Statistics

LinkedIn provides a great means to find people who have common interests, to exchange knowledge and perspectives, and to find opportunities or potential candidates for opportunities. The discussion group 'Research, Methodology, and Statistics in the Social Sciences' was created in February 2012 and counted more than 42.000 members hardly 2.5 years later.

Developing conceptual understanding of statistics requires an instructional format that adjusts cognitive load to the student’s level of expertise in order to optimize motivation to learn. Structuring the material to be learned and guiding self-explanation of what is learned will diminish fear and postponing behavior on the part of the student, it will stimulate students to engage in meaningful learning, which will help them to keep an overview and develop conceptual understanding of the subject matter. These aims of education form the pillars of the educational method presented in this paper: the method of propositional manipulation (MPM).

A new ten-item instrument for the measurement of intrinsic, extraneous, and germane load (IL, EL, GL) was developed, and a paper presenting the first validation studies has been submitted [1]. The purpose of this study was to explore the correlations between these three types of cognitive load (CL) as measured by the new instrument at the end of a lecture in a statistics course and exam performance in that statistics course five weeks later. The lecture covered sampling distributions and other concepts related to sampling theory. This content formed the very core of the statistics course and each of its modules, a course for first-year bachelor of psychology students in a Dutch university. Approximately 400 students followed the course, of which approximately 200 attended the lecture and a total of 174 students responded to the questionnaire.
The lecture lasted two hours, and students were instructed to complete the questionnaire at the end of the lecture. Leppink and colleagues [1] demonstrated that varying the order in which the items are asked does not influence factor loadings or internal consistency values to a noticeable extent, therefore the ten items were presented in the order presented in Box 1. All 174 students completed the questionnaire on paper at the very end of the lecture and handed it in right away.
The new instrument provides us with insight into students’ experienced IL, EL, and GL. Further, we can develop efficiency measures based on these scales. Usually, efficiency relates to reaching the highest possible performance with the lowest possible costs, and test performance is evaluated in relation to mental effort in either testing stage [2] or learning stage [3]. The new instrument, however, opens yet another perspective on instructional efficiency: GL as the fraction of extrinsic load (i.e., the sum of EL and GL) or overall CL (i.e., the sum of IL, EL, and GL).
Table 1 presents mean and standard deviation (SD) along with range, skew, and kurtosis for IL, EL, GL, and the two new efficiency measures (defined as IE1 and IE2, respectively). The IL scores give little reason to believe that the lecture covered highly complex subject matter, and the EL and GL scores appear to indicate that the instructions and explanations during the lecture were quite clear and stimulated the students to engage in processes that would contribute to learning. Three students had outlying scores on EL, but no outliers were detected on the efficiency measures.
Table 2 presents the correlations between IL, EL, GL, IE1, IE2, and final exam performance. Of the 174 students who responded to the questionnaire, a total of 151 also attended (and completed) the exam at the end of the course. The correlations between the CL variables and exam performance are therefore based on 151 students. These findings indicate that lower EL and higher efficiency scores in a learning stage to some extent predict better exam performance at the end of a course. Implications of these findings for research and teaching practice will be discussed.

References
[1] Leppink, J., Paas, F., Van der Vleuten, C. P. M., Van Gog, T., & Van Merriënboer, J. J. G. (submitted). Development of an instrument for measuring different types of cognitive load.
[2] Paas, F., & Van Merriënboer, J. J. G. (1993). The efficiency of instructional conditions: an approach to combine mental effort and performance measures. Human Factors, 35, 737-743.
[3] Van Gog, T., & Paas, F. (2008). Instructional efficiency: revisiting the original construct in educational research. Educational Psychologist, 43, 16-26.

Contrary to classical problem-based learning, in guided problem-based learning, the learning goals are predetermined by the instructor—on the basis of a detailed decomposition of the subject matter to be studied—to activate prior knowledge and to structure self-study and subsequent group discussion. This study investigated the effects of classical problem-based learning and guided problem-based learning, for different prior knowledge levels, on perceived value and usefulness of the learning activity and on conceptual understanding of statistics. Participants randomly assigned 110 students to 10 problem-based learning groups, and subsequently, the 10 groups were allocated randomly to classical problem-based learning or guided problem-based learning. The results indicate that guided problem-based learning tends to enhance conceptual understanding of statistics more thanbreak; classical problem-based learning once students have some prior knowledge of the subject. Furthermore, guided problem-based learning tends to increase students’ awareness of the value and usefulness of the learning activity.

