| Margaret E. M. Thomas | Department of Mathematics and Statistics |
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. (There is an Avenue to Learn page for this course, but it is just a link to the aforementioned Course Website.)...News pertaining to this section of STATS 3Y03/3J04 will appear here; for news about the course in general, it is your responsibility to check the Course Website regularly.
5 December 2018: Lecture notes from Lectures 37 and 38 now posted online.
I'm sure you have a lot to think about this week, but if you can take time for a ten-minute break and evaluate this course , to help make it better (as well as tell us what we're doing right!), then that would be much appreciated. Thanks in advance!
3 December 2018: Lecture notes from Lecture 36 now posted online.
Please remember to email in your requests for topics/questions to be covered in the Review part of this week's lectures (don't forget to include 3Y03 or 3J04 in the subject line of the email!).
28 November 2018: Lecture notes from Lectures 33, 34 and 35 now posted online.
22 November 2018: Lecture notes from Lectures 30, 31 and 32 now posted online.
19 November 2018: I've been asked to post the following concerning an on-campus study:
McMaster Drug Use Study - Participants Needed for Online Survey
We are collecting drug use data among undergraduate students. Participation involves the completion of a 17 question survey, which will take 2-10 minutes to complete, depending on your level of drug use. Participants will have the chance to win 1 of 33 Campus Store gift cards, including 3 grand prizes of $100.
To participate in the survey, please go to the following LimeSurvey.
If you have any questions or concerns, please contact: pavics@mcmaster.ca.
This study has been reviewed and approved by the McMaster University Research Ethics Board.
15 November 2018: Lecture notes from Lectures 27, 28 and 29 now posted online.
7 November 2018: Lecture notes from Lectures 24, 25 and 26 now posted online. Given that I didn't manage to complete the very last item on the agenda in Lecture 26 (two-sided testing for the mean of a Normal distribution with variance known), and so this might have been left in a confusing state, I've added some more commentary to the end of the notes that I encourage you to read, and that I hope untangle the knotty situation I left things in.
1 November 2018: Lecture notes from Lectures 21, 22 and 23 now posted online.
25 October 2018: Lecture notes from Lectures 18, 19 and 20 now posted online.
18 October 2018: Notice has just been given by SAS that notetakers are required for this course. If you want a further incentive to take good notes in class on a regular basis, please consider signing up. More information is available here .
17 October 2018: Lecture notes from Lectures 15, 16 and 17 now posted online. The marks from the first midterm may also now be found on the Course Website .
4 October 2018: Lecture notes from Lectures 12, 13 and 14 now posted online.
26 September 2018: Lecture notes from Lectures 9, 10 and 11 now posted online. Up to this point covers all of the material in the syllabus for the first midterm test (see the Course Website for more information). Also see the Course Website for organizational information relating to the first midterm.
19 September 2018: Lecture notes from Lectures 7 and 8 now posted online. (From now on the week's notes will be posted on Wednesdays.)
14 September 2018: Lecture notes from Lecture 6 are now posted online. In future, lecture notes for the preceding seven days (three lectures) will typically be posted after Wednesday's lecture.
13 September 2018: Lecture notes from Lectures 4-5 are now posted below as they relate to this week's assignment. Don't forget the deadline tomorrow!
12 September 2018: Office hours now changed. From now on they will be on Fridays at 10:30am.
7 September 2018: Lecture notes from Week 1 (Lectures 1-3) are now posted below.
3 September 2018: This page up and running.
Summaries of lectures and notes from class will be posted here as the semester progresses. (Lecture notes will typically be posted all together once a week, usually after the Wednesday lecture, but may be posted earlier if certain topics relate to an assignment with an earlier deadline.)
The lecture notes below are typically augmented versions of what was presented on screen during class; the augmentations are principally to be found in the form of extra comments (and corrections) written in light blue. Please send me an email if you ever find any mistakes or there are glitches in the documents.
