42 questions linked to/from Famous statistical quotations
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### Statistics Jokes

Well, we've got favourite statistics quotes. What about statistics jokes?
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### Regarding p-values, why 1% and 5%? Why not 6% or 10%?

Regarding p-values, I am wondering why $1$% and $5$% seem to be the gold standard for "statistical significance". Why not other values, like $6$% or $10$%? Is ...
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### How to describe statistics in one sentence?

When I first started learning statistics, procedures like the t-test, ANOVA, chi-squared and linear regression each appeared to be very different creatures. But now I realise these procedures each do ...
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### When to use Fisher and Neyman-Pearson framework?

I've been reading a lot lately about the differences between Fisher's method of hypothesis testing and the Neyman-Pearson school of thought. My question is, ignoring philosophical objections for a ...
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### How to test hypothesis of no group differences?

Imagine you have a study with two groups (e.g., males and females) looking at a numeric dependent variable (e.g., intelligence test scores) and you have the hypothesis that there are no group ...
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### How small a quantity should be added to x to avoid taking the log of zero?

I have analysed my data as they are. Now I want to look at my analyses after taking the log of all variables. Many variables contain many zeros. Therefore I add a small quantity to avoid taking the ...
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### Are all models useless? Is any exact model possible — or useful?

This question has been festering in my mind for over a month. The February 2015 issue of Amstat News contains an article by Berkeley Professor Mark van der Laan that scolds people for using inexact ...
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### Distribution hypothesis testing - what is the point of doing it if you can't “accept” your null hypothesis?

Various hypothesis tests, such as the $\chi^{2}$ GOF test, Kolmogorov-Smirnov, Anderson-Darling, etc., follow this basic format: $H_0$: The data follow the given distribution. $H_1$: The data do not ...
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### Is there an explanation for why there are so many natural phenomena that follow normal distribution?

I think this is a fascinating topic and I do not fully understand it. What law of physics makes so that so many natural phenomena have normal distribution? It would seem more intuitive that they would ...
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### Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR?

I have built a logistic regression where the outcome variable is being cured after receiving treatment (Cure vs. No Cure). All ...
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### Pitfalls in experimental design: Avoiding dead experiments

I've come across this quote numerous times: To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what ...
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### What's the name for this statistical fallacy?

I was told an anecdote by someone today who was trying to prove a point regarding safety. They said "50 people have been living in [area a] for the past two years one year (apparently I remembered the ...
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### What is effect size… and why is it even useful?

I have an introductory-graduate-level statistics background (assume I know mathematical statistics and probability at an undergraduate level (e.g., Wackerly et al., Ross' Probability), and have some ...
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### How to test if my distribution is multimodal?

When I plot a histogram of my data, it has two peaks: Does that mean a potential multi-modal distribution? I ran the dip.test in R (...
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### Is any quantitative property of the population a “parameter”?

I'm relatively familiar with the distinction between the terms statistic and parameter. I see a statistic as the value obtained from applying a function to the sample data. However, most examples of ...
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### When to use Student's or Normal distribution in linear regression?

I am looking at some problems, and in some, to test the coefficients, sometimes I see people using Student's distribution, and sometimes I see Normal distribution. What is the rule?
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### Is it appropriate to examine an interaction effect that is almost statistically significant?

I am conducting a 2x2 within-subjects design. When I plot my results it appears that there will be an interaction between my variables but unfortunately none is emerging p=0.08. I find it a shame that ...
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### When is a fixed effect truly fixed?

Consider a linear unobserved effects model of the type: $$y_{it} = X_{it}\beta + c_{i} + e_{it}$$ where $c$ is an unobserved but time-invariant characteristic and $e$ is an error, $i$ and $t$ index ...
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### Omitted variable bias in linear regression

I have a philosophical question regarding omitted variable bias. We have the typical regression model (population model) $$Y= \beta_0 + \beta_1X_1 + ... + \beta_nX_n + \upsilon,$$ where the ...
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### Is it better to select distributions based on theory, fit or something else?

This is bordering on a philosophical question, but I am interested in how others with more experience think about distribution selection. In some cases it seems clear that theory might work best (mice ...
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### Can we see shape of normal curve somewhere in nature?

I do not want to know if some phenomena in nature have normal distribution, but whether we can somewhere see shape of normal curve as we can see it for example in Galton box. See this figure from ...
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### Choosing a regression model

How can one objectively (read "algorithmically") select an appropriate model for doing a simple linear least-squares regression with two variables? For example, say the data seem to show a quadratic ...
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### Ways to overcome small number of survey responses

For one of my academic project I ran a sample survey. But unfortunately the respondents were not very proactive & I get just 25 responses for my study. With this small response I guess I can't do ...
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### Famous data visualizations [duplicate]

I am looking for famous, historical, beautiful, impressive, or otherwise noteworthy visualizations based on statistical concepts. I think of examples along the lines of Florence Nightingale's ...
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### What really happens when we transform the data using $f(x) = \sin(\sqrt{x})$?

I need to perform a two-way ANOVA on my data ($Y$: sleeping hours). My data is quite normal $p$-value = $0.07$ with Shapiro-Wilk test but when I run the normality test for my residual, $p$-value is ...
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### Using multiple comparisons corrections in Fisher p-value framework

I am wary of stepping into the civil war between Fisher vs Neyman-Pearson interpretations of $p$-value (which has been well elucidated here and here), but I've been pondering a question that I keep ...
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### Can a narrow confidence interval around a non-significant effect provide evidence for the null?

It is obviously fallacious to assume that failure to reject the null implies that the null is true. But in a case where the null is not rejected and the corresponding confidence interval (CI) is ...
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### Intuition for Gamma-Poisson / Negative Binomial

I have a data set which intuitively seems Poisson-like, but it's overdispered. So I'm investigating negative binomial. From this question and this page I understand one way of viewing this is to ...
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### Significance in Longitudinal Data

I feel like this question has a very silly (simple) answer, so I apologize. I have a data set that only has 5 points 41.9 32.2 113.3 110.2 102.6 Clearly ...
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### Using MLE to determine parameters for QQ plot

I just started playing around with a credit fraud dataset that I found online. I noticed that one of the variables looked something like this: Hey, that looks like a 3 parameter log-normal ...
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### How to choose between exponential and gamma distributions

I have same data and I would like to choose a model for it. To start with I fit an exponential distribution and a gamma distribution. Now I wanted to do a simple likelihood ratio test . However, I ...
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### Comparing patient and control group results of a survey

I have data from a survey given to a patient group and control group. Both groups completed the same exact survey (Likert scale). One group has an n of only 5 or 6, the other n was about 15. What ...
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### Hypothesis test of mean between groups with dependencies and pairing

I have two groups with small number of n (less than 10) where some observations are replicates for each other, some are paired difference observations, and some are completely independent. For example:...