STA110B: Course Overview
Below is a broad outline of topics to be covered in STA110B. Please
note that I will continue to update it as we move along. I have tried
to provide the chapter numbers where appropriate, but please note that
some topics will be introduced in lecture which are not included in
the text. For this reason, it will be necessary to keep up with
assigned readings, work through homework problems, and learn the
material discussed in lecture.
- 1. Basic probability and statistics (Wonnacott and Wonnacott, Chp. 1)
- Important vocabulary include: random sample, treatment, response, controlled, randomized, placebo, double-blind, etc.
- Discuss random sampling, particularly in the context of estimating
population proportions
- Compare and contrast controlled experiments and observational studies.
- 2. Descriptive Statistics (Wonnacott and Wonnacott, Chp. 2)
- Draw and interpret frequency tables and graphs
- Calculate percentiles and understand box plots
- Understand the concepts of center and spread; know which types of statistics are typically used to convey these two ideas.
- Find the average, median, and mode of a data set.
- Find the range, inter-quartile range, mean squared deviation,
variance, and standard deviation of a data set.
- Understand how linear transformations change the mean and standard
deviation, as well as the data set.
- Use the normal approximation for data.
- Be able to interpret and think critically about graphical displays.
- 3. Basic probability (Wonnacott and Wonnacott, Chp. 3, Sec. 1-3, 7)
- Understand what is meant by the chance, or probability, of an
event occurring.
- Draw and use a tree model to identify possible outcomes and their
associated probabilities.
- Discuss compound events using terminology such as "and", "or",
"mutually exclusive", "complements", etc.
- Express probabilities as "odds".
- Using "symmetric probability" to solve problems.
- 4. Conditional probability (Wonnacott and Wonnacott,
Chp. 3, Sec. 4-6)
- Understand and calculate conditional
probabiliies.
- Define statistical independence; relate
independence to the multiplication rule.
- Understand and apply Bayes Theorem.
- 5. Probability distributions (Wonnacott and Wonnacott, Chp. 4)
- Differentiate between discrete and continuous distributions
- Calculate population mean and variance
- Find probabilities under the binomial model
- Use the standard normal table and "z-scores"
- Given a population mean, calculate the mean if the data is
linearly transformed
- Be familiar with various notations for the mean (esp. that
refering to expected value)
- 6. Bivariate distributions (Wonnacott and Wonnacott,
Chp. 5)
- Understand joint and marginal distributions
- Determine whether two variables are independent or dependent
- Calculate covariance and correlation
- Calculate expectations and variances of linear combinations of variables
- 7. Sampling and point estimators (Wonnacott and Wonnacott, Chp. 6-7)
- Understand terminology such as population, random sample, sampling
with and without replacement
- Understand and apply the central limit theorem.
- Using the normal approximation rule for proportions (including the
continuity correction)
- Apply the SE reduction factor when faced with small-population sampling
- Calculate the bias of an estimator
- Be able to calculate the relative efficiency of estimators,
whether they are biased or unbiased
- 8. Confidence intervals (Wonnacott and Wonnacott,
Chp. 8)
- Find the 95% confidence interval for one mean or the difference in
means
- Know when to use the t-statistic rather than the z-statistic
- In the case of the difference of two means, know when to use the
two methods for calculating the standard error
- Know how to calculate a confidence interval for the difference
in means, given matched samples ("paired test")
- Know how to calculate confidence intervals for proportions (or the
difference in proportions)
- 9. Hypothesis testing (Wonnacott and Wonnacott, Chp. 9)
- Understand the procedure for conducting a hypothesis test
(one-sided and two-sided)
- Find and interpret p-values
- Define type I and type II errors
- Understand the relationship between confidence intervals and
hypothesis testing
- 10. Analysis of Variance (ANOVA) (Wonnacott and Wonnacot,
Chp. 10)
- Calculate and interpret the ANOVA table (one way)
- Understand the F-test (and corresponding hypotheses)
- Calculate and interpret the ANOVA table (two way)
- Understand the F-tests (and corresponding hypotheses)
- Construct confidence intervals for differences between the means
- 11.Linear regression (Wonnacott and Wonnacott, Chp. 11-12)
- Understand ordinary least squares (the criterion and the formulas)
- Calculate a least-squares fitted line
- Identify the assumptions inherent in the regression model
- Conduct hypothesis tests and confidence intervals for the slope of
the regression line
- Predict y for a given level of x
- 12. Multiple regression (Wonnacott and Wonnacott,
Chp. 13)
- Understand the multiple regression model and the OLS fit
- Construct confidence intervals for the parameters of the model
- Consider which regressors should be included
- Interpret the regression model
- 13. Chi-square tests (Wonnacott and Wonnacott, Chp. 17)
- Know when to use the goodness-of-fit test and when to use the
independence test
- Conduct and interpret the goodness-of-fit test (hypotheses,
statistic, assumptions, etc.)
- Conduct and interpret the test for independence (hypotheses,
statistic, assumptions, etc.)