You are strongly advised to go through these notes alongside your own notes carefully to make sure that you understand everything that was discussed!
Note: Since the first week had one more class than the other section (C02), the numbers of the lectures here are one higher than the number of the corresponding lecture in the Lecture Schedule on the Course Website (so Lecture 2 here = Lecture 1 on the Lecture Schedule, and so on).
(Tues 4 September 2018) -- Introduction to course, including introduction to the Course Website . Introduction to the role of Statistics and Probability Theory. (Wed 5 September 2018) -- Introduction to Probability Theory, i.e. 2.1: Sample Spaces and Events (distributive laws, De Morgan's laws), start of counting techniques (multiplication rule). (Fri 7 September 2018) -- Further counting techniques (k-permutations, permutations of similar objects, r-combinations). (Tues 11 September 2018) -- 2.2: Definition of probability, randomness, axioms of probability; 2.3: addition rule for probability. (Wed 12 September 2018) -- 2.4: Conditional probability; 2.5: Multiplication rule, Total Probability Rule. (Fri 14 September 2018) -- 2.6: Independence of events; 2.8, 3.1: Random variables (in particular discrete random variables). (Tues 18 September 2018) -- 3.2: Probability mass functions (pmf); 3.3 Cumulative distribution functions (cdf); 3.4 Mean and Variance of a discrete random variable. (Wed 19 September 2018) -- More on 3.4: More on Mean and Variance of a discrete random variable; Expected Value of a function of a discrete random variable. 3.6: Binomial distribution. (Fri 21 September 2018) -- 3.7: Geometric and Negative Binomial distributions; 3.8: Start of hypergeometric distribution. (Tues 25 September 2018) -- 3.8: Examples of hypergeometric distribution; 3.9: start of Poisson distribution. (Wed 26 September 2018) -- 3.9: Examples of Poisson distribution; 4.1: Continuous random variables; 4.2: Probability density functions (pdf). (Fri 28 September 2018) -- 4.3: Cumulative distribution functions; 4.4: Mean and variance of a continuous random variable; 4.6: Normal distribution. (Tues 2 October 2018) -- More on 4.6: Normal distribution; 4.7: Normal approximation to the binomial distribution. (Wed 3 October 2018) -- More on 4.7: Normal approximation to the binomial distribution; 4.8: Exponential distribution. (Fri 5 October 2018) -- 5.1 Two random variables (joint probability distribution functions, marginal distribution functions, independence of random variables). (Tues 16 October 2018) -- 5.2 Covariance and correlation of two random variables; 5.4 linear functions of random variables. (Wed 17 October 2018) -- More on 5.4: Linear functions of random variables, including sums and averages of random variables with the same distribution; 6.1 Data; Numerical Summaries of Data (sample mean, sample median, sample mode, sample variance, sample standard deviation, sample range). (Fri 19 October 2018) -- 6.2: Stem and Leaf Plots, quartiles and percentiles; 6.3: Frequency distributions and histograms. (Tues 23 October 2018) 6.4: Box (and whisker) plots; 6.7: Probability plots. (Wed 24 October 2018) -- More on 6.7: Probability plots; 7.1, 7.2: Point Estimates and Sampling Distributions (parameters, statistics, estimators, estimates, proportions), Central Limit Theorem. (Fri 26 October 2018) -- More on 7.2: Central Limit Theorem; 7.3: Concepts of Point Estimation (bias, trimmed mean, MVUE (Minimum Variance Unbiased Estimator), standard error). (Tues 30 October 2018) -- More on 7.3: Concepts of Point Estimation (estimated standard error, mean square error, relative efficiency, optimal estimator); 8.1: Confidence Intervals (general definition of a $100(1-\alpha)\%$ confidence interval; confidence interval for the mean of a Normal distribution, variance known; margin of error (ME)). (Wed 31 October 2018) -- More on 8.1: Confidence Interval for the mean