I just don’t get how the mode is gotten by tracing the intersection on the bar, is there any proof for this?

It seems strange to me that you often see final leaderboards where someone wins by multiple strokes—let's say at least three strokes. It's strange because everyone else is usually distributed such that no one else is more than a stroke or two ahead of anyone else. For example, take last week's Tour Championship: we have someone at -13, -12, bunch at -11, bunch at -10, etc. So you'd expect the winner to be at -14, or maybe win in a playoff after also being -13. But no—the winner was at -16! Is that some exceptionally rare result to have this big jump at the right tail of the distribution curve? Intuitively I would say yes, but it happens way too often. For example, the prior PGA tournament was the BMW Championship. Again, you have people who finished at -14, -13, -12, -10, -9, -8, etc. But the winner was at -17. Week prior, FedEx Championship, there are finishers at -9, -8, -7, -6, etc., and the winner was at -17 (!). Why is this distribution so common? Where one guy (and it's different guys week to week, not just someone who's way better than everyone else) trounces the field by three or more strokes?

Is this just a fact of the normal distribution? Like say you have 80 people, and each of them flips a fair coin 100 times. How often does someone flip at least three more heads than all other 79 competitors?

Thanks for any help getting me to understand this phenomenon.

I'm a Statistics major, currently in my 5th semester (3rd year of graduation), and I have a competitive exam coming up in about 6 months. Here's my honest problem: I feel like a 1st semester student would know more than me right now. My basics are shaky, and lately I genuinely can't study at all — my brain just shuts down. Simple things like basic addition/subtraction take me longer than they should, and I don't know if I actually forgot this stuff or never properly learned it in the first place.

A few specific issues I'm stuck on:

I don't know where to start or in what sequence to revise/study. Do I go back to basics first, or jump straight to exam-level topics?

Notes don't work for me. I only understand something when someone explains it to me directly — a YouTube video, a lecture, another person walking me through it. Reading on my own just doesn't click.

Classroom lectures and textbooks aren't helping either — I sit through them but barely absorb anything.

My mind goes completely blank when I try to solve problems, even ones I've supposedly "covered" before.

I think excessive scrolling/screen time has messed with my focus and attention span, and I don't know how to reverse that.

I have 6 months before my exam and I'm scared I'm starting from zero. If anyone's been in a similar spot — how did you rebuild your basics from scratch, what sequence did you follow, and how did you retrain your focus enough to actually sit and study again? Any advice, resources, or personal experience would help a lot.

How can every “normal” design have a 1/6 chance, while the “secret” one has only a 1/72 chance?

The only way this would make sense to me is if there’s an extra unit of the secret design in every 72 boxes. But if that’s the case, you could easily weight them accordingly, I guess. Or is there any other posible way?

Hi everyone, I have a question about choosing the appropriate background dataset when calculating SHAP values. I am using the kernelshap package in R, where we provide an X dataset containing the observations we want to explain and a bg_X dataset defining the background.

I have a binary classification model for disease vs non-disease, trained on a derivation dataset and evaluated on an independent validation dataset. My current understanding is that, if I want to explain predictions in the validation cohort, it makes sense to use the validation set as X and the derivation set as bg_X. In that case, the SHAP values for validation patients would describe how each feature moves their prediction relative to a baseline defined by the derivation population. Is this interpretation correct, and is this generally the recommended way to use the background when explaining an independent validation cohort?

My main question is about a more specific analysis. Suppose I want to investigate heterogeneity within patients who truly have the disease. More specifically, I want to see whether different disease patients receive high disease predictions through different combinations of features, and potentially cluster these patients based on their SHAP profiles.

In this case, I assume I should use only the true disease patients from the validation cohort as X, since those are the patients whose predictions I want to explain. However, I am unsure about the most appropriate choice for bg_X. Should I keep the full derivation cohort as the background, use only disease patients from the derivation cohort, or use the disease patients from the validation cohort themselves as the background?

If my main objective is to determine whether true disease patients have different model-attribution profiles, potentially reflecting different features through which the model identifies them as disease, which background would be the most statistically appropriate? Thank you!

I sort a cross-section of companies into deciles each month by a single continuous score, then record the mean forward one-month return of each decile. 185 monthly periods. The deciles are re-formed from scratch every month.

The result is not what I expected and I am not sure how to test it properly.

• Decile 1, the highest score, averages 1.623% per month.
• Deciles 2 through 9 sit between 1.12% and 1.35%, with no discernible order among them.
• Decile 10, the lowest score, averages 1.457%, which puts it above all eight of the middle deciles.

So it is not monotonic. It looks like a U with a much taller left arm. Separately, decile 1 beats decile 10 in 94 of the 185 months, which is 50.8%.

Three things I do not know how to handle.

1. Trend tests such as Jonckheere-Terpstra test against an ordered alternative. I do not have an ordered alternative; I have a shape I did not predict. What is the appropriate null and test when the alternative you actually want to state is "decile rank carries information" rather than "returns increase in decile rank"? Is fitting a shape (linear plus quadratic in rank, or an isotonic fit compared against an unconstrained one) more honest than a trend test here, or is that just choosing the shape after seeing it?

