Questions tagged [teaching]

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

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Biasness of an estimator depends on whether you take expectation of the estimator or its inverse

(Please read until the end) know Consider two ways of writing the exponential distribution- (A) $\frac{1}{\beta} e^{-\frac{x}{\beta}}$ and (B) $\theta e^{-x\theta}$ If I estimate $\beta$ or $\theta$...
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What kind of training in statistics should an undergraduate in ecology be subjected to? [closed]

How many 1 semester courses on statistics do you feel would be a bare minimum for a biologist? What are the topics that you think should be fundamental to be covered when providing a 1 semester module?...
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Is the non-multicollinearity assumption for OLS multiple regression just an assumption of convenience?

The four assumptions for bivariate regression are:     • (L)inearity     • (I)ndepdent observations     • (N)ormal errors     • (E)qual variance And for multiple regression we add a fifth assumption:  ...
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When do we REALLY need to distinguish interval from ratio measurement levels?

This question is specifically aimed toward the practice of statistics and data science and toward statistics educators (particularly introductory level statistics). In brief, ¿when do we really need ...
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Suggestions for an online course in graduate Statistical Inference?

I am looking for an online course (MIT OpenCourseWare style) in graduate-advanced statistical inference. I am now reading Casella and Berger (2008) "Statistical Inference", and I was ...
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7 votes
5 answers
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How to learn statistics for medical research?

I'm a last year medical student, as we say "Intern doctor". In the future I want to do research on the issue that I want to get in. Therefore I want to learn mathematics, statistics, R ...
1 vote
0 answers
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Normally distributed: examples like LTCM

I am looking for examples of organizations suffering dire consequences (losing money) because they have assumed that something was normally distributed hence underestimating the risk of tail events. ...
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3 votes
2 answers
137 views

Non-self-referential interpretation of confidence intervals?

Interpreting what a (say) 95% confidence interval actually means is obviously tricky, especially when you are trying to teach it to students just beginning to learn stats. One of the biggest ...
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4 votes
1 answer
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Resources or textbooks about teaching statistics (pedagogy)

I want to become a better teacher and, therefore, I am looking for resources or textbooks about how to teach statistics and quantitative methods to students or learners (focusing on hints on how to ...
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23 votes
7 answers
2k views

Explain in layperson's terms why predictive models aren't causally interpretable

Imagine that you are asked to infer some causal effect -- a change in an outcome $y$ in response to some variable $x$. But, the person asking for this directs you to use a predictive model to do so. ...
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1 vote
1 answer
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Central Limit Theorem - intuitive explanation without deep math [duplicate]

The Central Limit Theorem says that the distribution of the sample mean is approximately normal. Is there any intuitive explanation for why this should be so? I know it can be proven with deep math, ...
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2 answers
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In Bayes Theorem why do we say :given that" when "out of" is more understandable. (Why is Conditional on referred to as "Given") [closed]

I understood the answer to my problem here when I substituted the "given that" symbol with the phrase "out of" I got this idea from 3Blue1Brown where Grant points out that people ...
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3 votes
4 answers
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What are some references to teach statistics to business students?

I am going to teach a Statistics course next year and I should cover the basics of probabilities and statistics to undergrad students in business. They don't have any background in probability, so, at ...
3 votes
2 answers
250 views

Why is the formula for the density of a transformed random variable expressed in terms of the derivative of the inverse?

In this very nice answer, the intuitive explanation of the formula for the density of a transformed random variable, $Y = g(X)$, leads naturally to an expression like $$f_Y(y) = \frac{f_X(g^{-1}(y))}{...
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18 votes
1 answer
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Why do we use term “population” instead of “Data-generating process”?

I have always been confused about the use of the term “population” in statistics. In my first statistics course I was taught that we need a sample, because surveying the whole population is too costly....
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2 votes
2 answers
162 views

What concept comes before VAE and after GMM?

