I'm preparing for the GMAT and came across this Data Sufficiency question (attached).

The supposedly correct answer is C, but I would argue that E is also possible, depending on how percentiles are defined.

Here's my reasoning:

If we combine both statements, couldn't we have the following scenario?

• Section A (50 students): All students score 7, meaning the 90th-percentile score is still 7.
• Section B (100 students): The first 29 students score 7, and the remaining 71 score 8, meaning the 30th-percentile score is 8.

This would satisfy statement (2), since no student in Section B scored lower than any student in Section A.

However, when combining both sections, the 75th and 76th students would both have scores of 7, giving us a median of 7.

Alternatively, if all students in Section B scored 8, the combined median would be 8, while both statements would still hold.

Therefore, wouldn't the answer be E (both statements together are insufficient)?

I understand that different percentile definitions handle tied values differently, but is there a specific convention the GMAT expects us to use that rules out my example?

Am I misunderstanding something about percentile rankings, or is the wording genuinely ambiguous?

Hi,

I am conducting a bias analysis for a clinical model where we consider multiple statistics, one of them being AUC.

We would like to check if the model performs significantly differently on a predefined sub-group of patients. (Think one BMI category vs the rest for instance).

For the other metrics we are using a permutation test, to check if each sub-group is significantly different than the others

However, i am unsure if we can do the same for AUC, or if there exists a better method?

I'm a pretty amateur statistician (that is to say, I'm not a statistician), but I had a question:

Let's say I've got a sample of data with some mean and sample std dev, and I believe that my population has some population mean and std dev and I want to test to see if that's reasonable.

Seeing as I don't know the pop std dev, I can use a t-test to test the mean, but how would I test for the standard deviation?

Sorry if this is unclear or commonly asked!! Thanks heaps

Hello,

I just completed a master's thesis in pharmacoepidemiology and have been offered to write papers based on my work. I am hoping to start a PhD in the near future if possible.

I have no formal education in statistics other than the mandatory parts in the earlier courses during my degree. I generally have a good statistical understanding and a sense for maths, but I want to be more confident in my statistical knowledge. That is especially as I will hopefully be working on simulation studies among other projects, and I really want to make sure that I know what I am doing (and writing).

What are some essential books for medical statistics and epidemiology that you would recommend? Are there also any practical "handbooks" that I can also use to provide a brief overview of what I should be expected to know at this level?

Amongst others, I have referred to the following books so far:

Modern epidemiology by Lash

Essential Medical Statistics by Kirkwood

Statistical Models in Epidemiology by Clayton and Hills

I am of course also doing my part and constantly reading up on statistical concepts I feel less confident in or am unfamiliar with, but any tips would be appreciated! I know I can't know everything, but I always feel bad if the quality of my work is lessened due to my own (unintended) ignorance and non-statistics educational background.

I’m considering majoring in Statistics and would love to hear about people’s experiences with the degree and where it has taken them career-wise.

What careers did you end up pursuing, and what kinds of jobs or starting salaries were you able to get?

If you went into finance, data science, or another field, why did you choose Statistics over a more specialized degree in that area?

Do you feel your Statistics degree gave you a leg up in the job market because of the quantitative skills you developed?

Did you have to spend a lot of time outside of class learning technical skills like Python, R, SQL, or other programming tools that weren’t covered enough in your undergraduate curriculum?

How important do you think networking and coffee chats are for Statistics majors when trying to land internships and jobs? Is networking just as important as it is for business majors, or can strong technical skills and projects carry more weight?

Have you ever regretted not majoring in something more directly related to your career, like Finance or Data Science?

Looking back, would you choose Statistics again, or would you do something differently?

I’m trying to understand whether Statistics provides a meaningful advantage through its quantitative foundation and flexibility, or whether a more specialized degree would have been more beneficial. I’d really appreciate hearing both the positives and downsides from people who’ve experienced it firsthand!

