# Questions tagged [teaching]

For questions about the teaching of probability and statistics, at any level.

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111k views

### Intuitive explanation for dividing by $n-1$ when calculating standard deviation?

I was asked today in class why you divide the sum of square error by $n-1$ instead of with $n$, when calculating the standard deviation. I said I am not going to answer it in class (since I didn't ...
35k views

### Free statistical textbooks

Are there any free statistical textbooks available?
40k views

### Locating freely available data samples

I've been working on a new method for analyzing and parsing datasets to identify and isolate subgroups of a population without foreknowledge of any subgroup's characteristics. While the method works ...
164k views

### How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?

Maybe the concept, why it's used, and an example.
4k views

### Explaining two-tailed tests

I am looking for various ways of explaining to my students (in an elementary statistics course) what is a two tailed test, and how its P value is calculated. How do you explain to your students the ...
335k views

### Examples for teaching: Correlation does not mean causation

There is an old saying: "Correlation does not mean causation". When I teach, I tend to use the following standard examples to illustrate this point: number of storks and birth rate in Denmark; number ...
701 views

### What should a graduate course in experimental design cover?

I have been asked to propose a course in experimental design for advanced graduate students in agronomy and ecology. I have never taken such a course, and was surprised to find that the course might ...
76k views

### What's the difference between probability and statistics?

What's the difference between probability and statistics, and why are they studied together?
6k views

### Strategies for teaching the sampling distribution

The tl;dr version What successful strategies do you employ to teach the sampling distribution (of a sample mean, for example) at an introductory undergraduate level? The background In September I'll ...
2k views

### Why are regression coefficients in a factor analysis model called “loadings”?

In this thread @ttnphns writes that Because it is regression coefficients [...] I insist that it is better to say "factor loads variable" than "variable loads factor". I learned from here that a ...
14k views

### How to visualize what ANOVA does?

What way (ways?) is there to visually explain what is ANOVA? Any references, link(s) (R packages?) will be welcomed.
6k views

### Why continue to teach and use hypothesis testing (when confidence intervals are available)?

Why continue to teach and use hypothesis testing (with all its difficult concepts and which are among the most statistical sins) for problems where there is an interval estimator (confidence, ...
13k views

### Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regression when we don't have to?

I suppose I get frustrated every time I hear someone say that non-normality of residuals and /or heteroskedasticity violates OLS assumptions. To estimate parameters in an OLS model neither of these ...
32k views

### Any suggestions for a good undergraduate introductory textbook to statistics?

I am hoping you can give me some suggestions. I am teaching in a very diverse (made of minority groups) college and the students are mostly Psychology majors. Most students are fresh from high school ...
2k views

### Good text on Clinical Trials?

I'm an undergraduate statistics student looking for a good treatment of clinical trials analysis. The text should cover the fundamentals of experimental design, blocking, power analysis, latin squares ...
2k views

### Sequential hypothesis testing in basic science

I'm a pharmacologist and, in my experience, almost all papers in basic biomedical research use Student's t-test (either to support inference or to conform to expectations...). A couple of years ago it ...
7k views

### What is your favorite layman's explanation for a difficult statistical concept?

I really enjoy hearing simple explanations to complex problems. What is your favorite analogy or anecdote that explains a difficult statistical concept? My favorite is Murray's explanation of ...
2k views

### Why is it bad to teach students that p-values are the probability that findings are due to chance?

Can someone please offer a nice succinct explanation why it is not a good idea to teach students that a p-value is the prob(their findings are due to [random] chance). My understanding is that a p-...
120k views

### Real life examples of distributions with negative skewness

Inspired by "real-life examples of common distributions", I wonder what pedagogical examples people use to demonstrate negative skewness? There are many "canonical" examples of symmetric or normal ...
4k views

### What should be taught first: Probability or Statistics?

I have newly joined as a faculty member in a math dept. of a reputed institution. I will be teaching the course Probability and Statistics at the undergraduate level. The institution already has a ...
17k views

### Why is the standard deviation defined as sqrt of the variance and not as the sqrt of sum of squares over N?

Today I taught an introductory class of statistics and a student came up to me with a question, which I rephrase here as: "Why is the standard deviation defined as sqrt of variance and not as the sqrt ...
1k views

### Should we teach kurtosis in an applied statistics course? If so, how?

Central tendency, spread and skewness can all be defined relatively well, at least on an intuitive basis; the standard mathematical measures of these things also correspond relatively well to our ...
22k views

