Students' perception of effectiveness using different methodologies of teaching advanced business statistics.

Adams, C. Nathan ; Gober, Wayne ; Freeman, Gordon 等

INTRODUCTION

Most 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. This paper focuses on methods utilized in teaching statistics to 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). One of the reasons generally given for this lack of success is that current statistical teaching methodology neglects to establish a definitive linkage between statistics in the classroom and its use in "real world" applications (Yilmaz, 1996). The non-specialist does not aspire to be a mathematical theorist, but needs only to use statistics as a tool in analyzing or solving a problem. This paper does not intend to imply that mathematical theory is unimportant, but takes the position that the use of statistics as a tool is equally important to those people involved in the ongoing everyday activities of business and life. The teaching of applied statistics should be approached as a skill. The teaching of any skill involves repetition and the actual performance of an activity, i.e., "hands-on" training. In short, you cannot acquire statistical competencies via the passive role of listening to lectures or observing the professor solve a statistical problem--you can only acquire these skills by being an active participant, i.e. by performing the activities yourself. Smith (1998) states that students should design the study, collect the data, analyze the results, prepare written reports, and give oral presentations.

The successful use of statistics involves many components, for example, basic mathematical skills, problem selection, model building, data gathering (possibly from global databases or data warehouses), interpretation, computer literacy, software selection and utilization, and clearly communicating the statistical results to those interested parties. Ethics and legal issues also play a major role in the use and interpretation of statistics; however, these important issues are outside the scope of the current paper. It has been documented ad nauseam that when students enter universities they lack the basic foundation mathematical skills required to immediately enroll in mainstream mathematical courses. Perhaps this is because individuals tend to avoid what they are not successful in doing, which in this case, can lead to math anxiety or math phobia. Hogg (1991) found that "students frequently view statistics as the worst course taken in college." In the fall of 1998, there was a total of 2,583 first time freshmen at Middle Tennessee State University of which 1,106 freshmen had to take at least one developmental mathematics course (Bader, 1999). Many students hope that if they can just get past this course that everything will be all right, which is of course, is a non sequitur because they will have to utilize these statistical skills in many courses. Ideally, the statistical courses should view the entire scope of an individual's life (1) statistics is an important part of each student's professional development: and (2) statistics is an important part of each student's everyday life (Iversen 1985, Moore and Roberts 1989, Moore and Witmer 1991). Rumsey (1998) believes that selecting a textbook which contains relevant, real-world examples and exercises, real-world data sets of varying sizes, and text written in the general education themes is vital to satisfying these two goals.

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-depth understanding of the statistics which was the objective of the course. Additionally, students appear to be more interested in acquiring computer skills than mathematical skills, probably because it is much more fashionable to talk about computers than statistics, and, very importantly, students are aware that computer skills are advertised as a prerequisite for most jobs whereas they seldom find mathematical competencies advertised as a prerequisite for jobs.

The recommendations of the American Statistical Association and the Mathematical Association of America (ASA/MAA, 1998) 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-specialist: (1) the use of manual calculations by using a hand-held calculator, (2) the use of a computer package, and (3) a combination using both the manual and computer software package. A computer 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.

Considerable discussions among MTSU statistics faculty have occurred with opinions differing as to the effectiveness of a particular methodology and the resultant outcomes. Statements range from "you don't have to know how to build a car to be able to drive it" to "if you don't know how it works you can't fix it". In an attempt to satisfy instructors 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-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 staff is composed of graduate assistants whose assignment is to assist students who require additional information, as well as help then in utilizing statistical packages.

All students majoring in any field offered within the College of Business must take an introductory level course in statistics (Statistical Methods I) which covers topics in measures of central tendency, variation, probability theory, point and interval estimation, and hypothesis testing. This survey did not include students in this introductory statistic course

MTSU schedules over 10 sections of the junior level course in advanced business statistics (Statistical Methods II) each semester. While each faculty member teaching this course must cover specific core topics, the method of presentation is an individual decision. Topics covered include hypothesis testing and regression analysis. 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).

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. The students were asked to relate their views on the efficacy of the dual method of presentation, i.e., utilizing both the manual (hand-held calculator) and a computer package, as well as their evaluation of the effectiveness of more or less presentation with either of the methods (See Appendix for Questionnaire). A Likert-type scale from 1 (strongly disagree) to 7 (strongly agree) was utilized to determine the student's perceptions of the benefits of one teaching methodology over the others.