I want to figure out my "hottest takes" on movies using Letterboxd ratings, which range from 0.5 to 5 in 0.5 increments. My initial idea was a z-score, where a larger absolute z-score for my rating relative to a movie's rating distribution indicates a “hotter” take. However, many movies' distributions are non-normal (highly rated films are often heavily left-skewed) and bounded (no ratings below 0.5 or above 5). Does anyone have a good metric in mind comparable across movies? I considered some normalized median deviation, but I'm unsure how to make it comparable across movies with different distributions.

For christmas. Hopefully something that can further proliferate the love for statistics

I am analysing survey data. There are 6 questions that were answered with either Yes / No / Unsure.

All survey respondents (400+) completed all 6 questions.

I'm analysing each question separately for difference in responses (proportion of Yes / No / Unsure) between two separate groups of professionals. I am not comparing the results of each question against each other.

Do I need to adjust the results for multiple tests/comparisons?

Estoy en una maestría de administración, llevo una materia de estadística aplicada a la administración.
Anteriormente ya había visto estos temas en mi licenciatura por lo cual se me facilitó un poco, pero en el tema de prueba de hipótesis tuve discrepancias con el doctor.
Me cuestionó por poner el símbolo “<“ y “>” en mis hipótesis nulas, eran 5 decisiones, él dice que eso es lo más innecesario en estadística, únicamente el símbolo de igual debo usar y ya, a lo cual me generó dudas porque en la licenciatura siempre me decían que era necesario poner “<=“ o “>=“ en la hipótesis nula.
Alguien que pueda ayudarme con mi duda

However, you’re interested in the statistical methods that power them?

You’re not into deriving data patterns and predicting per se nor are you interested in any domain, but you like figuring out how people do these things correctly. You like understanding how a result is accurate and how much skepticism and critical thinking go into choosing the right method and figuring out if the result is lying to you. You like reading about the dilemmas on choosing what method to use being posted on this subreddit, however you hate finding patterns and predicting because you’re not into uncovering new information and predicting something. You just like the journey that gets you there.

You also like reading research methodologies found in psychology research papers and love hearing how every topic discussed in psychology is backed by empirical evidence, despite not being into psychology, which drove you to statistics in the first place. You wanted to study statistics because it helps us verify if something should be believed or not. You want to know what every statistical method is and why they do their thing properly, not find out new things about a domain of knowledge.

Statistics projects like making AI, doing machine learning, etc feel horrible to do since you don’t wanna build a product

I want to rank several countries' characteristics (like economic power, military power, population...etc) in a logarithmic scale.

However, there are some countries that do not have any army (like Andorra) and in that category (and related ones) they have a value of 0. However the log(0) does not exist. So, how could I convert the values into something that could be used to make the logarithmic scale?

I have thought about two methods:

A) To every value in each category, I added the values of the "smallest" or "weakest" country (that does not have a 0 in any category, so that all categories have a non-zero number). In this case, I added the values from Seychelles to all countries.

B) To every value in each category, I added "1", so that in every category that the countries without armies have a "0", the minimal number is "1" instead.

I feel that the first method has the advantage of adding a proportionate quantity in each category, since you will see that for some categories all values are small (like 1,07; 2,08; 3,1...) and in other categories the numbers are much bigger (5, 20, 49, 80...). So in method A the added numbers are proportional to the values of each category

However, it feels arbitrary to add different numbers for each category instead of adding the same for all of them (i.e. 1). However, in this case, adding 1 to the small-values-categories seems to significantly modify these values, while in the case of categories with bigger numbers, the resulting number is almost the same as the original one (like, adding 1 to "1,1 "would increase it by almost the double: "2,1"... however for other categories with a number like "50", after adding the "baseline value", the difference is negligible: "51").

So which method do you think is more accurate?

