests and non-parametric tests, the females tend to see MINITAB as being less helpful in their understanding of those statistical procedures than do the males. However, as the tests get more complex, both genders tend to disagree less with the statement that MINITAB aids understanding. The females continue to disagree that MINITAB aids their understanding even up to the complexity of regression analysis, while the males start to agree that MINITAB is helpful when the complexity of regression analysis is reached.

Further research is suggested to investigate the relationship between student's perception and actual performance using different teaching methodologies. Outcome assessment studies could be undertaken in order to analyze this relationship.

REFERENCES

American Statistical Association and the Mathematical Association of America. A review of and response to guidelines for programs and departments in undergraduate mathematical sciences ASA/MAA joint committee on undergraduate statistics. [Online],(http://www.maa.org/data/guidelines/asa%5Fresponse.html).

Casey, M. B., Nuttal, R. L. & Pezaris, E. (1997). Mediators of gender differences in mathematics college entrance test Scores: A Comparison of spatial skills with internalized beliefs and anxieties. Developmental Psychology, 33(4), 669-680.

Cobb, G. W. (1993). Teaching Statistics. In Heeding the Call for Change, ed. Lynn Steen, (MAA Notes No. 22). Washington: Mathematical Association of America, 3-23.

Dambrot, F. H., Watkins-Malek, M. A., Silling, S. M., Marshall, R. S. & Enzensberger, H. M.. (1999). Why no one knows we're living in a golden age of mathematics. Chronicle of Higher Education, XLV(34), B9.

Hyde, J. S., Fennema, E. & Lamon, S. J. (1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 107(2), 139-155.

Iggbaria, M. & Parasuraman, S. (1989). A path analytic study of individual characteristics, computer anxiety and attitudes toward microcomputers. Journal of Management, 15(3), 373-388.

Leo, J. (1999). Gender wars redux. U.S. News & World Report, 126(7), 24.

Mosteller, F. (1988). Broadening the scope of statistics and statistical education. The American Statistician, 42, 93-99.

Sells, L. W. (1973). High school mathematics as the critical filter in the job market. In R. T. Thomas (Ed.), Developing opportunities for minorities in graduate education (pp. 37-39). Berkeley: University of California Press.

Gordon Freeman, Middle Tennessee State University

Jacqueline Wyatt, Middle Tennessee State University

C. Nathan Adams, Middle Tennessee State University

Wayne Gober, Middle Tennessee State University

APPENDIX

Q.M. 362 CLASSES

Student Perception of Learning: Comparing Manual Procedures withMINITAB

In many Q.M. 362 classes a statistical topic is
introduced using manual techniques with hand-held calculators. Once the
basic principles and
procedures of the technique are presented MINITAB is then used to work
the same or similar problems. In an effort to ascertain the benefits
students obtain from the two approaches the following questionnaire
has been devised.

Please circle your response to each of the following questions on a
scale from 1 (strongly disagree) to 7 (strongly agree)

 Strongly Disagree Strongly Agree

1. I learn more from manual calculations than 1 2 3 4 5 6 7
 from problems solved with MINITAB
2. I retain more knowledge of statistical 1 2 3 4 5 6 7
 techniques from problems worked with
 MINITAB than problems worked manually
3. Introduction of statistical topics using 1 2 3 4 5 6 7
 manual procedures provide a good
 understanding of the rationale and
 techniques of the topics
4. Reinforcement of statistical topics using 1 2 3 4 5 6 7
 MINITAB after manual techniques have been
 covered strengthens and enhances my
 understanding of the topics
5. Manual exercises increased my knowledge of 1 2 3 4 5 6 7
 each statistical procedure
6. MINITAB exercises increased my knowledge 1 2 3 4 5 6 7
 of each statistical procedure
7. Manual computations distracted me in 1 2 3 4 5 6 7
 understanding and mastering concepts of
 statistical methodology
8. MINITAB procedures distracted me in 1 2 3 4 5 6 7
 understanding and mastering concepts of
 statistical methodology
9. I would prefer greater emphasis on manual 1 2 3 4 5 6 7
 calculations in the course
10. MINITAB procedures were clear and 1 2 3 4 5 6 7
 understandable
11. Manual procedures were clear and 1 2 3 4 5 6 7
 understandable
12. MINITAB procedures challenge and 1 2 3 4 5 6 7
 encourage independent thought
13. In the classroom MINITAB allows for 1 2 3 4 5 6 7
 better structure of content
14. In the classroom MINITAB allows for 1 2 3 4 5 6 7
 standardized delivery of content
15. In the classroom MINITAB allows for more 1 2 3 4 5 6 7
 interesting instruction
16. In the classroom MINITAB allows for 1 2 3 4 5 6 7
 longer retention of course material
17. It is easier to learn how to use MINITAB 1 2 3 4 5 6 7
 to perform a hypothesis than it is to learn
 how to perform the hypothesis test manually
18. MINITAB was particularly helpful in 1 2 3 4 5 6 7
 understanding one-sample parametric tests
19. MINITAB was particularly helpful in 1 2 3 4 5 6 7
 understanding one-sample non-parametric
 tests such as the Wilcoxon Signed Ranks
 test
20. MINITAB was particularly helpful in 1 2 3 4 5 6 7
 understanding two-sample parametric tests
 such as two-sample t test with pooled
 variance
21. MINITAB was particularly helpful in 1 2 3 4 5 6 7
 understanding two-sample non-parametric
 tests such as the Mann-Whitney test
22. MINITAB was particularly helpful in 1 2 3 4 5 6 7
 understanding multiple-sample parametric
 tests such as ANOVA
23. MINITAB was particularly helpful in 1 2 3 4 5 6 7
 understanding multiple-sample non-
 parametric tests such as the Kruskal-Wallis
 test
24. MINITAB was particularly helpful in 1 2 3 4 5 6 7
 understanding simple linear correlation and
 regression
25. MINITAB was particularly helpful in 1 2 3 4 5 6 7
 understanding multiple regression analysis
26. At the beginning of this course I was 1 2 3 4 5 6 7
 already familiar with some computer
 software

