Journal of Statistics Education Volume 12, Number 3 (2004), www.amstat.org/publications/jse/v12n3/ward.html
Copyright © 2004 by Barbara Ward, 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: Distance education; Online vs. traditional; Statistics education; Web enhanced
On the other hand, empirical studies that compare demographic characteristics have revealed a wide disparity in students who enroll in online courses as opposed to traditional courses in some settings. A comparative study at a community college concluded that typically online learners are female, Caucasian, twenty-six to fifty-five years of age, work full-time as professionals, and have more education and a higher family income than their traditional counterparts (Halsne and Gatta 2002). Other studies at state universities found that their online students are actually traditional students who sign up for the course because of scheduling or logistic conflicts (Ashkeboussi 2001; Utts et al. 2003). Online courses are often collaborations between universities and local industry (Stephenson 2001). Many are created to serve the educational needs of a particular population of students such as continuing education (MacGregor 2001) or graduate degrees (Ellis 2000; Ashkeboussi 2001; Gagne and Shepherd 2001).
In a survey of traditional and distance learning higher education members the National Education Association found that many distance learning students do not fit the previously established stereotype of older, part-time students who live far from campus and work full-time. The study found that there is an equal mix of students over and under twenty-five years of age, and who are full-time and part-time. Also the study finds that distance learning classes are not large, completion rates are high, and students live within one hour of campus (NEA 2000).
In many private and public universities, direct contact with students is an important part of teaching. Hybrid courses offer students the convenience of online technology and the comfort of personal contact with the professor. But, do performance and attitude differ for hybrid and traditional courses? Utts et al. (2003), in a study comparing traditional and hybrid models of Elementary Statistics, found no difference in students’ performance, but a slightly less positive attitude in the hybrid model. In the present study there was no significant difference in students’ performance as measured by grades, but hybrid students were less likely to complete extra credit assignments and appeared to have a more positive attitude.
Many different types of hybrid courses are being taught. At Stevens Institute of Technology, class is held in a computer lab where students complete online activities while the instructor is present (Levine 2002). In a second case, students have minimal contact with the instructor by attending class only for an orientation session and the final exam (MacGregor 2001). In an introductory statistics course, online students had three face-to-face meetings with the professor during the course to solve problems that were not resolved through electronic contact (Yablon and Katz 2001). Ohio State University is teaching a hybrid introductory statistics course where students may select from an offering of online and in-class activities that include lectures, Web based activities, videos, training modules, discovery laboratories, reviews, and projects (Rensselaer Polytechnic Institute 2001). As in the present study of Elementary Statistics, University of Central Florida offers hybrid courses that meet fifty percent online and fifty percent in the classroom. Some potential benefits of hybrid courses to students and the educational institution are:
The present study addresses the following questions:
Outliers were identified as students who withdrew before the end of the semester. One traditional student and three hybrid students did not complete the course and consequently were eliminated from the final data analyses. The final data analyses comparing performance, extra credit, and working in groups were conducted on 19 hybrid students and 55 traditional students. However, the outliers were included in the comparisons of retention rates, gender, classification, and major.
The hybrid class met once a week for seventy-five minutes during which the instructor answered questions on problems or worksheets and administered tests and quizzes. Two class sessions (a total of 150 minutes) were scheduled in the computer lab where the students had identical activities to the traditional class. An emphasis was placed on students coming to class having learned the material on their own using the textbook and tools from the course Web page. No new material was presented in class. The course Web page included course policies and hints for success, a daily study calendar, links to real data and statistics resources, a bulletin board for posting data and comments, a chat room, and course content modules. The course content modules included links to daily activities suggested by the study calendar. Activities included interactive worksheets, applet demonstrations of statistical concepts, review sheets and solutions, practice tests and solutions, computer labs, links to suggested readings on the Web, and Power Point reviews of the textbook material. The applet demonstrations, suggested readings, and Power Point reviews were made available to the traditional class.
Communication between instructor and students took place during scheduled office hours, before and after class, by telephone, and by email. Online office hours were scheduled for the hybrid class via an Internet chat room. Scheduled office hours and email were the most utilized form of communication for both hybrid and traditional students.
