Week 12: ANOVA, Chi-squared Tests

Slides

Analysis of Variance

Chi-squared Tests

• Chi-squared Tests
• Chi-squared tests for independence

Performance Outcomes

You should feel confident to perform the following outcomes:

Multiple linear regression

• Explain the purpose and basic concepts of simple linear regression
• Identify the variables involved and write the regression equation
• Interpret the slope and intercept in the context of real data
• Describe the assumptions underlying simple linear regression
• Fit a simple linear regression model using statistical software
• Interpret regression output, including coefficients and p-values
• Use the model to make predictions based on new data
• Evaluate the model fit using residuals and diagnostic plots
• Write the general form of a multiple linear regression equation and define its components
• Identify the key assumptions underlying multiple linear regression models, including linearity, independence, homoscedasticity, normality of errors, and absence of multicollinearity
• Fit a multiple linear regression model to a dataset using R
• Interpret the coefficients, R-squared, adjusted R-squared, and significance values from a multiple linear regression output.
• Evaluate model assumptions and use diagnostic plots to detect potential violations.
• Use the regression model to make predictions and interpret these predictions in the context of the study.
• Communicate the results and implications of a multiple linear regression analysis effectively.

ANOVA

• State null and alternative hypotheses appropriate for comparing means across multiple samples
• Select and justify the correct hypothesis test (such as ANOVA) for comparing more than two means
• Check and explain the assumptions for the selected hypothesis test
• Calculate the appropriate test statistic from sample data
• Determine and interpret the p-value in the context of the test
• Make a decision by comparing the p-value to the significance level
• Draw conclusions in context, explaining statistical significance
• Perform post-hoc analysis when appropriate to identify which means differ
• Conduct ANOVA and post-hoc tests using R
• Communicate the process, reasoning, and results of the hypothesis test clearly

Chi-squared test

• State appropriate null and alternative hypotheses for a chi-squared test
• Identify when it is appropriate to use a chi-squared test for categorical data
• Check the assumptions and requirements for conducting a chi-squared test
• Calculate expected frequencies for contingency tables
• Compute the chi-squared test statistic using observed and expected frequencies
• Find and interpret the p-value in the context of the test
• Make a statistical decision by comparing the p-value to the significance level
• Draw context-appropriate conclusions about the association or independence between variables
• Conduct a chi-squared test using R
• Communicate the process, reasoning, and results of the hypothesis test clearly

Resources

If you don’t feel yet confident after going through the teaching materials or would like further resources, then you are also encouraged to go through the following materials.

• Statistical Inference via Data Science: A ModernDive into R and the Tidyverse (2nd Edition)
  • Chapter 10: Inference for Regression
• OpenIntro Statistics (4th Edition)
  • Chapter 6.3: Testing for goodness of fit using chi-square
  • Chapter 6.4: Testing for independence in two-way tables
  • Chapter 7.5: Comparing many means using ANOVA
  • Chapter 9.4: Multiple regression case study: Mario Kart

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