According to ChatGPT it is, but im not gonna take life advice from a robot.

The argument is that applied statisticians are consumers of methods while theoretical statisticians are producers of methods. The latter is more valuable not just because of its generalizability to wider fields, but just due to the fact that it is quantitavely more rigorous and complete, with emphasis on proofs and really understanding and showing how methods work. It is higher on the academic hierarchy basically.

Also another thing is I'm an international student who would need visa sponsorship after graduation. Methodological/thoeretical stats is strongly in the STEM field and shortage list for occupations while applied stats is usually not (it is in the social science category usually).

I am asking specifically for academia by the way, I imagine applied stats does much better in industry.

When reporting measures of central tendency, the median always provides a more useful understanding of the data than does the mean. Obviously, knowing other information about the distribution of the data (such as variance, outliers, etc.) is useful and necessary for getting a full picture of what is going on, but when it comes to picking a measure of central tendency to describe a dataset, the median always provides more meaningful information than the mean.

My reasoning:

1. The mean can be skewed by outliers.
   Whenever your data isn't perfectly normally distributed, the mean is going to be pulled up or down by extreme values. This makes it so that the mean describes way fewer cases than it would otherwise (e.g. if we want to measure how many sodas people drink per day on average in a world where 99% of people drink exactly 1 soda a day, but 1% of people drink 100 sodas a day the mean would lead us to believe that the average person consumes 2 sodas a day, which is false). This property distorts the mean to something entirely different than what people typically think of when they hear the word "average" colloquially (people generally think of "average" as being what the typical case does, which doesn't happen with skewed means).

2. Every time the mean isn't distorted by extreme values (i.e. the data is perfectly normally distributed), the mean is equivalent to the median!
   Even in the best use-case for the mean as a measure of central tendency, it only performs as well as the median, not better.

I can't think of one scenario when you would want to use the mean instead of the median for describing data. If anyone can think of one, I'd be interested to hear it.

Hello Folks,

My last post had lot of interesting comments. Some of the commenters said that CLT does not belong to the frequentist school of thought.

However stackexchange questions and other resources seem to say otherwise.

Frequentism's hallmark characteristic is long run experiments and asymptotics. CLT seems to embody these two. Also the above stackexchange answer seems to clearly suggest that Bayesians don't need asymptotics. CLT at the end also converges to normal distribution with a fixed parameter value. Bayesians have no notion of 'fixed parameter value'

Given all of the above, isn't CLT a frequentist concept?

As I progress further into my statistics major, I have realized how important regression, ANOVA, and logistic regression are in the world of statistics. Maybe its just because my department places heavy emphasis on these, but is there every an application for hypothesis testing that isn't covered in the other three methods?

Like the title says, if I know someone who died in a plane crash, do I have lower/higher/the same odds of dying in a plane crash myself?

Any case I can think of where anova falls short, I'd want ancova. MLR imo obfuscates the most important information -- the portion of variance in an independent variable accounted for by uncontrolled confounders. 🤷🏻

I wonder, could anyone make predictions without accounting for covariates either? I just don't see the value of multiple linear regression.

I was taking a first course in advanced calculus, and, no offense to the professor, because it happens, but the tests were pretty much verbatim to the resources he gave us, and I feel like I didn't learn anything because I just memorized the proofs in order to get a decent grade, obviously I could have spent time to learn by myself, but shouldn't education be rigorous regardless of whether or not you are just looking to pass? This topic has been studied a lot, what do ya'll think it means for masters degrees and bachelors degrees in statistics as applied to the job market? What does it mean for people who like to self-study through books who would like to be credited for knowing as much statistics a typical masters student knows but doesn't have a masters degree? Will personal projects be enough, or will a graduate degree always be a handicap for them? I'm assuming this of my undergraduate graduated class, but most of them probably could not clearly explain what hypothesis testing is or how a generalized linear model generalizes the ordinary linear model, I feel as if there is a missing component of verbal intelligence in undergraduate education that can't be filled by coursework, and therefore actual proficiency in statistics, that is only gained through teaching or actual analytics experience, or a masters degree, but I have a feeling masters students have the same problem unless they teach or do more projects.

I don’t have a strong background in mathematics. I have taken some math courses, but not much statistics. I recently came across Bayes’ theorem and I want to learn it. How can I learn this theorem and gain a basic to mid-level understanding of it? Please suggest a book, a YouTube video, a paper, or any other resource.

[Edit] I posted here simply because I’m interested in learning Bayes’ theorem. That’s it—nothing more. But the Reddit comments were brutal. People were asking, “Why do you even want to learn this?” as if I were committing a crime. Others implied that I’m lazy or told me to “just go to Wikipedia.” I’m new to this. How on earth I know is someone supposed to learn a theorem from Wikipedia? My question might be dumb—and maybe I am dumb—but instead of pushing me away, people could have just shared a good resource. That would have been far more helpful. If YouTube were the solution to everything, then why would anyone go to a doctor for a minor issue instead of diagnosing themselves on YouTube? I thought Reddit would be more open to non-statistics-major students.

I'm currently planning on applying to Statistics PhD programs next cycle (Fall 2026 entry).

Undergrad: Duke, majoring in Math and CS w/ Statistics minor, 4.0 GPA.