Fisher’s Exact Test was used to compare retention rates. It appeared that the difference in retention rate for the two models was not significant (p = .066). Three students withdrew from the hybrid model before the end of the semester resulting in a retention rate of 86%. In the traditional model only one student withdrew resulting in a retention rate of 98%. Hybrid student comments such as “meeting once a week for a statistics class is very hard”, and “[the instructor] did not have much time to teach”, indicated that some students in the hybrid model would have preferred more scheduled class time. The students who withdrew from the hybrid model were all freshmen. Exit interviews indicated that the main reason for withdrawal was the unexpected nontraditional aspect of the hybrid class. The student who withdrew from the traditional model did so because of scheduling.
Each grade was equally weighted and worth 100 points. The students’ final averages were calculated by taking the total of these six grades plus extra credit points then dividing by six. Extra credit is described and analyzed in Section 5.3.
Multivariate Analysis of Variance (MANOVA) was conducted at the .05 level of significance to determine the effect of course model on performance as measured by the six grades. A limitation of the study was the small sample size of hybrid students. Prior to the MANOVA test, data were examined for outliers and fulfillment of multivariate test assumptions: normality, linearity, and homoscedasticity.
Before examining multivariate normality, univariate normality of each dependent variable (grade) for each treatment (model) was assessed at the .05 level of significance. Histograms and Kolmogorov-Smirnov tests for normality revealed that three dependent variables, Project Grade, Quiz Grade, and Test 1 Grade, were negatively skewed. The data for these three variables were reflected and a log transformation was applied: NewX=log (101-X). When reexamined with univariate normality tests, all transformed variables were distributed normally. The original variables were replaced with the transformed variables in the subsequent MANOVA analysis.
The assumption of multivariate normality implies that in addition to univariate normality, all linear combinations of dependent variables are normally distributed. Bivariate scatterplots of all possible pairs of the six grades for each course model were examined and found to be convincingly elliptical, showing that linear combinations of pairs of dependent variables were approximately normally distributed and correlated. A correlation table showed a strong linear relationship at the .05 level of significance between the dependent variables for each model except Project Grade. Even though Project Grade had a moderate to weak linear correlation with some other grades for each model, it was retained in the MANOVA analysis. Multivariate normality was further supported by mound shaped histograms of residuals for each of the six grades.
Even though the assumption of homoscedasticity is usually met when multivariate normality is assumed, it was further supported by visually examining the MANOVA Residuals Versus Fitted Values plots for each of the six grades. Each residual plot showed about the same spread of residuals for both models, indicating that the variability in fitted values for each dependent variable is approximately the same for hybrid and traditional models.
MANOVA results indicated at the .05 level of significance that model does not significantly affect performance (F = .87, p = .52) as measured by the six grades. This F value for Wilks’ Lambda had 6 degrees of freedom in the numerator (due to the hypothesis of no difference in performance of the two models) and 67 degrees of freedom in the denominator (due to sampling error). Since there was not multivariate significance in performance of students in hybrid and traditional models, subsequent univariate tests for significant model differences in individual grades were not conducted.
Kolmogorov-Smirnov tests for normality indicated that Extra Credit Grade was normally distributed in the traditional model and positively skewed in the hybrid model as illustrated in Figure 1. The hybrid students’ Extra Credit Grade median was 28 and the traditional students’ Extra Credit Grade median was 68. The majority of hybrid students did not make the effort to complete and turn in extra credit assignments. A Mann-Whitney test for medians conducted at the .05 level of significance indicated that the median Extra Credit Grade of the hybrid model was significantly less than the median Extra Credit Grade of the traditional model (Mann-Whitney W = 2338.5, p < .001).
Figure 1. Extra Credit
The contradictory results between Performance (no difference) and Extra Credit Grade (significant difference) could mean that the hybrid students had less motivation to complete work on their own when the activity was not a requirement of the course. Hybrid students’ comments such as, “We had to learn and work through at least one chapter, if not more, per week”, and “It was sometimes hard to keep up on homework assignments”, seemed to indicate that the amount of independent work required outside of class had an adverse effect on the extra credit effort.
In the hybrid model, 12 students formed groups of two or three people to complete the final project and in the traditional model 34 students formed similar groups. Remaining students in both models worked alone on the final project. A chi-square test conducted at the .05 level of significance indicated no significant relationship between the number of students who worked in groups and course model (chi-square = .01, df = 1, p = .92).
There was a positive correlation between the average Likert scores by question for the two models (r = .67, p = .04), indicating a comparatively constant difference in average responses on the questions. A paired t-test conducted at the .05 level of significance comparing the 10 average scores for each question for hybrid to the 10 average scores for each question for traditional showed that the mean average score for the hybrid model was greater (indicating a more positive attitude) than the mean average score for the traditional model (t = 6.17, df = 9, p < .01). The mean average Likert score by question was 4.22 with a standard deviation of .33 for the hybrid model and 3.67 with a standard deviation of .35 for the traditional model.