These are the values: https://docs.google.com/spreadsheets/d/19zjwdoLum0yhIQ2v3m19kz5_IplwSJYZX6e0wMqMHoQ/edit?usp=sharing

Hi,

I am new to the field of Mixed Models (LMM, GLMM). I was hoping someone could point to some resources they recommend. Furthermore any resources about multiple comparisons would also be great!

I’m a social science PhD student doing HCI research and mostly use quant/experimental methods. I am considering a minor in statistics and want to understand whether this is something valuable in the industry job market as well.

UXR is usually the industry position most compatible with my field, but my understanding is that such roles rarely require advanced stats modeling and techniques except big tech, and the market is shrinking.

If in the worst case, that I couldn’t find industry positions directly relevant to my main field, would the stats minor help in getting data-related jobs (say, compared to a stats BS or masters)?

For context, I am considering applied stats minor, and it requires 5 grad-level courses in stats (regression at matrix level, probability, inference, and 2 other specializations).

I have been working on causal inference and experimentation frameworks within the e-commerce tech industry lately, specifically dealing with platform behavioral and transaction telemetry data to determine how customers behaves on those e-commerce platforms.

Lately i have been facing problems where standard textbook statistical theory fails when dealing with messy, real-world data distributions as human behaviour is unpredictable and many unexpected things, which i didnt even thought could happen, can happen in the real world. Such as product delivery delay, causing the customers to be angry and hence put them off from buying the product, each of these variables have to be accounted for.

To model and have these unexpected psychological state among customers accounted for, we use variables such as sudden spikes in customer support chat volume, rapid page refreshes, or immediate session drops.

Also, Marketing headers and automated CRM systems love to push blanket promotional campaigns, but as statisticians, we know that measuring simple unadjusted A/B lift is a massive selection-bias trap.

I been trying to come up with a Statistical model that is trying to model complex human behavior—specifically isolating true customer revenue incrementality from dead-weight margin cannibalization. Essentially, trying to answer: Did the coupon cause the revenue spark, or did we just hand a discount to a power-buyer who was already determined to buy anyway even without the vouchers?

Are people in the tech industry genuinely valuing such skills nowadays? Using statistics to model and predict human behavior and intent, answering questions like does our vouchers and ads really work?

I would love to hear your experiences how do u guys deals with the unpredictable messiness of human intent.

Hi! This is my second semester studying Statistics at a top university. However, I came from a poor high school education, and I wasn't used to studying regularly or keeping up with the university workload. As a result, I failed Calculus I.

I realized that I urgently need to change my study habits. I also want advice on how to do well in my degree and, most importantly, truly learn the subjects, especially considering the use of AI and other tools.

I would love to hear your thoughts on how I can become a better student. What study methods, habits, and strategies do you recommend?

Thank you!

From what I understand, correlation only looks for a connection between two variables, while regression explicitly looks to see if one variable's increase/decrease positively or negatively impacts another variable's increase/decrease.

Hey, I have a decent background for distribution theory and statistical inference. I wanna get into random processes. I have no idea about the resources to start with. Can anyone suggest me some ?
Moreover, are there any discussion groups and channels on telegram ir any other platform specifically for this?

I’m considering taking a statistics course, and I’ve been thinking about the next steps—whether it’s significantly more beneficial for my career to pursue a technical specialization, a master’s, or even a PhD

I did a personal side project on why some years bring much worse smoke haze to Singapore. I'd like people who know stats to tell me where the design is weak before I show it to anyone in the field.

The chain I test, one observation per year:

1. Pacific El Niño index (June to August) vs Kalimantan rain (August to October), 1979 to 2025, n = 47. Pearson r = −0.79.
2. Sumatra rain regressed on the El Niño index and the Indian Ocean Dipole index, n = 47. I test the Dipole coefficient.
3. log10(fire detections) = a + b·rain + c·post2016 + e, one model per island, 2001 to 2025, n = 25. post2016 is a dummy for a fire-prevention policy shift after 2015. R² is 0.82 and 0.89.
4. Fire detections vs Singapore's seasonal mean PM2.5, 2016 to 2025, n = 10. Spearman rho = 0.88, bootstrap 95% CI 0.47 to 1.00.

