Using a video presentation on variance and covariance in the teaching of statistics

1 INTRODUCTION

Many students report disinterest in quantitative methods and perceive them as irrelevant for their future career and at the same time fear statistics courses as very difficult [7, 17] with high failure rates: negative attitudes or beliefs toward statistics are widespread [9, 18, 21] and non-statistics students regard statistics courses as something that “must be passed” [1].

Thus, many tools have been developed to support students' learning, change negative attitudes, and foster the understanding and perceived relevance of statistics. It has been found that visualizations can enhance the understanding [12, 16], and that students evaluate video tutorials on statistics positively [8]. Furthermore, appropriate, current, and relevant examples can foster engagement and meaningful insights in statistical problems [6, 11]. Stockwell et al. [20] showed that watching learning videos, compared with reading textbook sections, accompanying a science course, influenced engagement and motivation positively, and van der Meij and Dunkel [14] found positive effects of brief video reviews of statistical topics on students' self-efficacy.

The present article introduces a video presentation consisting of PowerPoint slides and narrative covering the principles of variance, SD, covariance, and correlation with visualizations and case examples, combining the helpful features mentioned above. The presentation was developed to motivate students to actively review and process the content, foster a positive attitude toward statistics and enhance their skills in the reviewed topics. It was offered online for German psychology students enrolled in an introductory statistics course. However, the basic statistical concepts of variance and covariance are prerequisites for the understanding of further statistical procedures and are commonly taught throughout different subjects. Thus, we evaluate usability and effects for students of diverse subjects in which statistics are obligatorily taught.

2 THE VIDEO PRESENTATION

Our 16-minutes video presentation contains key terms and definitions, formulas, and graphical representation accompanied by verbal explanations. Different from learning with traditional tools like textbooks, learners can concentrate on the essentials while simultaneously being provided with further details, instead of switching their focus back and forth between text and illustrations. On nine slides, the topics variance and covariance are presented. The applicability is emphasized and examples with a practical orientation are used to increase interest and motivation.

On the first two slides, the meaning and the computation of the arithmetic mean, as prerequisite for understanding variance and covariance, are summarized, including an everyday life sample calculation (ie, computing average grades). Afterward, dispersion measures (ie, variance and SD) are introduced by a graphical presentation of a distribution of a continuous variable (ie, the preference to do sports rated on a 6-point Likert scale) in a sample and a population, by means of a normal distribution. Derived from the example, the calculation of variance and SD is presented, including a definition and detailed explanation of the corresponding formulas (Figure 1). Characteristics of the dispersion measures are summarized in the next slide.

Then, the concept of covariance and its calculation formula is explained by an everyday life example (ie, the relation of weight and blood pressure, Figure 2) and summarized on the next slide. Finally, the concept and formula for correlation, as standardized shared variance of two variables, are discussed.

3 EVALUATION

In an experiment with repeated measures (Figure 3), we examine the effects of the video presentation (experimental group: Video) on basic skills improvement regarding the taught content compared with a control group receiving a traditional learning method, that is, reading a statistics textbook section with the same structure and content for 16 minutes (control group: Text). Thus, the conveyed information is equivalent in both conditions, but in the Video group is guided through the content via narrative and, for example, formulas and graphics are explained step by step. Accompanying, we compare the rating of the video presentation and the textbook section. This measure serves as an indicator for motivation to use the learning tool and to engage with the content. We postulate:

To further control for effects of watching simply any video concerned with statistics, a third group (control group: YouTube) watched a YouTube video [15] for 16 minutes, dealing with the relevance of science and statistics in everyday life, but not providing any knowledge about variance and covariance.

Data were collected by an online study at the beginning of the winter term 2020/21, promoted online (ie, groups and forums of beginning students) and in introductory statistics courses at our university. Out of 315 persons who opened the study link, 117 completed the survey. After excluding three participants who did not provide information on all relevant variables for testing our hypotheses, the final sample consists of N = 114 (n = 18 male, n = 94 female, n = 2 diverse) students from different subjects in which statistics courses must be passed. Age ranges from 18 to 48 (M = 23.87, SD = 5.81).

First, students' statistics anxiety as a control variable, which may influence test performance, was assessed by the BEVAST-EWL [10]. Participants rated 17 items (eg, “I would be very uncomfortable if I had to work on a statistical problem”) on a 4-point Likert scale (1 = does not apply, 4 = applies in full, α = .95). Afterward, participants took a first statistics test (Test A), consisting of seven allocation or multiple-choice exercises covering the content of the video presentation or textbook section, respectively, with a maximum of nine points to achieve.

Participants then were randomized and either watched the video presentation (n = 38), read the textbook section (n = 36), or watched the YouTube video (n = 40). Afterward, the Video group and the Text group rated the received learning method on four self-constructed items, addressing enhancement of understanding, helpfulness, recommendation to others, and willingness to further use the respective method, on a 6-point Likert scale (1 = does not apply at all, 6 = applies perfectly, Video: α = .87, Text: α = .89). Then, sociodemographic characteristics were assessed as well as the last math school grade, which may also have an impact on test performance or the ability to grasp new content quickly and thus functions as a control variable. Participants achieved M = 10.97 (SD = 3.42) points in math (15 points = best grade, 0 points = worst grade).