Figure 2. Average Likert Scores by Questions
Figure 3 shows a dot plot comparison of the average Likert score for each student for both models. There appeared to be several disgruntled students in the traditional model. A two sample t-test conducted at the .05 level of significance indicated a significant difference in mean average Likert scores of students for the two models (t = 2.91, df = 29, p < .01). The mean average score by student was 4.22 with a standard deviation of .63 for the hybrid model and 3.67 with a standard deviation of .75 for the traditional model.
Figure 3. Average Likert Scores by Student
The results of individual Mann-Whitney tests to compare medians of each question for the two course models are presented in Table 1. A more conservative .01 level of significance was used to analyze individual tests in this multiple-test comparison, resulting in an experiment-wise error rate less than .10. It appears that there were differences in median attitude scores for questions measuring: Knowledge of Instructor (p = .003), Presentation of Subject Matter (p = .006), Academic Motivation (p = .001), and Overall Rating of Instructor (p = .008). In each comparison the hybrid class had a higher median attitude score indicating a more positive attitude on these particular questions. Written comments like, “I did not spend enough time studying”, seemed to indicate that this difference in median attitude could be a result of hybrid students taking more accountability for their performance on the required components of the course. There was no evidence to support differences in median attitude scores at the .01 significance level for questions measuring: Course Content (p = .032), Course Organization (p = .013), Course Requirements (p = .114), Grading and Evaluation (p = .237), Attitude Toward Students (p = .114), and Overall Rating of Course (p = .233). It should be noted that the scores of individual questions are not summated Likert Scores and do not possess a normal distribution. The reported p-values are not adjusted for ties, thus are more conservative if ties are present. For complete questions see the Appendix.
|Question Title||Median Score |
|1. Course Content||4.5 (4.0)||681.0||0.032|
|2. Course Organization||4.5 (4.0)||707.0||0.013|
|3. Course Requirements||4.0 (4.0)||636.0||0.114|
|4. Grading and Evaluation||4.0 (4.0)||602.0||0.237|
|5. Knowledge of Instructor||5.0 (4.0)||744.0||0.003|
|6. Presentation of Subject Matter||4.0 (3.0)||727.0||0.006|
|7. Academic Motivation||5.0 (3.5)||775.5||0.001|
|8. Attitude Toward Students||5.0 (4.0)||636.0||0.114|
|9. Overall Rating of Instructor||4.5 (4.0)||720.5||0.008|
|10. Overall Rating of Course||4.0 (4.0)||603.0||0.233|
A significant difference was found in the Extra Credit Grade. The hybrid model median was less than the traditional model median, suggesting that hybrid students did not take as much extra initiative beyond the course requirements as traditional students. Student comments seemed to indicate that the hybrid students had so much independent work that they were less likely to “go the extra mile” when the assignment was optional.
There was no significant difference in the number of students who chose to work in groups on the final project.
There were significant differences on a Likert scaled attitude survey in mean average scores by student for hybrid and traditional models as well as mean average scores by question for the two models. For both of these measures, the hybrid model appeared to have a more positive attitude. When individual survey questions were compared, there appeared to be no differences in median attitude scores for questions asking about Course Content, Course Organization, Course Requirements, Grading and Evaluation, Attitude Toward Students, and Overall Rating of Course. The hybrid model appeared to have a more positive (higher) median attitude score for survey questions asking about Knowledge of Instructor, Presentation of Subject Matter, Academic Motivation, and Overall Rating of Instructor. Hybrid students’ comments seemed to indicate that the difference in attitude is a result of their taking more accountability than traditional students for their performance on required components of the course.
Much research has been conducted at a myriad of undergraduate, graduate and professional courses at urban and suburban, public and private universities and community colleges. As in the present study, many of the online classes that were subjects of research were actually hybrid courses where students met with the professor several times. While there appears to be no difference in the performance and attitude of online students and traditional students in some settings, there can be differences in their demographic characteristics. However, in institutions that don’t require true “distance” education, where students are able to attend an occasional face-to-face class, a hybrid model of the course makes sense. When the benefits of online learning are combined with the versatility and personal contact of a traditional setting, the instructor, educational institution, and students have the “best of both worlds.”
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Barbara B. Ward
Department of Mathematics and Computer Science
1900 Belmont Blvd.
Nashville, TN 37212-3758
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