2. Am I even using the right unit of observation? Ten decile means computed from the same 185 months are not ten independent samples. Within any given month the returns are heavily cross-sectionally correlated (everything moves with the market), and each decile mean is itself a mean of a mean. My instinct is that the right object is the 185 monthly differences between decile 1 and decile 10, treated as a time series with its own autocorrelation, and that the ten-row table is a description rather than something to test. Is that the standard framing?

3. How do I state the gap between the two summaries without misleading anyone? Decile 1 beats decile 10 by a wide margin in the means, and beats it in 50.8% of months, which is indistinguishable from a coin flip at n=185. I assume the answer is that the mean difference is carried by a small number of large months, i.e. skew and fat tails, and that a sign test is simply low-powered against that. But "the mean says one thing and the sign frequency says another" is exactly the kind of sentence that gets used to sell things, and I would rather report it in a way that a statistician would not object to.

Not asking whether this is a good trading rule. I am asking how to test and report the shape without either overstating it or quietly dropping the inconvenient half.

Question is in the post title.

Thank you very much

and one that has the paper's metadata publicly available and with a sample size of less than 60 ish

any help would be greatly appreciated, thank you!

Hi everyone,

I'm a beginner in Machine Learning working on a binary classification problem. My dataset contains over 180 variables (both numerical and categorical), consisting of a mix of panel/longitudinal data and static features.

I am currently working on the Exploratory Data Analysis (EDA) phase. Given the large number of features, doing univariate and bivariate graphical analysis variable-by-variable feels unfeasible and time-consuming.

Is there a structured approach, strategy, or automated workflow to handle EDA efficiently for a dataset of this scale?

Any advice on best practices would be greatly appreciated!

Thanks in advance for your help.

Help me with understanding what is null hypothesis

I came across this article on Medium for Conjoint analysis. For those who understand it, is it good one?

https://medium.com/data-science-collective/beyond-the-black-box-understanding-conjoint-analysis-in-market-research-d19384c8336a

Hi! I am working on a meta-analysis of ten studies (I'm permitted to get advice about the stats elements!), and am getting confused around the heterogeneity statistics. My I2 is around 85%, and Cochran's Q = 44 (p= 0.00). However, my tau2 is low at 0.10.

It seems that in most papers I've read, a high I2 is accompanied by a high tau2. I assume that for mine, this means that while a high proportion of the variation is due to heterogeneity, the absolute magnitude of the variation is low. This makes sense in theory, but the point estimates of each study do vary quite a lot.

If anybody knows how this might be interpreted, I would really appreciate any advice :)

In my small simulation, requiring an independent verification PASS reduced false approvals, but one fraud still passed the independent check.

How should I represent imperfect verification reliability without pretending my score is calibrated?

Hello, I have a fractional design (2^4-1) with variables A, B, C, ABC and response R, but I am unsure how to include the measurement repeatability of the response when analysing the results.

For example, I know my response variable measurement has a repeatability of 0.234 (3-sigma value), and from my DOE analysis I got that the absolute effect of variable A on the response variable is 0.1.

As the effect of A is less than my repeatability does that mean I cannot really conclude anything about the impact of A on R?

Thanks for your help

Hi all, I am an incoming fresher in undergraduate pursuing economics as my majors. Have no prior knowledge of in-depth research but have read few literature reviews. Want to learn the basics of atleast one language in my first semester. Which language should I start from? R or Stata or Python

Edit: You guys are amazing. Really grateful for the insights. So, I have decided to start with Python in the first Semester ........will learn R later on. Looking forward to share my journey in this community.

I’m planning to play slots on an upcoming cruise expecting to lose money but also to get free cruise offers.

I’m planning to have $2500 cash with me and to do 750 $10 spins. I don’t know exact payback percentages but assuming an 80% payback rate how much would I lose on average with the 750 $10 spins. Also, what is the risk of ruin before reaching 750 spins? Thanks.

Hi there, I'm currently working on my master thesis where I have a parallel mediation. I am working on the method section but i am so completely lost in how to check all the assumptions for the model.
From what I do understand I can do a visual inspection for the scatterplot (after using model 4) to inspect the linearity, homoscedasity and outliers.
The other 2 assumptions are normality and multicolinearity but I just don't understand how to do this. Could anyone help me? some explanation or links to proper resources would be greatly appreciated!

When building a calibration curve for a process that is linear over most of the observed range, how to determine the best choice between the following options?

(A) increasing the number of values tested, to get more x axis points;

(B) increasing the number of replicates of each measurement –less x points, but more precise estimate of y for each

For example, if an experimental setup lets me run 12 measurements for a linear calibration curve, is it better to run 4 values in triplicate? Or 6 in duplicates?

So I'm playing a videogame that shows you some statistics at the end of a mission, one of those stats is damage taken, and it comes as a percentage. Suppose it is a squad of 2 players, and both take 0 damage. Should the final stats show 50% for both of them, or 0%?

50% would make the percentage work, and it would be statistically correct, but it would also imply that damage was taken, which isn't the case

0% feels right, but it would also be the only case in which these stats do not add up to 100%

I have cgpa of 3/4 in bsc maths

I am going to apply at

Texas A &m

Uni of georgia

Kentucky state

Should i try any more unis?

Also what are the chances i get in?

Question for statisticians , would it be a good choice to pursue ms stats in 2027 given the job market?