Abstract:

Statistics can be an interesting tool to study the results of students in Higher Education. For example, a widely used Learning Management System (LMS) such as Moodle has a statistical module to automatically evaluate the scoring results of quizzes taken by students. There are several typical statistical parameters such as average, median, or standard deviation. There are other less used parameters such as score distribution skewness and kurtosis. All these parameters have to do with the normality of the distribution of marks in a given exam question or in the final marks of the exam.

There are also other parameters, such as the facility index, who represents the amount of students who got the question correct. This value of the facility index determines how difficult a question has been for students. The discrimination index is the correlation between the score for a question and the score for the whole quiz or exam. That is, for a good question, the lecturer hopes that the students who scored highly on a particular question are the same students who scored highly on the whole exam. Both parameters allow to discriminate between easy, intermediate or difficult questions. These indexes can be compared or correlated with a difficulty rating for each question established by the teacher. With all this information the lecturer can check if there are questions that might have been set up incorrectly or are too easy or too difficult, and / or to identify contents in which the students may be weaker. The teacher also has the possibility of establishing a pool of questions, classified in terms of difficulty, to be used in the following assessments.

The complete study can allow teachers to learn about and to improve the evaluation of students, classifying the questions as more or less appropriate to the required level and at the same time establishing the level that students have acquired and the possible lacks of study. It is therefore possible to achieve an improvement in the questions of future exams based on the previous results.

In this study, the usefulness of several statistical parameters for the treatment of students' academic results has been evaluated and it has also been applied to several real cases of marks from theory exams of a subject in the field of Chemical Engineering.

Keywords:

Higher Education, statistics, academic results.