### Why do we say the outcome variable “is regressed on” the predictor(s)?

Is there some intuitive explanation for this terminology? Why is it this way, and not the predictor(s) being regressed on the outcome? Ideally I'm hoping that a proper explanation of why this ...
13k views

### Test of independence vs test of homogeneity

I am teaching a basic statistics course and today I will cover the chi-squared test of independence for two categories and the test for homogeneity. These two scenarios are conceptually different, but ...
3k views

### What can one tell a school kid about statistics and machine learning?

Next week we have an intern from a local school in the house. The concept behind his short internship is to get an idea how the real world works and what certain jobs deal with, how the daily work ...
1k views

### Explaining quantile regression to nonstatisticians

I recently submitted a paper, in which I used quantile regression, to a psychology journal. Although I thought I had already put enough thought in a clear exposition of quantile regression, the ...
806 views

### Why do US and UK Schools Teach Different methods of Calculating the Standard Deviation?

As I understand UK Schools teach that the Standard Deviation is found using: whereas US Schools teach: (at a basic level anyway). This has caused a number of my students problems in the past as ...
11k views

### What is the hardest statistical concept to grasp?

This is a similar question to the one here, but different enough I think to be worthwhile asking. I thought I'd put as a starter, what I think one of the hardest to grasp is. Mine is the ...
31k views

### Tiny (real) datasets for giving examples in class?

When teaching an introductory level class, the teachers I know tend to invent some numbers and a story in order to exemplify the method they are teaching. What I would prefer is to tell a real story ...
4k views

### Self study vs a taught education?

There is a question with similar intent on programmers.SE. That question has some quite good answers, but the general theme seems to be that without self study, you get no-where. Obviously there are ...
1k views

### Suggestions for improving a probability and statistics cheat sheet

Context: In an effort to structure the center pieces that I have came across in probability theory and statics, I created a reference document focussing on the mathematical essentials (available here)...
10k views

### How to best display graphically type II (beta) error, power and sample size?

I'm asked to write an introduction to statistics and I'm struggling how to graphically show the way p-value and power relate. I've come up with this graph: My question: Is there a better way of ...
1k views

### Learning statistical concepts through data analysis exercises

I find that simple data analysis exercises can often help to illustrate and clarify statistical concepts. What data analysis exercises do you use to teach statistical concepts?
9k views

### Datasets for data visualization examples, teaching and research

I am searching for existing datasets that we can use to test several datavis techniques we are researching. I know several resources like those included in R (try ...
3k views

### Examples of processes that are not Poisson?

I am looking for some good examples of situations that are ill-suited to model with a Poisson distribution, to help me explain the Poisson distribution to students. One commonly uses the number of ...
532 views

### Are there any “esoteric” statistic tests with very low power?

Background In computer science, mathematics, and sometimes in other fields, “esoteric” examples cannot only be entertaining, but helpful to illustrate certain concepts, for example: Bogosort and ...
628 views

### Good online resource with tips on graphing association between two numeric variables under various conditions

Context: Over the while I've acquired a set of heuristics on how to effectively plot the association between two numeric variables. I imagine most people who work with data would have a similar set ...
343 views

### References for consulting statisticians to offer their clients

This question illustrates the difficulty of a person mastering statistics and probability on their own, in the face of weakly developed resources like Wikipedia. It occurred to me that consulting ...
467 views

### What factors make for a great stats book? [closed]

What factors make for a great statistics book? In other words, what writing styles, visualizations, explanatory methodologies, text length(!), tone, depth, etc, etc contribute to giving the audience a ...
223 views

### how would you approach giving an introductory class about Bayesian statistics?

I need to give a lecture about Bayesian statistics, introducing it to people who have already basic knowledge of classic statistics (but not too much of it in general). I want to start with some ...
268 views

### Help explaining (offering intuition/examples of) the score function and fisher's information to students

Next week I will teach my students the score function and its variance (i.e.: fisher information). I am looking for way(s) to illustrate these concepts so to help my students understand them (and not ...
28 views

### Master's-level Quantitative Methods / Statistics textbook for Management, Marketing, Economics students

What are some good textbooks for a master's (or upper undergraduate) level course in Quantitative methods / Statistics for students in Management, Marketing or Economics?
I have to teach the Bayes formula to some undergraduates, in the form: $$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(B|A)P(A)}{P(B)}$$ I was wondering if anyone had any really thoughtful or ...