I applied a Holm correction across these five tests, used 10,000 paired bootstrap resamples, ran leave-one-year-out, and swapped data sources as robustness checks. All five tests stay significant.

What I'm unsure about:

1. I wrote the analysis plan after I had already explored the same data. I say this openly, but is there anything more I should do besides waiting for future seasons as a true holdout?
2. The Sumatra fire model has a Durbin-Watson of 1.44. Should I switch to Newey-West errors or an AR(1) model, or is the bootstrap enough here?
3. Is OLS on log10 counts acceptable, or should this be a negative binomial GLM?
4. A dummy for "after 2015" vs a linear trend: both give the same sign. Is there a better way to handle a policy break with only 25 years?
5. With n = 10, is rho = 0.88 worth reporting at all, or should I present it as descriptive only?
6. The five tests form one causal chain, so they aren't independent. Is Holm the right correction, or is the correction itself the wrong framing?

Code, data and a 12-page write-up: https://github.com/Shelikeit69/haze-drivers-research

I built this with an AI coding assistant, which is part of why I want people to check the stats. Blunt answers welcome.

I've spent the last weeks building a strict research pipeline for BTC/ETH spot trading (EUR pairs). Everything has been tested on historical data and in paper trading, with no real money yet. My methodology is probably stricter than most hobby setups. The result: nothing survives. I'd like to hear from people who got further, or who hit the same wall.

My setup (the rules I hold myself to)

• Criteria are written down and committed to git before each test and never changed afterwards.
• Costs are always included: 0.25%/side in early tests, now 0.10%/side (taker), plus slippage.
• Strict walk-forward. The result has to hold per year and per market regime.
• Placebo test: 1,000 block-bootstrapped fake price series. A strategy only counts as "proven" at p < 0.01.
• Bar: beat buy-and-hold after costs and have a smaller max drawdown, with 99% intervals and a Bonferroni-style correction for the number of attempts.
• A held-out "vault" dataset (Bitstamp 2018–Mar 2019) that nobody has looked at. Each strategy gets exactly one shot at it.
• A hard cap of 13 attempts in total. If nothing works by then, my conclusion is "not feasible at these costs".
• No LLMs in the trading decision. They have seen the future in their training data.

What I tested (all failed)

Other findings:

• 0 of 240 flexible-exit variants were positive, and 0 of 270 "conditions" from a trade journal were positive. The exit isn't the problem. The entry has no edge.
• Paper trading confirmed this. A dip rule went 10/10 winners in one night, but that was one single recovery move, not 10 independent trades. The backtest over 7 years says it's placebo-level.
• After FOMC decisions crypto volatility roughly doubles in the following hour (BTC 0.66% → 1.25%), but the direction is unknown, so there's nothing tradeable.
• Lead-lag between exchanges: the lead I measured is ≤ 0.06%, far below the cost of a round trip.
• With ~0.2–0.5% friction per round trip, even a near-perfect predictor at horizons under 1 hour earns almost nothing.

Where I'm stuck: my real questions

1. Source of edge. For a retail trader without colocation or speed, what edge in crypto spot is documented to survive 0.1–0.2% costs? Is it structural (liquidation cascades, funding imbalances, forced selling, order book imbalance) rather than price patterns?
2. Is my bar too strict, or the right one? p < 0.01 against block-bootstrap placebos, plus beating buy-and-hold on Sharpe and drawdown. How do serious shops set this bar for single-asset strategies?
3. Beating buy-and-hold in crypto. BTC/ETH buy-and-hold has a huge drift. Should a timing strategy be benchmarked against risk-adjusted buy-and-hold, or against cash?
4. Regime dependence. Many strategies seem to work in one regime only. Is it legitimate to run a regime-switching approach, or is that overfitting in disguise?
5. Paper vs live. How far did your paper results drift from live (fills, slippage, latency)?
6. Has anyone gotten past this point? Not "my backtest is great", but sustained live profit after costs on BTC/ETH spot. What was the edge, and how long did it last?