The current experiment examined the potential effects of the method of propositional manipulation (MPM) as a lecturing method on motivation to learn and conceptual understanding of statistics. MPM aims to help students develop conceptual understanding by guiding them into self-explanation at two different stages: First, at the stage of propositions (statements referring to single statistical concepts and ideas), and subsequently, at the stage of more complex problems that comprise a set of relevant propositions. A total of 71 bachelor students in psychology who were preparing for the re-sit of their inferential statistics exam participated in one of two possible lectures. Topic, content, lecturer, and duration of both lectures were the same, and in both lectures five true/false hypotheses were presented. Students in the first lecture (control group) discussed interactively the truth or falsity of each hypothesis. In the second lecture (MPM group), this interactive discussion was structured by presenting a number of short open-ended questions along with each hypothesis. Conceptual understanding was measured by means of a twelve items multiple choice test. Further, the intrinsic motivation inventory was administered to examine motivation to learn. The results indicate that MPM does not lead to enhanced motivation to learn but can facilitate conceptual understanding development among students.

This study investigated the effects of four instructional methods on cognitive load, propositional knowledge, and conceptual understanding of statistics, for low prior knowledge students and for high prior knowledge students. The instructional methods were (1) a reading-only control condition, (2) answering open-ended questions, (3) answering open-ended questions and formulating arguments, and (4) studying worked-out examples of the type of arguments students in the third group had to formulate themselves. The results indicate that high prior knowledge students develop more propositional knowledge of statistics than low prior knowledge students. With regard to conceptual understanding, the results indicate an expertise reversal effect: low prior knowledge students learn most from studying worked-out examples, whereas high prior knowledge students profit most from formulating arguments. Thus, novice students should be guided into the subject matter by means of worked-out examples. As soon as students have developed more knowledge of the subject matter, they should be provided with learning tasks that stimulate students to solve problems by formulating arguments.

The applications of statistics in every-day and professional context are almost endless, and there are even more examples of the misuse of statistics in such a context. Given the importance of statistics in research, politics, policy, et cetera, it is of crucial importance that students and professionals develop a good understanding of statistics. This requires a structured and staged approach. Core feature of this approach is that instructional guidance decreases in subsequent stages, while receiving feedback on learning output remains possible.

This study investigated the effects of different teaching and learning methods for statistics for 2 levels of prior knowledge on cognitive load, propositional knowledge, and conceptual understanding. Teaching methods were whether or not to provide students with propositional information, and learning strategies were self-explaining the learning material and explaining in pairs. The results indicate that prior knowledge facilitates propositional knowledge development and leads to differential effects of teaching and learning methods on conceptual understanding: Only low prior knowledge students profit from additional information in the learning task and/or explaining in pairs. An implication of these findings is that low prior knowledge students should be guided into the subject matter by means of working in pairs on learning tasks that comprise additional information. Once students have developed more knowledge of the subject matter, they should be stimulated to work individually on learning tasks that do not comprise additional information.

The method of propositional manipulation (MPM) aims to help students develop conceptual understanding of statistics by guiding them into self-explaining propositions. To explore task- and student-related factors influencing students‟ ability to learn from MPM, twenty undergraduate students performed six learning tasks while thinking aloud. The results indicate that whether students learn from MPM depends on their statistics proficiency level, the subject matter, the number of propositions in the learning task, and the instructions. MPM learning tasks should be tailored to the students‟ level of expertise and students should be instructed more than once to integrate all propositions in the learning task into their arguments.

A comparison of the relative yields of Upsilon resonances in the mu(+) mu(-) decay channel in PbPb and pp collisions at a centre-of-mass energy per nucleon pair of 2.76 TeV, is performed with data collected with the CMS detector at the LHC. Using muons of transverse momentum above 4 GeV/c and pseudorapidity below 2.4, the double ratio of the Upsilon(2S) and Upsilon(3S) excited states to the Upsilon(1S) ground state in PbPb and pp collisions,(Upsilon(2S+3S)/Upsilon(1S)[PbPb])/(Upsilon(2S+3S)/Upsilon(1S)[pp]), is found to be 0.31 - 0.15 + 0.19 (stat.) +/- 0.03 (syst.). The probability to obtain the measured value, or lower, if the true double ratio is unity, has been calculated to be less than 1%.