Simpson's Paradox is an example of the Reversal Paradox, where an association appears in several different groups of data but disappears, or even reverses in sign, when these groups are combined.

71 questions
Filter by
Sorted by
Tagged with
38 views

Confounding Variable in Regression Model: Simpson's Paradox

I am working on a mixed effects regression model where Yi = exam score of student i. The explanatory variables are the following: Level 3: school type (public vs. private) and school's socioeconomic ...
625 views

I am building GLMs to investigate the effect of environmental variables on frog occupancy and abundance (negative binomial). I am having an issue of reversal of estimates which, from what I found on ...
5 views

How to figure out if Simpson's paradox in FE performance where errors go down, latency goes up

As per the question, our latency when I look at pages one on one seems about the same as before, sort of not great - barely passable. But after a recent release our error rate dropped to about a 5th ...
• 133
637 views

Odds Ratios paradox? Pooled OR inconsistent with subgroup ORs

I have two groups (A and B) that each produce ORs of 1.44 and 1.50. However, if I combine the frequencies for the two groups to create a pooled dataset, I get an OR of 1.40. I get that it's not going ...
• 342
400 views

I have to do a binary logistic regression with two dichotomous independent variables. I found myself faced with a paradox that I don't know how to handle. In the complete database I have 21 (5.6%) ...
• 213
142 views

Interpreting sub-sample analysis when coefficient signs are opposite

Suppose I run the following OLS regression: $y = \beta_0 + \beta_1 D + \varepsilon$ where $D$ is a binary variable for treatment group, and $y$ is the outcome variable, say income. $D$ is randomly ...
• 201
591 views

average revenue per user increases each country but decreases when combined

I'm trying to figure out what could be some reasons when we do the AB testing we're seeing average revenue per user increases for each country but when we calculate the overall average revenue per ...
407 views

How do I know if I'm seeing Simpson's paradox?

I need some guidance on how to analyse the results of a subgroup breakdown in an A/B test. I have the results of an (ongoing) A/B test and need to do an interim analysis on The overall headline ...
• 149
24 views

How do we draw parallels between the BBG drug example and the businessman (affected by the election) anecdote in "The book of why"?

In "The book of why", Dr Pearl concludes that a BBG drug cannot exist after phrasing the sure-thing principle in 'a more correct way' (pg 214). He does this by first "insisting" ...
54 views

Algorithm for Creating 2x2 Tables to Demonstrate Simpson's Paradox

Suppose I have a 2x2 table: $T = \lbrace a,b,c,d \rbrace$, where $a=T(1,1), b=T(2,1), c=T(1,2), d=T(2,2)$, where all entries of $T$ are positive integers. Let us assume that $\frac{ad}{bc} > 1$. ...
• 333
131 views

Combining biased noisy measurements

I'm looking for a way to combine noisy biased measurements to find confidence intervals. As an example, we have two people Tom & Mary that are each taking free throws on separate days, we have the ...
• 113
41 views

How do i explain the difference of correlation between mean income and total income?

I am doing a report on the complaints made to the municipality by the people of an italian city. I'm doing the part of the analysis where I try to understand where people complain the most. The ...
• 15
316 views

Negative correlation in two groups (separately) but overall data shows positive correlation

Regression on the overall data gives positive correlation coefficient. However, if I divide the data by gender (male and female) and run the same regression model separately on each group - I get ...
• 33
1 vote
34 views

Why does my predictor in two-way fixed effects models have opposite signs in the full panel data vs. period time subsets?

I have a heavily unbalanced panel data set in which certain entities are missing on the DV in certain years. On this data set, I run the two-way fixed effects model: ...
• 11
21 views

Linear Mixed Model in lme4 package- estimate is correct magnitude but wrong direction

I am using lmer in lme4 to do linear mixed modeling. I have simplified my model to just one fixed effect and one random effect to isolate the problem. I have a continuous DV (score), a dichotomous ...
242 views

Is a 2-way ANOVA immune to Simpson's Paradox?

Sometimes continuous data is of the type that would result in Simpson's Paradox findings if groups were simply aggregated. (See, for example, "Example #2: Baseball" on this page https://www....
• 3,377
103 views

How to decompose total slope into between-group and within-group contributions?

Consider the following data (I put the data as a table in the bottom of this question.) These data are in two groups, blue and orange. In each group there is a positive relationship, while pooling ...
125 views

I am measuring 2 responses in patients from different age cohorts. Each response is negatively correlated with age. This gives me a positive correlation of ResponseX and ResponseY in a total ...
• 718
266 views

Making a ML model robust to Simpson's paradox

Suppose a model which predicts which location/landmark a walking tourist is going to visit next, based on two geographical input features: the last neighborhood this person has walked through the ...
• 571
768 views

I need some help figuring out whether the phenomenon of Simpson's paradox has occurred. Here is a plot of the first dataset (correlation between probability of contracting a disease vs. hours slept ...
• 43
1 vote
30 views

Is there a phenomenon like this?

It's like the mean of every part increases, but the overall mean decrease; or the mean of a group is larger in every part but is smaller in all samples; or something like this. I remember there is a ...
• 433
512 views

What is the solution of simpson paradox?

In my nonexperimental data, when running regression, I faced the Simpson Paradox. Simplistically speaking, Pearl,2014 said: Simpson’s paradox refers to a phenomena whereby the association between a ...
• 639
3k views

Simpson's "paradox" is a well-known phenomenon that can be counter-intuitive for beginners: it is possible, say, for a medical trial to reveal that a certain treatment is beneficial to men ...
• 301
110 views

Alternative Aggregation Method to Avoid Simpson's Paradox

The table below shows an example of Simpson's Paradox arising from some fictitious data for the success of operations performed by two doctors from the Simpsons TV show. Dr Hilbert Dr Nick Heart ...
377 views

Is it possible that marginally independent random variables are conditionally dependent?