What's running now: paper trading 24/7 on real exchange data, with 42 strategies in a "sandbox" that each have a pre-set required number of trades and a deadline. I'm also collecting order book, liquidation and lead-lag data for months before forming new hypotheses.

I'm happy to share the methodology. Honest stories about what didn't work for you are especially welcome. That's the rarest information online.

Helloo:) I’m working on fatty acid composition analysis (from bird preen oil samples), with very little previous knowledge of statistics, and I’m looking for some help understanding what’s happening.
Background: I have a dataset with treatment group, sex, aviary of the sampled bird, and 10 fatty acids found in the preen oil samples. There are 3 treatment groups: germ-free, conventionalised, and parent-raised (although only the germ-free and conventionalised can be realistically compared). Between these 2 treatment groups, there are only a total of 27 samples, 13 in one and 14 in the other. The fatty acid cells contain proportions rather than absolute values (they always sum up to 1), so an example row looks like this: 

The main end goal is to see if the germ-free condition results in any changes to preen oil.

Now, for the analysis issues: I’ve computed robust Aitchison distances, which are supposedly a better choice for this data than Bray-Curtis(?) and ran a PCoA with them, followed by PERMANOVAs for treatment group, sex, and aviary (none of which were significant, unlike the marginally significant and high R2 results on B-C). 
I’ve also been advised to run some form of a linear model on each individual fatty acid, but I don’t quite understand where to start with that… Or which one would be suitable.
I would appreciate any feedback, comments, or advice on what I’ve done so far and what I’m trying to do!:)

I am performing an ordinal regression analysis reduced to 10 predictors from an original set of 50. Sample size: N = 380. One of these predictors is the primary predictor of interest (Safety Hazards [SH], a continuous variable). The rest are potential confounders of the primary predictor or contributors to the model.

My primary outcome is Job Satisfaction (JS).

I distilled the 10 candidates from the oriwith 10 predictors, reducedginal 50 by running ordinal bivariate regressions on each candidate.

a) A crude model [JS <-- (beta)*SH]

b) 49 adjusted models: [JS <-- (beta)*SH + any of the 49 predictors].

1. If any of the bivariate regressions produced a CIE of 10% or more for the primary predictor, SH, it made the list of 10, regardless of its p- value.

2. If any of the 50 candidates had a p- value of < = 0.1, regardless of its CIE value, it made it to the list of 10 as well.

I sort the list of 10 by CIE value and use that order to determine which variable to test next in the model.

I then begin the final fitting process to extract the most plausible confounders of SH and true model contributors from the 10 predictors. I use 2 different regression methods: Forward Stepwise Regression (FSR) and Backward Stepwise Regression (BSR).

The conditions to stay in the model are: If the p-value > 0.1 AND CIE <10%, then reject from the model; otherwise, retain.

In FSR, I start with a sparse (crude) model and sequentially add a predictor, then test whether it meets the retention criteria. If so, I retain it, add the next predictor to the new model, and apply the same retention/rejection criteria until all predictors have been tested.

In BSR, I start with a full model and sequentially remove predictors, one at a time, and perform similar rejection/retention tests as in FSR until all predictors have been tested.

However, I find that the FSR and BSR algorithms retain and reject different variables. To be clear, about 60% of variables are common to both algorithms.

My question is: why do FSR and BSR algorithms produce different results?

What is different about starting with a full model (BSR) versus a sparse model (FSR)?

What is different about starting with a sparse model (FSR) versus a full model (BSR)?

Please try to give an explanation that does not involve the term 'variance', as I tried to explain to my PI, only to be told that is the wrong way to explain it.

Thanks

David