Skew

Overview

In general, we find that students tend to confuse skew in an everyday sense (distribution with long tail) with skew in a strict statistical sense (distorted, incorrect). Research shows that this confusion is very frequently not resolved even after a student has completed an introductory course.

Student Notions

When presented with a prompt such as: "The researcher reported that the data were skewed. What does skewed mean in this context?", student responses have been summarized into the following categories (in this case, categories are exclusive):

• Statistical Notions
  • Having a tail when graphed
  • Samples or results based on an experimental design flaw (Statistical Bias)
  • Vague references to distribution shape
  • Problems created by outliers
  • Data spread out; "All over the place"

• Colloquial Notions
  • Incorrect, Different
  • Sudden change in direction
  • One-sided, lean in one direction (Colloquial Bias)

Activities

The following HILT activities have been designed to address student misconceptions regarding "Skew" and have research that suggests they improve student learning

Distorted Distributions