An Analysis of the Discrepancy between the Students' Responses to Multiple-Choice and Open-Ended Questions

Guidelines for Assessment and Instruction in Statistics Education (GAISE)provide a framework for revising introductory statistics courses. GAISE promotes statistical literacy and statistical thinking, where students not only understand concepts but are able to critically evaluate and make arguments based on quantitative information.There are multiple definitions of statistical literacy and statistical thinking inthe literature. In this thesis we are interested in the aspect of statistical literacythat aims for an educated consumer, one who can process everyday statisticalinformation. Further, Statistical thinking is present when students can apply the statistical information learned to situations such as: 1) using statistics to solve real world problems, 2) critique and interpretation of statistical information reported in the mass media, and 3) interpretation and communication of statistical findings within context .Despite this growing consensus that students must acquire higher-order think-iing and performance skills in order to apply statistical reasoning and thinkingto their research problems successfully, a gap still exists between course objectives and student outcomes. After completion of the coursework, students are more likely to forget the materials learned in course and continue to struggle with applying statistical reasoning and thinking. The type of assessment used in statistics courses provides one explanation for this gap. With the increase number of students enrolled in introductory courses, instructors rely heavily on multiple choice questions to evaluate students0undesrtanding of course materials and principles. Furthermore, in subjects such as mathematics, statistics, chemistry, biology, and physics, research has shown that about 70% of the questions are at the recall or comprehension level with very little attention paid to the questionsthat target application, analysis, synthesis, and evaluation. Therefore, and based on Bloom's taxonomy, the student outcomes focus on lower level thinking skills (knowledge and comprehension), whereas the course objectives and expectations involve higher level of thinking skills (application, analysis, synthesis, and evaluation). In order to bridge the gap between objectives and outcomes, tests must provide students opportunities to employ higher order thinking.The objectives of this thesis include:1. Comparison of students'responses to open-ended questions on condenceinterval and P-value.2. Prediction of the students' final scores from their scores on "upper levelthinking", "application", "lower level computation and "upper level computation".3. Pinpoint the students'misconceptions of the P-value by comparing the pro-portion of correct answers under two conditions including: a) deciding aboutthe null hypothesis by comparison of the P-value Vs. level of signicanceor alpha, and b) deciding about the null hypothesis by examination of thecondence interval and the interpretation of the P-vlaue