Suppose I am designing a course on generative models and I have just finished discussing GMM. My goal is to teach VAE. However, VAE's technicality is very high. Does there exist some model in between ...
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3 votes
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LCA - how to include predictors (conceptual difference between one-step and bias-corrected three-step approach?)

I am trying to teach LCA as part of a modelling course, but I haven't quite made sense of how to deal with testing whether certain (demographic variables) predict class membership. Question: (Why) ...
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1 vote
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Why does the Standard deviation formula when using coded data not account for the addition or subtraction of coded part

When we code data from x to x-b the standard deviation formula is: Sd(x)=sd(x-b)= (sum of(x-b)^2)/n - (sum of (x-b)/n)^2 Why do they not use (sum of (x-b)/n +b )^2 for the second part since this is ...
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3 votes
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Textbook default estimator of Bernoulli variance

Why do "most" (basically all) statistics text books use $\hat{\sigma}^2=\hat{p} (1-\hat{p})$ as an estimator for the variance of a Bernoulli process which we know is biased. Should the first ...
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2 votes
2 answers
52 views

Is this problem calculable only due to the parameter choices?

I am looking at a problem form Hogg, Tannis & Zimmerman (Ed. 10), and I am curious if the given problem is calculable (for an upper-level undergrad math/stats course) because of the choice of the ...
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3 votes
1 answer
528 views

Trick to remember when to reject null (p-values vs alpha)

I teach introductory statistics to undergraduates and they are often confused with hypothesis testing. In particular, while the rule is we reject the null hypothesis at significance level $\alpha$ ...
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3 votes
0 answers
135 views

Why don't textbooks on statistics start with an introduction to probability?

I recently read through Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik (free online version available here), and what I liked most about it is that it starts off ...
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1 vote
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Is there any university program that offers an intro statistical methods class that is bayesian -instead- of a frequentist one? [closed]

Is there any university program that offers an introductory statistical methods class that is bayesian -instead- of a frequentist one? Surely every intro to stats class in every program in the world, ...
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1 vote
2 answers
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Does anyone in practice actually develop supervised model from scratch outside of classroom setting?

I have a question in regards to why bother with developing a model from scratch and perform hyperparameter tuning when you can just use transfer learning for supervised learning. The way that a ...
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66 votes
32 answers
4k views

What are the worst (commonly adopted) ideas/principles in statistics?

In my statistical teaching, I encounter some stubborn ideas/principles relating to statistics that have become popularised, yet seem to me to be misleading, or in some cases utterly without merit. I ...
3 votes
5 answers
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Pedagogical order of study for named distributions

I've seen myriads of named probability densities or distributions in multiple books and courses, usually both Binomial and Bernoulli are among the first discrete ones, while for continuous they use ...
4 votes
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Reference for flawed randomized controlled trial

For a seminar, I am preparing an overview of advantages and shortcomings of randomized control trials (RCT; one shortcoming is, for example, often a limited external validity). To illustrate ...
0 votes
1 answer
68 views

Web apps for visualization of probability distributions

I am looking for a tool to demonstrate how the shapes of some basic probability distributions (binomial, hypergeometric, Poisson, exponential and normal) change as a function of their parameters. I ...
2 votes
4 answers
231 views

Intuition of terms P(θ) and P(y) in Bayes' Theorem [duplicate]

I am struggling with the intuition behind terms in the Bayes' Theorem. In the simple example of a deck of cards we have: $$ P(King | Red) = \frac{P(Red | King)P(King)}{P(Red)} $$ The terms in this ...
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7 votes
2 answers
160 views

Spurious relationships: flavours, terminology

The following types of relationships come to my mind when I think of the term "spurious" (as in "spurious regression" or "spurious correlation"): A statistical ...
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9 votes
2 answers
344 views

Quick test of quality of an econometrics textbook

When encountering an econometrics textbook for the first time, you might wish to assess its quality. What is the first thing you check? Is there a certain topic or a definition you examine, knowing ...
79 votes
12 answers
8k views

Famous statistical wins and horror stories for teaching purposes

I am designing a one year program in data analysis with a local community college. The program aims to prepare students to handle basic tasks in data analysis, visualization and summarization, ...
3 votes
0 answers
48 views

