# 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):

- Numerical summary of a sample; Representing or describing a sample
- Numerical summary of a population; Representing or describing a population
- Information or a calculated value with no reference to a sample or population
- A very specific example, often involving context like GPA or Batting Average
- 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"

- 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".
- Definition limited to a specific mathematical example like the "average" or "proportion"
- 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 |