# Statistic

## Overview

In general, we find that students tend to confuse statistic in an everyday sense with statistic in a strict statistical sense. 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: "Write a sentence using the word statistic, then give the definition of statistic as you used it in the sentence", student responses have been summarized into the following categories (in this case, categories are exlusive):

1. Numerical summary of a sample; Representing or describing a sample
2. Numerical summary of a population; Representing or describing a population
3. Information or a calculated value with no reference to a sample or population
4. A very specific example, often involving context like GPA or Batting Average
5. A statement emphasizing the use of a statistic for inference
• e.g., "Data used to make inferences" or "A statistic is data that can be used to learn information"
6. A number or set of numbers that were observed as opposed to derived or calculated; often similar to a definition of "sample", "observation", or "datum".
7. Definition limited to a specific mathematical example like the "average" or "proportion"
8. Statistics as a Discipline or Class

The three groups are Pre-Test - before instruction, HILT - students who received instruction from HILT activities,and Comp - students who received standard instruction from the "comparison group", i.e., not including HILT activities.

While both post-test groups had a much higher proportion of responses in category 1 (the most statistically rigorous response,) the HILT group had a much larger increase. The HILT group also decreased the number of category 3s, a less rigorous response, while the comparison group remained about the same proportion in that category.

## Activities

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

 All vs. Small Candy Jar