# ASSESSING PROSPECTIVE HIGH SCHOOL TEACHERS’ UNDERSTANDING OF STATISTICAL HYPOTHESES

In spite that statistical tests are widely used in research, its interpretation and application have been discussed in the past 50 years. An explanation of this paradox is that statistical tests are difficult, because performing these tests requires students to understand and be able to relate many abstract concepts such as those of parameter and statistics, sampling distribution, level of significance, null and alternative hypotheses, and p-value.

Most previous research on this topic deals with understanding the concepts of level of significance and p-values and has described many related misconceptions. However, there is also confusion between the roles of null and alternative hypotheses; other students state their hypotheses in terms of the sample statistics (for example, the sample mean) instead of using the parameter (the sample population), set non complementary hypotheses or else the hypotheses do not cover the parametric space.

Statistical tests have been included in the Spanish high school curriculum periodically, as well as in the test that are compulsory for students to enter University (University Entrance Tests, UET). Moreover a basic knowledge of this topic as well as elementary competence in solving simple tests problems are important for high school teachers, since results of applying statistical tests often appear in educational research papers. However, the statistical knowledge of those preparing to become mathematical teachers in this educational level in the past years is varied, because due to the economic crisis, their background is not always a Bachelor in Mathematics or Statistics, but include a variety of different previous studies. A poor competence of prospective teachers with statistical tests may easily be transmitted to their students, who will reproduce the errors described in the previous paragraphs.

Taking into account these considerations, the aim of this research was assessing prospective high school understanding of hypotheses in statistical tests. In this paper we describe the responses to an open-ended problem, similar to those proposed at the UET for high school students in the past years. The sample consists of 73 students preparing to become secondary and high school mathematics teacher in the Master of Secondary School Teachers, specialty of mathematics, which is compulsory for those who want to apply for a position as mathematics teacher in Spain.

A qualitative analysis of the responses in a question where the participants were requested to describe the hypotheses in a statistical test provided the following categories of responses:

1. Correct hypotheses and notation (70.7% participants).

2. Correct hypotheses verbally established or using incorrect notation (8%).

3. Errors in establishing the hypotheses, such as hypotheses that does not cover the parametric space, exchanging the null and alternative hypotheses, setting the hypotheses in terms of the sample statistics, including the hypothetical value in the alternative hypotheses, or setting non-mutually exclusive hypotheses or non-complementary hypotheses (21.3%).

Although the majority of students provided correct hypotheses, only 60,8% established the correct critical region consistently with the established hypotheses and only 31,1% correctly finished the whole procedure. Consequently, it is important to organise educational activities directed to help teachers increase their statistical knowledge concerning statistical tests.