(Teaching) references for computational complexity

Background: I am going to teach computational complexity (time complexity) within an introductory course in machine learning. I would like to gently introduce the notion of computational complexity ...
1 vote
0 answers
23 views

Ways to make parametric statistics work with real time (often non-normal) data

BACKGROUND: I have been tasked with teaching basic data analysis methods with R to a group of people in a business setting. While my stance is that I am most difinitely not at the level where I ...
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0 votes
0 answers
58 views

Poisson process as a spatial process

Let's consider a Poisson process on the line with rate parameter $\lambda$. There are two ways to think about this: In any interval $[a,b)$ the expected number of events is distributed as a Poisson ...
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4 votes
0 answers
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Reproducing a didactic example of Lindley (1993)

Lindley (1993) discusses the following mixed discrete and continuous prior for the tea tasting lady experiment, where $\pi$ is probability of a correct classification: $p(\pi=0.5) = 0.8$ (discrete ...
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2 votes
1 answer
774 views

chi squared goodness of fit test to check for normality

I have the following data: I would like to use the chi-squared goodness of fit test to test whether it comes from a normal distribution. How shall I go about it? In particular, I would like to know ...
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8 votes
3 answers
755 views

Teaching students about non-significant results and large effect size

This year I am going to teach statistics to sophomore year students of psychology. We'll be training such methods as one-way ANOVA. The example will be the time-reaction of a cognitive task among ...
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2 votes
1 answer
108 views

What does one expect from a great course of time series? [closed]

I usually teach finance (asset pricing and equilibrium models), quantitative economics (linear algebra and optimization), econometrics, computer science introduction to programming and machine ...
1 vote
1 answer
143 views

“t-tests are too fundamental for academia” [closed]

I just heard a PhD student claim: The $t$-test is really fundamental and nobody in academy is gonna do it. He added that these tests serve more as a beginning exercise in order to get an idea of ...
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0 votes
1 answer
730 views

How do you calculate an exact two-tailed P-value using binomial distribution? [closed]

First, I will preface this question with my ulterior motive: I would like more evidence that the use of 19th and 20th century approximations play little to no pedagogic advantage in modern intro stats ...
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2 votes
0 answers
45 views

A book-chapter long nontechnical introduction / overview of neural networks

I will be teaching an introductory course in machine learning for students in management who have minimal quantitative skills. I am looking for a brief and gentle introduction to neural networks that ...
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2 votes
1 answer
2k views

Explain Root Mean Square Error to non-technical audience

My company is in the process of switching equipment from one vendor to another. We measured several metrics from the existing and new equipment and compared the time series. The ideal is to have no ...
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1 vote
0 answers
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How do you explain 'explained variance'?

What is the best definition of 'explained variance' from a teaching perspective? I quite like this one: "Explained variance (also called explained variation) is used to measure the discrepancy ...
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2 votes
1 answer
53 views

Accounting Student taking Master in Stat, need your help regarding taking subjects

I had a Bachelor in Accounting and now I'm doing a Masters in Statistics. This is my first semester and I have to Choose at least 3 out of 6 offered subjects for this semester. These subjects Are: ...
12 votes
2 answers
692 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 ...
2 votes
2 answers
154 views

How can we best explain causality for the uninitiated?

How can we best explain causality in layman's terms? There seem to be two main types of causality. One is probabilistic causation, the other is called determinism in philosophic circles or just ...
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4 votes
3 answers
117 views

Teaching a new, large topic: present in class or assign as homework first?

In spring 2019, I will be teaching a master's level course in applied statistics for students in economics and management. The main topics are linear regression, explanatory and confirmatory factor ...
2 votes
0 answers
39 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?
7 votes
1 answer
820 views

Why start with measures of central tendency?

In teaching descriptive statistics, measures of central tendency come up early on, e.g. before measures of spread. For me it is natural enough to learn about central tendency, or location, of the data ...
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