Suppose that $X,Y$ and $Z$ are random variables. If $X$ is independent of $Z$ and $Y$ is independent of $Z$, is it possible that $X$ is dependent on $Z$ given $Y$ and $Y$ is dependent on $Z$ given $X$?...
• 5,110
293 views

Simpson's paradox in Judea Pearl's book?

I'm looking at the following question in Judea Pearl's primer on causality In an attempt to estimate the effectiveness of a new drug, a randomized experiment is conducted. In all, 50% of the patients ...
• 561
1 vote
35 views

Can we calculate the correlation between 2 variables just from the correlations between subsets of the data?

If I have two variables X, Y and I already have correlations for subsets of the data that that are mutually exclusive and exhaustive, can I compute the overall correlation directly from this? It seems ...
180 views

This site has a couple of nice questions and answers dealing with Simpson's paradox and random effects (e.g. Simpson's Paradox & Random Effects, Understanding Simpson's paradox with random effects)...
• 1,908
1 vote
118 views

Stochastic independence, but functional dependence

Here is an extract from "Comment: A Fruitful Resolution to Simpson's Paradox via Multiresolution Inference" by Keli Liu and Xiao-Li Meng of Harvard University (The American Statistician, ...
537 views

How to see Simpson's paradox effect via glm in R

I am using the UCBAdmissions dataset and glm from R to check for Simpson's paradox. I am ...
• 277
1k views

Understanding Simpson's paradox with random effects

Simpson's paradox is well known as a situation where the correlation between 2 variables in groups (ie within-group slope) is of opposite sign to the overall correlationed between the 2 variables, ...
• 64k
4k views

Examples of Simpson's Paradox being resolved by choosing the aggregate data

Most of the advice around resolving Simpson's paradox is that you can't decide whether the aggregate data or grouped data is most meaningful without more context. However, most of the examples I've ...
3k views

Intuition behind Partial Residual Plots

I've been reading how univariate analysis in data with a lot of variables can be misleading due to "Simpson's paradox". I found the explanation of this phenomenon pretty fascinating but easy to ...
• 400
1 vote
1k views

Does Linear Regression solve Simpson's Paradox?

I'm facing a problem where I think I might be falling into Simpson's Paradox. I remember proving Linear Regression by using partial derivatives, so I'm thinking that even though Linear Regression is a ...
• 660
4k views

Can someone explain what is the difference between the two? They seem to me to be identical. In both paradoxes you start from a narrow distribution and find out the correlation switches when you move ...
• 3,520
499 views

I am trying to understand if the following statement is an example for Simpson paradox: "In the US elections a certain candidate got more votes than the other, but the other one was elected". I ...
118 views

UC Berkeley gender bias study formulation in terms of probabilities

I'm trying to strengthen my foundations of statistics, and I thought it would be interesting to turn the problem below into some set of equations instead of a more qualitative treatment as is done in ...
• 41
245 views

Estimate the effect of dummies with unbalanced data

Imagine having a factory with jobs of different complexity, and a few machines that can execute these jobs; a job can succeed or fail. However, jobs are not assigned completely randomly, there is some ...
• 111
146 views

HELP: LM shows no relationship, but LMM does

My research question is assessing if a variable (let’s call it ‘x') can predict another variable (let’s call it ‘y’). The two variables x and y are in the same units, but they just come from ...
226 views

Looking to identify a book by a top statistician with a chapter on Simpson's Paradox

It was more than 20 years ago. I had just gotten acquainted with Simpson's paradox. I was browsing in a bookstore and saw a book by an eminent statistician -- eminent in the sense that I had come ...
35 views

Relationship between correlation and multiple hierarchial regression [duplicate]

I got a negative correlation value between two variables. Results of running Multiple hierarchical linear regression on the same variables indicated a positive beta coefficient between them. Explain ...
730 views

Distribution to match an example with collider bias?

I am doing exercises from "Causal Inference in Statistics: A Primer", by Pearl et al (2016). In chapter 1.2 there is a training challenge that goes like: In an attempt to estimate the effectiveness ...
• 353
1 vote
299 views

When should we use the segregated as opposed to the aggregated data?

In the book "Causal Inference In Statistics" by Pearl et al., there is the following problem (study question 1.2.2.) A baseball batter Tim has a better batting average than his teammate Frank. ...
1 vote
54 views

Recovering hidden confounder in Simpson's paradox trends

I just watched a video of an interested talk from PyData LA: "Using Simpson’s Paradox to Discover Interesting Patterns in..." - Nazanin Alipourfard, Peter Fennell (https://www.youtube.com/watch?v=...
• 121
345 views

Disclaimer: This is not a duplicate of How to resolve Simpson's paradox. As given in this blog, the following is the data of people on the titanic: This is the same data when divided on basis of ...
• 633
1 vote
317 views

I am playing with a toy data where the Simpson's paradox exists for two variables NO2 and temperature: A scatter plot clearly shows that the correlation between NO2 and temperature was reversed when ...
2k views

Does Simpson's Paradox cover all instances of reversal from a hidden variable?

The following is a question about the many visualizations offered as 'proof by picture' of the existence of Simpson's paradox, and possibly a question about terminology. Simpson's Paradox is a fairly ...
• 1,997
2k views

Intuition needed when using weighted average to explain Simpson's paradox

In Freedman's Statistics (chapter 2), the author uses Berkeley's admission statistics (that 44% men and 35% women were admitted to graduate programs in general) to illustrate Simpson's paradox: the ...
• 210
1 vote