of a Normal distribution, variance known (more on Margin of Error; one-sided confidence bounds; confidence interval for the mean of any distribution, variance known, large sample size; confidence interval for the mean of any distribution, variance unknown, large sample size); (Fri 2 November 2018) -- More on 8.2: Confidence interval for the mean of a Normal distribution, variance unknown ((Student) t-distribution, t-tables); 8.4: Confidence interval for the population proportion (large sample). (Tues 6 November 2018) -- 9.1: Hypothesis testing (null hypothesis $H_0$, alternative hypothesis $H_1$, test statistic, critical values/regions, Type I and Type II errors, significance level). (Wed 7 November 2018) -- More on 9.1: Hypothesis testing (power, p-value, relationship to confidence intervals); 9.2: Hypothesis testing for the mean of a Normal distribution, variance known ($Z_0$). (Fri 9 November 2018) -- More on 9.2: Hypothesis testing for the mean of a Normal distribution, variance known ($z$-test, connection with confidence intervals, Type II Error/$\beta$ and sample size); 9.3: Hypothesis testing for the mean of a Normal distribution, variance unknown ($T_0$, $t$-test). (Tues 13 November 2018) -- More on 9.3: Hypothesis testing for the mean of a Normal distribution, variance unknown (p-value); 9.5: Hypothesis testing for the population proportion (p-value, Type II Error/$\beta$ and sample size). (Wed 14 November 2018) -- 10.2: Hypothesis testing for the difference of means of two normal populations, variances unknown (equal and not equal cases). (Fri 16 November 2018) -- 11.1 and 11.2: Simple Linear Regression (least squares regression line, least squares estimates/estimators $\hat{\beta}_0, \hat{\beta}_1$, least squares normal equations, residuals, sums of squares error, total sum of squares, regression sum of squares). (Tues 20 November 2018) -- 11.3: Properties of the Least Squares Estimators ($\hat{\beta}_0, \hat{\beta}_1$); 11.4: Hypothesis Tests in Simple Linear Regression (t-test for $\hat{\beta}_0, \hat{\beta}_1$, Analysis of Variance Approach (ANOVA) and $F$-tests). (Wed 21 November 2018) -- 11.4: More on Hypothesis Tests in Simple Linear Regression (more on ANOVA); 11.5 Confidence intervals (on $\hat{\beta}_0, \hat{\beta}_1$); 11.6: Prediction of New Observations (prediction intervals). (Fri 23 November 2018) -- More on 11.6: Prediction of New Observations (prediction intervals); 11.7: Adequacy of the Regression Model (probability plots for residuals, coefficient of determination $R^2$); 11.8 Correlation ($R$). (Tues 27 November 2018) -- More on 11.8 Correlation ($R$ v. $R^2$); 13.2: Single-factor Experiments and Analysis of Variance (ANOVA) (factors, treatments, Experiment-wise Error Rate EER, completely randomized experimental design). (Wed 28 November 2018) -- More on 13.2: Single-factor Experiments and Analysis of Variance (ANOVA) (dot notation, total sums of squares $SS_T$, treatment sums of squares $SS_{\textrm{Treatments}}$, error sums of squares $SS_E$, mean squares treatments $MS_{\textrm{Treatments}}$, mean squares error $MS_E$, $F$-test). (Fri 30 November 2018) -- More on 13.2: Single-factor Experiments and Analysis of Variance (ANOVA) (confidence intervals for individual treatment means, and for the difference between two treatment means; multiple comparisons and Fisher's LSD (least significant difference) method). (Tues 4 December 2018) -- More on 13.2: Single-factor Experiments and Analysis of Variance (ANOVA) (validity of assumptions, unbalanced setup). Review: Bias and standard error of estimators; mean and variance of linear functions of random variables (including total and sample mean). (Wed 5 December 2018) -- Review: How to find $E(X^2)$ (in the context of finding expectation/variance/bias/standard error of estimators); how to navigate the z-tests and t-tests on the formula sheet; Normal approximation to the binomial distribution.