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83 votes
Accepted

How do DAGs help to reduce bias in causal inference?

Causal Inference is an important topic in statistics generally, for both observational research and controlled experiments such as clinical trials. A DAG is a Directed Acyclic Graph. A “Graph” is a ...
Robert Long's user avatar
  • 61.5k
69 votes
Accepted

Intuitive explanation of "Statistical Inference"

Sometimes it's best to explain a concept through a concrete example: Imagine you grab an apple, take a bite from it and it tastes sweet. Will you conclude based on that bite that the entire apple is ...
Isabella Ghement's user avatar
56 votes

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

I'll present one novice error (in this answer) and perhaps one error committed by more seasoned people. Very often, even on this website, I see people lamenting that their data are not normally ...
52 votes
Accepted

Two-tailed tests... I'm just not convinced. What's the point?

Think of the data as the tip of the iceberg – all you can see above the water is the tip of the iceberg but in reality you are interested in learning something about the entire iceberg. Statisticians, ...
Isabella Ghement's user avatar
46 votes

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

Post hoc power analysis That is, using power analysis after a study has been completed rather than before, and in particular plugging in the observed effect size estimate, sample size, etc. Some ...
44 votes
Accepted

What is a good, convincing example in which p-values are useful?

I will consider both Matloff's points: With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis. The logic here is that if somebody reports highly ...
amoeba's user avatar
  • 105k
41 votes
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Why does basic hypothesis testing focus on the mean and not on the median?

Because Alan Turing was born after Ronald Fisher. In the old days, before computers, all this stuff had to be done by hand or, at best, with what we would now call calculators. Tests for comparing ...
Peter Flom's user avatar
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41 votes
Accepted

Differences between prior distribution and prior predictive distribution?

Predictive here means predictive for observations. The prior distribution is a distribution for the parameters whereas the prior predictive distribution is a distribution for the observations. If $X$ ...
periwinkle's user avatar
  • 3,523
41 votes

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

The idea that because something is not statistically significant, it is not interesting and should be ignored.
40 votes

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

Removing Outliers It seems that many individuals have the idea that they not only can, but should disregard data points that are some number of standard deviations away from the mean. Even when there ...
34 votes
Accepted

Flaws in Frequentist Inference

I am a Bayesian, but I find these kinds of criticisms against "frequentists" to be overstated and unfair. Both Bayesians and classical statisticians accept all the same mathematical results to be ...
Ben's user avatar
  • 126k
32 votes

What are the factors that cause the posterior distributions to be intractable?

I had the opportunity to ask David Blei this question in person, and he told me that intractability in this context means one of two things: The integral has no closed-form solution. This might be ...
jds's user avatar
  • 1,714
32 votes

How to calculate standard deviation when only mean of the data and sample size is available?

It's impossible. Consider any vector that has a mean of $0$ - multiply the values by $100$, and the standard deviation also increases by a factor of $100$, but the mean and sample size are unchanged. ...
Nuclear Hoagie's user avatar
31 votes
Accepted

Performing a statistical test after visualizing data - data dredging?

Briefly disagreeing with/giving a counterpoint to @ingolifs's answer: yes, visualizing your data is essential. But visualizing before deciding on the analysis leads you into Gelman and Loken's garden ...
Ben Bolker's user avatar
30 votes

What is a good, convincing example in which p-values are useful?

I take great offense at the following two ideas: With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis. Almost no null hypotheses are true in the ...
Cliff AB's user avatar
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30 votes
Accepted

Why do we need multivariate regression (as opposed to a bunch of univariate regressions)?

Be sure to read the full example on the UCLA site that you linked. Regarding 1: Using a multivariate model helps you (formally, inferentially) compare coefficients across outcomes. In that linked ...
civilstat's user avatar
  • 4,263
29 votes

Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution?

This question has likely been considered already on this forum. When you state that you "have the posterior distribution", what exactly do you mean? "Having" an available$-$in the ...
Xi'an's user avatar
  • 106k
28 votes

Kullback-Leibler divergence WITHOUT information theory

There is a purely statistical approach to Kullback-Leibler divergence: take a sample $X_1,\ldots,X_n$ iid from an unknown distribution $p^\star$ and consider the potential fit by a family of ...
Xi'an's user avatar
  • 106k
28 votes

What does it mean for a linear regression to be statistically significant but has very low r squared?

It means that you can explain a small portion of the variance in the data. For instance, you can establish that a college degree impacts salaries, but at the same time it's just a small factor. There ...
Aksakal's user avatar
  • 61.5k
28 votes

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

Not addressing multiple hypothesis testing problems. Just because you aren't performing a t.test on 1,000,000 genes doesn't mean you're safe from it. One example of a field it notably pops up is in ...
26 votes

Why are hypothesis tests still used when we have the bootstrap and central limit theorem?

Hypothesis tests are still used because they are motivated by a different need in statistical inference than interval estimators are motivated by. The purpose of a hypothesis test is to make a ...
Alexis's user avatar
  • 30k
25 votes

How to interpret a QQ plot?

A very helpful (and intuitive) explanation is given by prof. Philippe Rigollet in the MIT MOOC course: 18.650 Statistics for Applications, Fall 2016 - see video at 45 mins https://www.youtube.com/...
Xavier Bourret Sicotte's user avatar
25 votes

Intuitive explanation of "Statistical Inference"

I'm assuming that you're asking in here about statistical inference. Using the definition from All of Statistics by Larry A. Wasserman: Statistical inference, or “learning” as it is called in ...
Tim's user avatar
  • 139k
23 votes

Rule of thumb for number of bootstrap samples

I start by responding to something raised in another answer: why such a strange number as "$599$" (number of bootstrap samples)? This applies also to Monte Carlo tests (to which bootstrapping is ...
Alecos Papadopoulos's user avatar
23 votes

Inference after using Lasso for variable selection

Generally, refitting using no penalty after having done variable selection via the Lasso is considered "cheating" since you have already looked at the data and the resulting p-values and confidence ...
Greenparker's user avatar
  • 15.6k
23 votes
Accepted

Finding minimum/maximum peaks in a n-modal distribution

A very long time ago I learned an effective technique in the geological literature. (I apologize for not remembering the source.) It consists of studying the modes of a kernel density estimator (KDE)...
whuber's user avatar
  • 325k
22 votes

Why does basic hypothesis testing focus on the mean and not on the median?

I would like to add a third reason to the correct reasons given by Harrell and Flom. The reason is that we use Euclidean distance (or L2) and not Manhattan distance (or L1) as our standard measure ...
meh's user avatar
  • 2,070
22 votes

Two-tailed tests... I'm just not convinced. What's the point?

I think when considering your question it helps if you try to keep the goal/selling points of null-hypothesis significance testing (NHST) in mind; it's just one paradigm (albeit a very popular one) ...
jsakaluk's user avatar
  • 5,514
22 votes

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

This seems like low hanging fruit, but stepwise regression is one error which I see pretty frequently even from some stats people. Even if you haven't read some of the very well-written answers on ...
22 votes

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

ARIMA!!! - a marvel of theoretical rigor and mathematical elegance that is almost useless for any realistic business time series. Ok, that is an exaggeration: ARIMA and similar models like GARCH are ...

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