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Stats 101: Chapter 2

Chapter 2 is now ready for downloading—it can be found at this link.

This chapter is all about basic probability, with an emphasis on understanding and not on mechanics. Because of this, many details are eliminated which are usually found in standard books. If you already know combinatorial probability (taught in every introductory class), you will probably worry your favorite distribution is missing (“What, no Poisson? No negative binomial? No This One or That One?”). I leave these out for good reason.

In the whole book, I only teach two distributions, the binomial and the normal. I hammer home how these are used to quantify uncertainty in observable statements. Once people firmly understand these principles, they will be able to understand other distributions when they meet them.

Besides, the biggest problem I have found is that people, while they may be able to memorize half a dozen distributions or formulas, do not understand the true purpose of probability distributions. There is also no good reason to do calculations by hand now that computers are ubiquitous.

Comments are welcome. The homework section (like in every other chapter) is unfinished. I will be adding more homework as time goes on, especially after I discover what areas are still confusing to people.

Once again, the book chapter can be downloaded here.

8 thoughts on “Stats 101: Chapter 2 Leave a comment

  1. Chap 2 is okay, maybe a little confusing for an Intro to the subject, however. More verbal explication of the equations might be helpful to the stat newbie.

    It might also help me to help you if you presented a rough Table of Contents. If I knew where you were going, it might help me to judge whether these early chapters are sufficient. For instance, you say you plan to present only two distributions. Okay, but where are you going with non-parametric stats? Will you get to visual methods? Survival analysis? Generalized linear models? What’s the scope?

  2. Here’s a rough Table of Contents. Chap 12 is being pushed to the end, the regression chapter might be merged and a new one on logistic might appear.

    Chapter 1. Logic 1
    1. Certainty & Uncertainty 1
    2. Logic 2
    3. What is probability? 6
    4. Why isn?t probability subjective? 8
    5. Randomness 9
    6. A taste of Boolean algebra 10
    7. Mechanics 11
    8. Homework 12
    Chapter 2. Probability 15
    1. Probability rule number 1 15
    2. Probability rule number 2 16
    3. Probability rule number 3 17
    4. Probability rule number 4: Bayes?s rule 20
    5. Extra: More Bayes?s rule 22
    6. Homework 23
    Chapter 3. How to Count 27
    1. One, two, three… 27
    2. Arrangements 28
    3. Being choosy 28
    4. Counting meets probability: The Binomial distribution 30
    5. Homework 32
    Chapter 4. Distributions 35
    1. Variables 35
    2. Probability Distributions 38
    3. What is Normal? 41
    4. Homework 47
    v
    vi CONTENTS
    Chapter 5. R 49
    1. R 49
    2. R binomially 51
    3. R normally 53
    4. Advanced 55
    5. Homework 55
    Chapter 6. Normalities & Oddities 57
    1. Standard Normal 57
    2. Nonstandard Normal 58
    3. Intuition 60
    4. Homework 62
    Chapter 7. Reality 65
    1. Kinds of data 65
    2. Databases 68
    3. Summaries 69
    4. Plots 71
    5. Extra: Advanced topics 72
    6. Homework 73
    Chapter 8. Estimating 75
    1. Background 75
    2. Parameters and Observables 77
    3. Classical guess 78
    4. Confidence intervals 80
    5. Bayesian way 85
    6. Homework 88
    Chapter 9. Estimating and Observables 91
    1. Binomial estimation 91
    2. Back to observables 92
    3. Even more observables 95
    4. Homework 98
    Chapter 10. Testing 101
    1. First Look 101
    2. Classical 1 105
    3. Classical 2 110
    4. Modern 111
    5. Homework 112
    CONTENTS vii
    Chapter 11. More Testing 115
    1. Proportions 1 115
    2. Testing differences in proportions 2 117
    3. Testing differences in proportions 3 117
    4. Homework 117
    Chapter 12. Cheating 119
    1. Statistics on the loose; or, How to cheat 119
    2. Surveys & Polls 120
    3. Data 121
    4. Homework 121
    Chapter 13. Modelling 123
    1. Regression 1 123
    2. Regression: continuous variable 125
    3. Regression: reading output 126
    4. Homework 128
    Chapter 14. More Modelling 131
    1. Regression: categorical variables 131
    2. Regression 5 131
    3. Regression 6 131
    4. Homework 131
    Appendix A. List of R commands 133

  3. Steve,

    Apparently, Vicki Crawford, must have forgotten to include credit to me and John for writing the piece. Thanks for the heads up. I went and posted this:

    Vicki,

    Thanks for quoting from our original zombie article at wmbriggs.com (search for zombie). But I notice you forget to credit for me and John Briggs for writing the first half.

    Must have slipped your mind.

    The zombie article, which we wrote on 31 January, was very popular and was linked all over the web.

    We also wrote some follow up zombie articles. Come on by and take a look.

    William Briggs


  4. This chapter is all about basic probability, with an emphasis on understanding and not on mechanics.

    Hmmm, this seems to be the modern mantra in math education as well. Kids don’t have to do such boring things as memorize their multiplication tables, they should simply “understand” math …

    I am skeptical … it seems to me that it’s like saying that we can teach people to become hotshot computer programmers who can debug complicated deadlocking problems simply by telling them about lock ordering and other deadlock avoidance techniques. However, until you have actually been involved in one of those situations you actually have no deep understanding …

    The devil is always in the details, and being able to recognize the relevance of a solution to another area seems to me to require that you have done the hard work of pushing the numbers around and solving the equations.

    Maybe I am just old fashioned.

  5. I’m with you Richard, but I do not mean “understand” in the watered-down “tell me how the numbers feel” sense. I mean that you must know what it is you are doing when you say that a certain statement has a probability of being true.

    Too often in statistics classes, routine memorization of confusing, ill-introduced, and mysterious formulas take the place of teaching students how to understand uncertainty.

    Besides, as I hope to show, many of these formulae are ridiculous and do not mean what you think they do.

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