The Midterm Exam

Quick Guidelines:

• Take-Home Exam with 24-hr submission limit

• 2 parts, 10 questions each

• Open Notes

• Must be done using Rmarkdown, and must be submitted as knitted PDF.

• The majority of the exam is similar to the problems done in Homework and Labs.

For more details visit the Exams page in the course website.

Frequently Asked Questions

• What’s going to be on the test?

• What will the test questions be like?

• What content would be helpful in answering test questions?

• How should I be studying for the exam?

FAQ

What’s going to be on the test?

What content would be helpful in answering test questions?

Topics - Types of Variables

• Identify numerical variables

  • Discrete

  • Continuous

• Identify categorical variables

  • Ordinal

  • Nominal

Topics - Explanatory and Response Variables

• Explanatory variable

  • This is also called the independent variable or the predictor

• Response Variable

  • This is also called the dependent variable.

Topics - Studies, Populations, and Samples

• Observational study

• Experimental study

• Population and parameter

• Sample and statistic

Topics - Sampling

• Sampling Strategies

  • Simple Random Sampling

  • Stratified Random Sampling

  • Clustered Sampling

• Sampling Styles

  • Sampling with replacement

  • Sampling without replacement

Topics - Basic Probability Rules

• Sample space and Event space

• Discrete vs continuous random variables

• Independent events

• Simple probability rules which includes the union and intersection of probabilities.

Topics - Probability functions

• Basic Probability functions, which can be given as a table or plot.

• Binomial probability mass function (pmf)

• Normal probability density funtion (pdf)

  • This includes the standard normal distribution

Topics - Linear Regression

• Simple linear regression

  • One predictor and one response

  • Assumptions of the linear regression

• Computing the slope and intercept using the least-squares method

• Interpreting the slope and intercept

• Computing and interpreting the correlation

• Computing residuals and evaluating the model based on the residuals

  • Interpreting the coefficient of determination, \(R^2\).

• Multiple Linear regression

  • Interpreting the adjusted coefficient of determination, \(R_{adj}^2\).

Topics - Hypothesis Testing (1/2)

• The null and alternative hypothesis

• Point estimates

• Difference in Proportions

  • Randomization test (permutation test or shuffling), not to be confused with bootstrapping

  • Purpose of the Randomization test: to simulate an experiment when randomly assigning people into two groups assuming the independence of the explanatory and response variables

Topics - Hypothesis Testing (2/2)

• The p-value from the randomization test

• Interpreting the p-value

• Decision errors

  • Type I error

  • Type II error

• The significance level

Topics - Confidence Intervals

• Estimating the true population parameter using a confidence interval

  • Single proportion

  • Single Mean

• Estimating confidence intervals using percentiles from the bootsrapping approach

  • Bootstrapping, which is sampling with replacement, not to be confused with the randomization test

  • Purpose of bootstrapping: instead of using a “resample from the population” approach, bootstrapping uses a “resample from the sample” approach

• Interpreting the confidence interval

FAQ

What will the test questions be like?

R - Data set and R Libraries

• Able to load R libraries and know what its purpose and usage.

• Able to load data frames from a CSV file.

• Able to plot data - scatterplot, historgrams, bar plot, etc.

• Able to knit an Rmd File into a PDF (not into HTML and then converted into PDF). I will demonstrate this in tomorrow’s lab.

• Able to solve common (minor) R errors and R Markdown errors by yourself. I will demonstrate how I avoid and fix minor errors in tomorrow’s lab.

2 Parts - 10 Questions Each

• Part 1 - Hypothesis Testing and Confidence Intervals

  • Given a data set (CSV) and a research question. (This involves a little bit of computing true probabilities)

  • Perform the randomization test and the bootstrapping approach using R.

  • Write the null and hypothesis testing correctly.

  • Interpreting the p-value and confidence intervals.

  • Writing your analysis.

• Part 2 - Linear Regression

  • Given a data set (CSV) and a research question.

  • Perform the least squares method in R to compute the slope and intercept.

  • Interpreting the slope and intercept.

  • Writing your analysis.

FAQ

How should I be studying for the exam?

• I recommend going through the Lab assignments and Lab demonstrations for R coding.

• Go through Homework problems and solution to see what kind of answers I am looking for.

Today’s Activity

We will use the remaining time for Question-Answering.

• What topic do want to discuss in detail today?

• What do you need during the midterm exam?

• What information do you need that needs to be on the course website that might help you on the midterm exam?