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ANOVA (1)

Bayes (1)

ChatGPT (1)

Class sessions (14)

DAGs (1)

DRAFT (1)

Hypothesis testing (1)

LST companion (1)

LST package (1)

Null hypothesis (2)

R (2)

SAT (1)

accuracy (1)

adjustment (1)

alternative hypothesis (1)

bayesian updating (1)

belief (1)

blocking (1)

causality (1)

classifier (1)

confidence intervals (2)

covariate (1)

dot plots (1)

effect size (1)

estimation (2)

experiment (1)

false-positive/false-negative (1)

graphics (1)

histograms (1)

hypothesis (definition) (1)

intervals (1)

likelihood (5)

likelihood ratio (2)

linear model shapes (1)

logistic regression (1)

loss function (1)

model function (1)

model value (1)

null hypothesis (1)

odds (2)

one- and two-sample tests (1)

outliers (1)

overview (2)

p-test (1)

p-value (2)

p-values (2)

population (1)

posterior (5)

precision (1)

prediction (5)

presentation (2)

prevalence (2)

prior (5)

probability distribution (3)

random assignment (1)

reduction (1)

residual (1)

response value (1)

rlm() (1)

sampling variability (1)

sampling variance (1)

self-driving cars (1)

sensitivity (1)

sensitivity/specificity (1)

shuffling (1)

signal and noise (2)

significance (2)

simple regression (1)

specificity (1)

t-test (1)

textbook example (1)

threshold (1)

variance (2)

variation (1)

A Model Statistics Course

presentation

overview

These are presentation notes for the October 2023 StatChat meeting. For more than 15 years, statistical educators in the Twin Cities region of Minnesota have been gathering…

Hypothesis testing and likelihood

Null hypothesis

likelihood

Instructors who have taught introductory statistics in a conventional way know that…

Instructor’s note: `model_train()`

R

LST package

DRAFT

DRAFT, DRAFT, DRAFT

Instructor Orientation: Steamlining Graphics

graphics

histograms

dot plots

It’s typical for conventional introductory statistics courses to use the early part of the course to handle descriptive statistics (means, medians, sd, etc.) and graphical…

Personality and Academic Performance

textbook example

prediction

This post provides details of an example of predicting a quantitative outcome from Lessons Chapter 22 . The example concerns predicting a college student’s overall grade-point average (GPA) from predictor variables that could be available at…

The indispensible tool for statistical work

presentation

overview

Calculators, Hollerith cards, Fisher’s quote, MCMC, machine learning.

Trade deficits and the Opium Wars

p-values

significance

William Playfair (1759-1823) is credited as the…

Instructor’s Orientation

population

DRAFT: Explain why we don’t push the distinction between population and sample.

Instructor’s Orientation

p-values

significance

To judge from the tables of contents of the most widely used introductory statistics texts, there is strong consensus about the appropriate topics to include in a…

Outliers

outliers

rlm()

Consider a data frame with two variables, x and y. Here are annotated point plots of the individual variables.

Stats Vocabulary

reduction

When reviewing for a course, it’s often a good idea to start with the specialized words and phrases that are used in the subject.

Hypothesis testing and poker

Hypothesis testing

Null hypothesis

p-value

shuffling

A Bayes interpretation of Hypothesis testing

likelihood

prior

posterior

likelihood ratio

odds

The Bayesian paradigm provides a complete framework for…

Lesson 36 take-aways

Class sessions

likelihood

null hypothesis

alternative hypothesis

prior

posterior

p-value

confidence intervals

We are spending this week on a topic…

Named tests from Stat 101

one- and two-sample tests

p-test

t-test

ANOVA

simple regression

A Stat 101 course will cover many…

A bad graph for medical screening

prevalence

sensitivity

specificity

prior

posterior

In Lesson 35, in the context of medical screening tests, we presented diagrams like this one.

Competing two hypotheses

likelihood

prior

posterior

likelihood ratio

odds

The idea of competing two hypotheses …. [UNDER CONSTRUCTION]

Lesson 35 take-aways

Class sessions

hypothesis (definition)

sensitivity/specificity

prevalence

prior

posterior

Define a hypothesis (in a statistical sense) as “a statement that might or might not be true.” This is really just a wordy way of…

Lesson 34 take-aways

Class sessions

classifier

logistic regression

threshold

loss function

false-positive/false-negative

A classifier is a machine that, based on measurements of some sort assigns a categorical level to the object the measurements came from. We can make this less abstract by talking about classifiers in the context of…

Lesson 32 take-aways

Class sessions

experiment

blocking

random assignment

The data analysis techniques we have been using apply equally well…

Lesson 28 take-aways

Class sessions

covariate

adjustment

Recall that the fundamental method in the second half of Math 300Z is linear regression. That involves identifying a response variable and one or more explanatory variables.¹

Lesson 27 take-aways

Class sessions

In our original plan for Math 300Z…

Lesson 26 take-aways

Class sessions

prediction

probability distribution

bayesian updating

In Lesson 25 we pointed out that the proper form for a prediction is a list of the potential outcomes, each matched to a probability of…

Lesson 25 take-aways

Class sessions

prediction

estimation

intervals

probability distribution

We contrasted the very different tasks of ….

Case study: Prediction vs estimation

SAT

prediction

estimation

This case study is motivated by the common misconception that “estimation” is more appropriate than…

Bayesian updating for self-driving cars

self-driving cars

prediction

belief

Bayes

probability distribution

likelihood

Suppose ordinary new-ish…

Lesson 24 take-aways

Class sessions

effect size

Model coefficients are a convenient and historically important way to present a model. For fundamental, however, is the idea of a model function that takes as inputs the explanatory variables and returns a corresponding output to be interpreted as…

Lesson 23 take-aways

Class sessions

confidence intervals

precision

accuracy

lm() creates a model, which we can summarize in several ways. These numerical summaries—for instance, the coefficients reported by lm()—are called sample statistics. Mathematically, the sample statistics are exact, that is, the arithmetic is done correctly and everyone will get the same sample statistics when building the same model on…

Lesson 22 take-aways

Class sessions

signal and noise

sampling variability

sampling variance

We will use DAGs for three purposes:

Lesson 21 take-aways

Class sessions

signal and noise

linear model shapes

model function

model value

residual

response value

DAGs (“directed acyclic graphs”) have three properties, all of which are essential for representing causality.

Lesson 20 take-aways

Class sessions

variance

DAGs

causality

Interpretation: The heights of the people in the Galton data frame…

Lesson 19 take-aways

Class sessions

variance

Response variable will always be quantitative/numerical in a regression model.

Statistical or not?

variation

Some questions and answers are statistical in nature, and others not. How can you know which is which?

Can ChatGPT help in interpreting or correcting R commands?

R

ChatGPT

The results are pretty good, to judge from a couple of initial trials. But, clearly, you cannot be completely oblivious about how R works to make sense of the results.

Idiom & idiosyncracy

LST companion

Writing Lessons in Statistical Thinking involved making choices. Among them: When to stick to conventional expositions or expressions and when to avoid them as misleading, adding unnecessarily to cognitive load…