The material is an interactive application developed in shiny to demonstrate the Chi-Square Goodness of Fit Test using simulations. This material is great for using in class to demonstrate the choice of sample size, number of categories, and number of simulations on tests for equiprobable null and different null probabilities.
The Chi-Square Goodness of Fit Test is applied when you have categorical variables from a population. When an analyst attempts to fit a statistical model to observed data, he or she may wonder how well the model actually reflects the data. How close are the observed values to those which would be expected under the fitted model? One statistical test that addresses this issue is the chi-square goodness of fit test.
Type of Material:
Simulation
It is a web page with background context , visualizations and interactive components that are accessible via different tabs.
Recommended Uses:
This would be a companion site for getting hands on understanding of Chi-Square goodness of fit. Under the explore tab there is a short assessment quiz.
In class, homework, individual, team, lecture, self-paced.
Technical Requirements:
Any browser
Identify Major Learning Goals:
The purpose of the application is to provide an understanding of Chi-Square Goodness of fit tests using simulations. The application has interactive elements for sample size, number of categories, number of simulations and choice between equiprobable null probabilities or different null probabilities between the categories. It generates the distribution of p-values for each situation.
Target Student Population:
High School, College Lower Division, College Upper Division, Graduate School
Prerequisite Knowledge or Skills:
Basic knowledge of sampling distribution, hypothesis tests, and goodness of fit test. Some of which is provided under prerequisites tab
Content Quality
Rating:
Strengths:
Interactive learning of sample size, number of categories and probability distribution across category results in the distribution of p-values.
There is an assessment quiz under the “Let’s Practice” which can be used as a formative assessment to check for understanding.
Concerns:
The takeaway of the p-value distribution of the goodness of fit statistic is fairly limited. Perhaps grounding it in examples using some common distributions would have provided the necessary context.
It would have been great to include context on the chi-square distribution to see it as a making decision tool.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This material can be used in class for demonstrating the concept by the instructor or by students to explore and assess.
Concerns:
Before interacting with the material, the students need to have a background in sampling distributions, the chi-square distribution, and hypothesis tests.
It is unclear how one would use the distribution of the p-values generated from the various situations.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The instructions are clear.
There is an assessment as well under the “Let’s Practice” tab to check for understanding.
Creative Commons:
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