Statistical reasoning with the sampling distribution

Abstract

Statistical reasoning surrounding the sampling distribution is necessary for formal statistical inference. Our study of introductory statistics students aged 16-18 suggests that knowledge of the characteristics of a sampling distribution and experiences with generating sampling distributions do not provide a sufficient basis for this reasoning. Following instruction on the sampling distribution and its characteristics, the students in this study were given the opportunity to draw a sample before making an informal inference based on a sampling distribution. The majority of the students took several samples and/or considered generating a second sampling distribution for comparison. These are not incorrect statistical notions; but instead indicate that their statistical reasoning with the sampling distribution was still developing. The results are discussed in relation to students’ prior informal inferential reasoning and their subsequent formal inferential reasoning.