Lecture 24 Slides

.pdf

School

University of Michigan *

*We aren’t endorsed by this school

Course

250

Subject

Statistics

Date

Feb 20, 2024

Type

pdf

Pages

Uploaded by SargentAtom11392

Welcome to our last week of Stats 250! stats250F23@umich.edu v Due Wednesday, December 6, by 7:00 pm v HW 8 v Updated optional Lab schedule and Office hours are posted on Canvas v Extra credit opportunities v Exam 2 Playbook v ECoach End of Term Survey v Stats 250 Student Experience Survey

This test is used for assessing if a particular discrete model is a good fitting model for a discrete characteristic. Example 1: Is the color distribution (red, green, etc.) in a bag of M&Ms the same as the one stated on the Mars Candy website? Example 2: Has the model for the method of transportation (drive, bike, walk, other) used by students to get the class changed from that 5 years ago? Chi-Square Goodness of Fit Test

This test helps assess if two discrete (categorical) variables are independent for a population, or if there is an association between the two categorical variables. Example 1 : Is there a relationship between academic grade level (first year, second year, etc.) and living situation (dorm, apartment, house, etc.) for the population of UM students? Example 2 : Is there an association between satisfaction with quality of public schools (unsatisfied, neutral, satisfied) and political party (Republican, Democrat, etc.) for the population of all adults? Note: Chi-square Test of Independence is similar to regression but the two variables are categorical (not quantitative). Chi-Square Test of Independence

Chi-Square Distributions Both tests based on a Chi-Square test statistic that, under the null hypothesis, follows a Chi-Square distribution with some degrees of freedom, ࠵? ࠵? (࠵?࠵?) Shape of a Chi-Square distribution changes based on the degrees of freedom

BIG IDEA Behind a Chi-Square Test 1. Sample data will consist of observed counts 2. Compute expected counts assuming the null is true 3. Check assumptions (based on expected counts) 4. Compare observed counts to expected using a ࠵? ! test statistic The larger the difference in counts à the. _____________ the ࠵? " test statistic, à the ____________ evidence against ࠵? 0 . ࠵? " = ( ࠵?࠵?࠵? − ࠵?࠵?࠵? " ࠵?࠵?࠵?

Scenario: Many UM courses have adopted flexible course modalities: In-Person, Synchronous streaming, asynchronous videos. Question: Among all undergraduate students at UM, is there an association between preferred course modality and whether a student commutes to campus or not? One Population: All UM ugrad students Two Variables: Preferred Modality (In-person, Synchronous, Asynchronous) and Commuter Status (Non-Commuter, Commuter) Chi-Square Test of Independence

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version