DATA ANALYSIS

To identify all statements, with which students either strongly agreed or strongly disagreed a null hypothesis that the midpoint of responses = 4 was tested for each of the twenty-five statements (4 could be considered the point of indifference).

The appropriate statistical procedure to be utilized in the analysis considered the following : a t-test requires an assumption of normality; all statements were tested using an Anderson-Darling test for normality and all 25 statements were found to have responses that were not normally distributed at the 0.000 level of significance. Hence, the Wilcoxon Signed-Rank test should be used to analyze data significance. But, since the data are ordinal the Sign Test should possibly be used. To try to satisfy as many objections as possible, all 25 statements were tested using both the Wilcoxon Signed-Rank test and the Sign test. See tables 1 and 2.

From table 1 (the Wilcoxon Signed Rank test) the statements with the strongest effects (P=0.000) are: 1, 2, 3, 5, 7, 9, 10, 11, 16, 18, 19, 20, 21 and 23.

From table 2 (the Sign test) the statements with the strongest effects (P=0.000) are: 1, 2, 3, 5, 7, 9, 11, 16, 18, 19, 20, 21 and 23.

Using the Sign test, statement 10 is only significant at the 0.001 level of significance, so was not included in the common set of thirteen statements showing the strongest effects. These thirteen statements may be further broken down as follows:

Statements showing the highest levels of agreement: {1, 3, 5, 9 and 11}.

Statements showing the highest levels of disagreement: {2, 7, 16, 18, 19, 20, 21, and 23}.

Ranking those statements with the strongest levels of agreement could be done by simply ranking the computed value of the t-test statistic. However, this approach would not be appropriate for the Wilcoxon Signed-Rank test (ranking by the computed values of the Wilcoxon statistic) or for the Sign test (ranking by the number of values above the median), because in both of these procedures the number of values equal to the median are not used. One approach is to calculate the appropriate Z-value for each computed value of the test statistic and then rank the Z-values.

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.

These Z-values and their ranks are shown in Table 1.

For the Sign test, the normal approximation formula is:

Z = [Above - (n')/2]/sqrt[(n')/4].

These Z-values and their ranks and are shown in Table 2.

Both the Wilcoxon Signed-Rank test and the Sign test have the same rank order for the five statements for which the students showed the largest amount of agreement. This order was:

Highest agreement to lower (but still very significant) agreement 5, 3, 1, 11, 9.

However, the Wilcoxon Signed-Rank test and the Sign test have a slightly different rank order for the eight statements that the students showed the largest amount of disagreement. These orders were:

Wilcoxon Signed-Rank test

Highest disagreement to lower (but still very significant) disagreement 7, 2, 18, 16, 20, 21, 19, 23.

Sign test

Highest disagreement to lower (but still very significant) disagreement 2, 7, 18, 21, 19, 16, 20, 23. The statements are marked: H for manual (hands on) and M for MINITAB. H& Positive H M H M H M M H H M H M M Statement 1 2 3 4 5 6 7 8 9 10 11 12 13 Negative M H H M Positive M M M M M M M M M M M M Statement 14 15 16 17 18 19 20 21 22 23 24 25 Negative H The most agreed with statements will be designated A1, A2, A3, A4 and A5. Most Agreed With Statements A3 A2 A1 A5 A4 H& Positive H M H M H M M H H M H M M Statement: 1 2 3 4 5 6 7 8 9 10 11 12 13 Negative M H H M Positive M M M M M M M M M M M M Statement 14 15 16 17 18 19 20 21 22 23 24 25 Negative H

In every statement where manual calculation is placed in a positive connotation (H above the statement number), it is in the set of statements with which the students' agreement was at the highest level. The most disagreed with statements will be designated D1, D2, D3, D4, D5, D6, D7 and D8 and will be rank ordered determined by the Sign test. Most Disagreed With Statements D1 D2 H& Positive H M H M H M M H H M H M M Statement: 1 2 3 4 5 6 7 8 9 10 11 12 13 Negative M H H M D6 D3 D5 D7 D4 D8 Positive M M M M M M M M M M M M Statement 14 15 16 17 18 19 20 21 22 23 24 25 Negative H

In two of the three statements where manual calculation is placed in a negative connotation (H below the statement number), it is in the set of statements with which the students' disagreement was at the highest level. In fact, these two were the two statements with the highest level of disagreement. The other statement (17) where manual calculation is placed in a negative connotation (H below the statement number), that it is easier to learn to perform a hypothesis test with MINITAB than to learn to perform it manually was generally disagreed with by the students surveyed but not significantly so (Wilcoxon p = 0.262 and Sign p = 0.5940).