TABLE 1

Mann-Whitney-Wilcoxon Test

Test of median of females = median of males versus median of females
not = median of males

 Mann-
 N N Whitney-
 N for for Wilcoxon
Statement Missing Females Males Statistic

C17 1 130 105 14274.5

C18 0 130 106 14331.0

C19 0 130 106 13859.0

C20 0 130 106 13929.0

C21 0 130 106 13900.5

C22 1 130 105 13767.5

C23 0 130 106 13794.0

C24 0 130 106 14002.5

C25 0 130 106 14183.0

 Z for
 Mann-
 Female Male Whitney- Z
Statement P Median Median Wilcoxon Ranks

C17 0.0398 3.000 4.000 2.05647 9

C18 0.0396 3.000 3.500 2.05871 8

C19 0.0031 3.000 4.000 2.96348 3

C20 0.0047 3.000 4.000 2.82929 5

C21 0.0039 3.000 4.000 2.88393 4

C22 0.0024 3.000 4.000 3.03500 2

C23 0.0020 3.000 4.000 3.08807 1

C24 0.0072 4.000 4.000 2.68841 6

C25 0.0192 4.000 5.000 2.34241 7

TABLE 2

Nine Statements With The Most Significant Gender Differences

 Females

 Wilcoxon
 Signed-
 N for Rank
Statement Test Statistic P Above P

C23 92 490.5 0.000 18 0.0000

C22 97 950.5 0.000 25 0.0000

C19 91 350.0 0.000 11 0.0000

C21 93 394.0 0.000 15 0.0000

C20 93 372.0 0.000 15 0.0000

C24 99 1412.0 0.000 39 0.0444

C25 104 2215.5 0.096 52 1.0000

C18 95 399.0 0.000 14 0.0000

C17 107 1721.5 0.000 37 0.0020

 Males

 Wilcoxon
 Signed-
 N for Rank
Statement Test Statistic P Above P

C23 68 814.0 0.028 29 0.2751

C22 73 1259.5 0.619 35 0.8149

C19 77 904.5 0.002 30 0.0682

C21 70 758.5 0.005 25 0.0232

C20 75 851.0 0.002 29 0.0647

C24 85 1871.5 0.849 49 0.1931

C25 84 2069.5 0.205 54 0.0121

C18 74 670.5 0.000 21 0.0003

C17 89 1848.0 0.529 44 1.0000

TABLE 3

Nine Statements with the Most Significant Gender Differences

 Females

 Z
 N for Z for
Statement for Females W Rank Above Rank

C23 92 -6.41909 5 -5.83840 5

C22 97 -5.13108 6 -4.77213 6

C19 91 -6.89863 3 -7.23317 1

C21 93 -6.86430 4 -6.53280 3.5

C20 93 -6.94859 2 -6.53280 3.5
C24 99 -3.71018 7 -2.11058 8

C25 104 -1.66842 9 0.00000 9

C18 95 -6.98201 1 -6.87405 2

C17 107 -3.62860 8 -3.19023 7

 Males

 N Z Z
 for for for
Statement Males W Rank Above Rank

C23 68 -2.19362 5 -1.21268 5

C22 73 -0.50028 7 -0.35112 6

C19 77 -3.03125 2 -1.93733 4

C21 70 -2.83246 4 -2.39046 2

C20 75 -3.03104 3 -1.96299 3

C24 85 0.19280 8 1.41005 8

C25 84 1.26881 9 2.61861 9

C18 74 -3.86265 1 -3.71992 1

C17 89 -0.63211 6 -0.10600 7

TABLE 4

Nine Statements with the Most Significant Gender Differences

 Females

 [alpha] = 0.05
 A = Agree S = significant
Statement D = Disagree I = insignificant

C23 D S

C22 D S

C19 D S

C21 D S

C20 D S

C24 D S

C25 D I

C18 D S

C17 D S

 Males

 [alpha] = 0.05
 A = Agree S = significant
Statement D = Disagree I = insignificant

C23 D I

C22 D I

C19 D I

C21 D S

C20 D I

C24 A I

C25 A I

C18 D S

C17 D I

TABLE 5

Level-of-disagreement Ranks Catagorized

 Parametric Statistical Procedures

 Females Males

Statement Wilcoxon Sign Wilcoxon Sign
 Ranks Ranks Ranks Ranks

C18 1 2 1 1

C20 2 3.5 3 3

C22 6 6 7 6

C24 7 8 8 8

C25 9 9 9 9

 Non-Parametric Statistical Procedures

 Females Males

Statement Wilcoxon Sign Wilcoxon Sign
 Ranks Ranks Ranks Ranks

C19 3 1 2 4

C21 4 3.5 4 2

C23 5 5 5 5