Finally, a parallel post-test B assessed skill improvement. Three experts judged Tests A and B to guarantee comprehensibility of the items, adequate difficulty, as well as comparability of the tests (for sample items, see Figure 4). Test A (M = 6.32, SD = 1.66) and Test B scores (M = 7.05, SD = 1.89) were rather high with a wide dispersion (1 to 9). Guess probability for two items of each test was 50%, which makes it likely to achieve at least some points by chance. It might be argued that we did not optimally reach the intended target group with little knowledge in statistics. Nevertheless, we decided to analyze all complete cases, but additionally perform exploratory analyses without participants with full score in Test A (Appendix A).

4 RESULTS

As Table 1 shows, there is a small positive change in the test score in the Text and YouTube groups. However, the test score of the Video group descriptively improves more compared with the control groups. To further control for effects of the covariates, that is, statistics anxiety and math grade, on test performance, we conducted a stepwise regression (see Table 2). Whereas the covariates do not show any predictive value, greater prior knowledge in Test A is associated with higher scores in the post-test B. The results reveal support for H1: adding group membership to the model significantly increases explained variance. Test B achievement in the Video group improves compared with the Text group.

Regarding H2, a one-sided t-test reveals that the Video group and the Text group differ significantly in their rating of the learning method, t(72) = 1.79, P = .039, d = .42. Students evaluate the video presentation (M = 4.65, SD = 1.02) more positively than the textbook section (M = 4.18, SD = 1.21).

5 CONCLUSIONS

Our aim was to improve educators' ability to provide students a suitable learning tool to enhance understanding and motivation to engage with the statistical content. The results show that while controlling for math school grade and statistics anxiety, participants' skills improve after watching the video presentation in comparison to reading the textbook section (H1). Further, participants assessed the video presentation as more positive than the textbook section (H2). We conclude that our video presentation is suitable for the investigated students.

However, students in our Video group did not significantly improve in their knowledge compared with the YouTube group. Retrospectively, the control condition may not have been as neutral as expected: presumably the control video supported the perceived relevance of statistics and did motivate students to do well in the post-test. Subsequent further analysis showed that when excluding students with very high skills, the Video group did indeed improve compared with the YouTube group (cf. Appendix A). Furthermore, despite the experimental design, a self-selection bias of participation cannot be ruled out. A high number of participants quit the survey before completing Test A, which leads to the conclusion that our sample may consist of students with a rather positive attitude toward statistics and at least some motivation to deal (voluntarily) with statistical content. Hence, a positive selection due to the voluntary nature and the content of our study might have caused that the target group (students with little previous knowledge) was not optimally met, also indicated by the rather high mean test scores. As an implication for lecturers, we generally suggest considering if teaching materials are sufficiently challenging, match students' knowledge but also enable learning progress. The topic we chose seems to be rather easy and well known among students. Thus, knowledge (only) improved to a small part in the control groups and somewhat more in the Video group.

Differential effects, depending on the amount of prior knowledge, as well as subject-specific effects, could not be examined since subgroups were too small to draw reliable conclusions. Also, generalizations regarding alternative learning content should be addressed in further research. Moreover, effects on students' attitudes and motivation should be analyzed in more detail by using validated measures and by examining effects on self-concepts, self-efficacy, or anxiety. In this regard, van der Meij [13] found video reviews in combination with other learning materials to enhance not only test performance but also self-efficacy. Finally, long-term and further-reaching effects on academic success in general, for example, exam grades or later study satisfaction, should be examined since it has already been shown that flexible online-learning materials can foster those outcomes [3, 5].

Regarding more general implications, we expect flexible blended learning materials to become even more important during the present shift from attendance to distance learning, due to COVID-19, which, at least partially, is expected to be retained after the pandemic [19]. In this regard, video presentations provide a summary of the most important aspects and combine different helpful features (graphical representation, verbal explanations, sample calculations, step-by-step guidance). Students can watch them at any place and anytime and can individually organize their learning pace. This flexibility may be an advantage over presentations in face-to-face lectures. The positive rating of our video presentation suggests that students likely prefer it over learning with a textbook section and possibly other traditional learning materials.

However, advantages beyond the ones we considered may hold true for learning with texts: students can highlight parts, make notes, and later they can quickly flip pages to find certain content. It remains an open question, whether and under which conditions students choose a video presentation for their individual learning process among other materials, even though previous research provides evidence that students make use of support services meeting their individual needs [2, 4]. Further, the active practice of the content through exercises seems to be an important next step in the learning process, which also may be supported by videos.

It should be mentioned that a great amount of video materials imparting statistical content is available online. Nevertheless, it makes sense for instructors to create their own video content: learning materials derived from university sources (like teachers or tutors) have a high credibility through quality assurance regarding scientific standards. They are tailored to the corresponding lectures, their specific content, special foci, and language, and thus students' needs. In addition, they are usually developed based on substantial theoretical models and evaluated through scientific methods (see, eg, [13]). Videos from other sources may simplify content and thus not meet the most important points. However, future research should differentiate between effects of application orientation and effects of motivation for video content from various sources in more detail. Presumably, the matching of user's and creator's intentions might be relevant for the effects. For example, students who intend to learn about a topic for an exam might be more likely to profit from videos created exactly for this purpose and less from those primarily designed to raise interest or motivation. Therefore, students would probably choose a video in line with their situational goal, when given the possibility. To provide students a well-founded decision, the preconditions and advantages of learning with such a tool should be already picked up in the instructions (cf. expectancy-value theory, [22]). Thus, individual expectancies and values are likewise conceivable as relevant factors in this research area.