For each of these statements the null hypothesis that student responses were essentially the same for all instructors was tested. Anderson-Darling test results precluded the assumption of normality for any statement, thus suggesting the inappropriateness of one-way ANOVA. Therefore a Kruskal-Wallis and a Mood's Median test were used for each statement to test there was no difference in responses based on instructor. No significant differences were found at the 0.05 level of significance. Statement 10 came the closest with a p-value of 0.062 using a Kruskal-Wallis test adjusted for ties.

DISCUSSION OF RESULTS

An analysis of the results indicates that students in advanced business statistics at MTSU exhibited a strong opinion and preference regarding the use of the manual (hand-held calculator) method of learning instead of the use of a computer software package. However, as the level of computational complexity increases the level of disagreement with MINITAB usage decreases.

SUMMARY AND CONCLUSION

A questionnaire was administered to students at MTSU who were enrolled in advanced statistics in the fall of 1998 in an effort to investigate their perceptions of the effectiveness of various methodologies of teaching, i.e., manual (hand-held calculator) or utilizing a computer software package. The students clearly preferred utilizing the manual method.

Further research is suggested to investigate possible difference in preferences in teaching methodologies between gender, instructor, age, and instructor, as well as ease of use between the different methodologies. Additionally, outcome assessment studies could be undertaken in order to analyze the relationship between students perception and performance.

APPENDIX

Q.M. 362 CLASSES Student Perception of Learning: Comparing Manual Procedures with MINITAB

[ILLUSTRATION OMITTED]

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).

Bader, C. H. (1999). Chairman, Developmental Studies, MTSU, (personal communication, on January 22, 1999).

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

Hogg, R. V. (1991). Statistical education: Improvements are badly needed, The American Statistician, 45, 342-343.

Iversen, G. (1985). Statistics in liberal arts education, The American Statistician, 39, 17-19.

Moore, T. & Roberts, R. (1989). Statistics at liberal arts colleges, The American Statistician, 43, 80-85.

Moore, T. & Witmer, J. (1991). Statistics within departments of mathematics at liberal arts college, The American Mathematical Monthly, 98, 431-436.

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

Rumsey, D. J. (1998). A cooperative teaching approach to introductory statistics, Journal of Statistics Education, [Online], 6(1). (http://www.stat.ncsu.edu/info/jse/v6n1/rumsey.html).

Smith, G. (1998). Learning statistics by doing statistics, Journal of Statistics Education, [Online], 6(3). (http://www.stat.ncsu.edu/info/jse/v6n3/smith.html).

Yilmaz, M. R. (1996). The challenge of teaching statistics to non-specialists, Journal of Statistics Education, [Online], 4(1). (http://www.stat.ncsu.edu/info/jse/v4n1/yilmaz.htm).

C. Nathan Adams, Middle Tennessee State University

Wayne Gober, Middle Tennessee State University

Gordon Freeman,, Middle Tennessee State University

Jacqueline Wyatt, Middle Tennessee State University Table 1 Wilcoxon Signed Rank Test Test of median = 4.000 versus median not = 4.000 Boldface for P-value = 0.000 Statement N N N for Wilcoxon Missing Test Statistic C1# 104# 0# 91# 3767.5# C2# 104# 0# 88# 476.5# C3# 104# 0# 88# 3628.0# C4 104 0 86 2042.0 C5# 104# 0# 95# 4308.0# C6 104 0 84 1080.0 C7# 103# 1# 93# 496.0# C8 104 0 82 1606.0 C9# 104# 0# 82# 2832.5# C10# 104# 0# 83# 901.5# C11# 104# 0# 90# 3359.0# C12 104 0 87 1798.0 C13 103 1 72 776.0 C14 103 1 72 1140.0 C15 103 1 84 1168.5 C16# 104# 0# 84# 747.5# C17 103 1 88 1688.0 C18# 104# 0# 71# 358.0# C19# 104# 0# 72# 556.0# C20# 104# 0# 70# 481.5# C21# 104# 0# 68# 454.5# C22 103 1 69 818.0 C23# 104# 0# 63# 448.0# C24 104 0 76 1431.5 C25 104 0 78 1842.0 Statement P Estimated Z for W Rank Median C1# 0.000# 5.500# 6.6275# 23# C2# 0.000# 2.500# -6.1643# 2# C3# 0.000# 5.500# 6.949# 24# C4 0.462 4.000 0.73848 19 C5# 0.000# 6.000# 7.5277# 25# C6 0.002 3.500 -3.14414 10 C7# 0.000# 2.000# -6.4735# 1# C8 0.661 4.000 -0.44149 17 C9# 0.000# 5.000# 5.2285# 21# C10# 0.000# 3.000# -3.8205# 9# C11# 0.000# 5.000# 5.2771# 22# C12 0.625 4.000 -0.49096 16 C13 0.003 3.500 -3.01909 11 C14 0.330 4.000 -0.97643 15 C15 0.006 3.500 -2.74945 12 C16# 0.000# 3.000# -4.6270# 4# C17 0.262 4.000 -1.12343 14 C18# 0.000# 3.000# -5.2715# 3# C19# 0.000# 3.000# -4.2537# 7# C20# 0.000# 3.000# -4.4535# 5# C21# 0.000# 3.000# -4.3903# 6# C22 0.020 3.500 -2.32880 13 C23# 0.000# 3.500# -3.8338# 8# C24 0.872 4.000 -0.16309 18 C25 0.134 4.500 1.50170 20 Note: P-value = 0.000 indicated with #. Table 2 Sign Test Test of median = 4.000 versus not = 4.000 Boldface for P-value [less than or equal to] 0.000 Statement N N * Below Equal Above C1# 104# 0# 14# 13# 77# C2# 104# 0# 76# 16# 12# C3# 104# 0# 7# 16# 81# C4 104 0 34 18 52 C5# 104# 0# 7# 9# 88# C6 104 0 54 20 30 C7# 103# 1# 79# 10# 14# C8 104 0 42 22 40 C9# 104# 0# 17# 22# 65# C10 104 0 57 21 26 C11# 104# 0# 18# 14# 72# C12 104 0 44 17 43 C13 103 1 44 31 28 C14 103 1 38 31 34 C15 103 1 53 19 31 C16# 104# 0# 61# 20# 23# C17 103 1 47 15 41 C18# 104# 0# 60# 33# 11# C19# 104# 0# 54# 32# 18# C20# 104# 0# 52# 34# 18# C21# 104# 0# 53# 36# 15# C22 103 1 45 34 24 C23# 104# 0# 46# 41# 17# C24 104 0 36 28 40 C25 104 0 29 26 49 Statement P Median Z for Rank Above C1# 0.0000# 6.000# 6.60419# 23# C2# 0.0000# 3.000# 6.82242# 1# C3# 0.0000# 6.000# 7.88843# 24# C4 0.0668 4.500 1.94099 19 C5# 0.0000# 6.000# 8.31042# 25# C6 0.0121 3.000 2.61861 10 C7# 0.0000 2.000 6.74019 2# C8 0.9121 4.000 -0.22086 16 C9# 0.0000# 5.000# 5.30071# 21# C10 0.0010 3.000 -3.40269 9 C11# 0.0000# 5.000# 5.69210# 22# C12 1.0000 4.000 -0.10721 17 C13 0.0771 4.000 -1.88562 13 C14 0.7237 4.000 -0.47140 15 C15 0.0219 3.000 -2.40040 12 C16# 0.0001# 3.000# -4.14614# 6# C17 0.5940 4.000 -0.63960 14 C18# 0.0000# 3.000# -5.81523# 3# C19# 0.0000# 3.000# -4.24264# 5# C20# 0.0001# 3.500# -4.06378# 7# C21# 0.0000# 3.000# -4.60818# 4# C22 0.0161 4.000 -2.52810 11 C23# 0.0004# 4.000# -3.65366# 8# C24 0.7308 4.000 0.45883 18 C25 0.0315 4.000 2.26455 20 Note: P-value [less than or equal to] 0.000 indicated with #.