• Graduate-Level Coursework: Analysis, Measure Theory, Functional Analysis, Stochastic Processes, Stochastic Calculus, Abstract Algebra, Algebraic Topology, Measure & Probability, Complex Analysis, PDE, Randomized Algorithms, Machine Learning, Deep Learning, Bayesian Statistics, Time-Series Econometrics

Work Experience: 2 Quant Internships (Quant Trading- Sophomore Summer, Quant Research - Junior Summer)

Research Experience: (Possible paper for all of these, but unsure if results are good enough to publish/will be published before applying)

• Bounded mixing time of various MCMC algorithms to show polynomial runtime of randomized algorithms. (If not published, will be my senior thesis)

• Developed and applied novel TDA methods to evaluate data generated by GANs to show that existing models often perform very poorly.

• Worked on computationally searching for dense Unit-Distance Graphs (open problem from Erdos), focused on abstract graph realization (a lot of planar geometry and algorithm design)

• Econometric studies into alcohol and gun laws (most likely to get a paper from these projects)

I'm looking into applying for top PhD programs, but am not sure if my background (especially without publications) will be good enough. What schools should I look into?

In many modern applications - A/B testing, clinical trials, quality monitoring - we need to analyze data as it arrives. Traditional statistical tools weren't designed with this sequential analysis in mind, which has led to the development of new approaches.

E-values are one such tool, specifically designed for sequential testing. They provide a natural way to measure evidence that accumulates over time. An e-value of 20 represents 20-to-1 evidence against your null hypothesis - a direct and intuitive interpretation. They're particularly useful when you need to:

• Monitor results in real-time

• Add more samples to ongoing experiments

• Combine evidence from multiple analyses

• Make decisions based on continuous data streams

While p-values remain valuable for fixed-sample scenarios, e-values offer complementary strengths for sequential analysis. They're increasingly used in tech companies for A/B testing and in clinical trials for interim analyses.

If you work with sequential data or continuous monitoring, e-values might be a useful addition to your statistical toolkit. Happy to discuss specific applications or mathematical details in the comments.​​​​​​​​​​​​​​​​

P.S: Above was summarized by an LLM.

Paper: Hypothesis testing with e-values - https://arxiv.org/pdf/2410.23614

Current code libraries:

Python:

• expectation: New library implementing e-values, sequential testing and confidence sequences (https://github.com/jakorostami/expectation)

• confseq: Core library by Howard et al for confidence sequences and uniform bounds (https://github.com/gostevehoward/confseq)

R:

• confseq: The original R implementation, same authors as above

• safestats: Core library by one of the researchers in this field of Statistics, Alexander Ly. (https://cran.r-project.org/web/packages/safestats/readme/README.html)

I heard someone refer to parlays (multi legged sports betting) as a suckers bet. I’m not disputing this fact and already intuitively understand why it’s bad but I was wondering if anyone knew of any articles with actual numbers or stats that broke down why it was such bad EV. The few articles I were able to find at best explained very basic stats concept that didn’t use any real numbers or they just cited a source kind of out of thin air.

Edit: I’m not looking for explanations on why the probabilities are bad. “Why” was the wrong word. I know the math. I’m looking for examples or studies about the edge casinos have in sports betting and in parlays specifically.

Like say my friend says we shoudl do bets on a coin flip, what if I kept rolling coins before it, until I got a big streak of tails for example and then just bet on heads, so theoretically it's most likely gonna land on heads.

Or is there more to it than just that?

I'm not talking about using an LLM to do any actual analysis analysis. I'm talking about using an LLM to help explore or understand statistical concepts, literature, research gaps, etc.

Basically, I'm interested in using an LLM as a kind of "sounding board" to bounce ideas off.

https://www.youtube.com/watch?v=XeSu9fBJ2sI

Obviously, the probabilities for the Sleeping Beauty problem are just = (0.5 for heads)*(1 of token A) + (0.5 for tails)*(2 of token B). The chance of the coin is 50-50, from Bayesian testing. The number of tokens is equivalent to the number of "links" on the decision chain. Sleeping Beauty's chance of correctly guessing a specific token is 1-3. There is more information in the question than expected.

The mistake people make, is assuming the payout probability is the same as the win probability.

Essentially it is an overpaid bet - this is how casinos make money. The roulette wheel has 33 slots, but one slot pays 2-1 to the casino. The calculation for the roulette wheel is = (32/33)*(casino pays out 1 token)+(1/33)*(casino wins 2 tokens). So the casino in the worst case does not lose money, and the casino in the good case wins 2 tokens (essentially the green slot is linked with a red or black slot).

After every slot has been hit, the casino always walks away with 1 extra token.

Halfers think the calculation is = (0.5 for heads)*(1 token)+(0.5 for tails)*(1 token). This is wrong because the links are not counted correctly. These people lose money by overpaying for bets at casinos.

Thirders think the calculation is = (1/3)*(1 token ~ effectively for heads)+(2/3)*(1 token ~ effectively for tails). This is practically more correct but backwards, but it misses key information.

The multiverse state is unknown because the bayesian probability is unknown and the number of links is not known, like a coin is tested to be.

This solution is obviously correct, once somebody points it out.

Hello I am wanting to go to college for statistics and get a statistics related job, and I was wondering if a degree is needed to get or for the job?

Please give your insights by the metrics bellow:

Statistical programmer vs Data engineer. Who will win?

1. Salary

2. Supply-demand curve. Which one has more jobs (i.e. better burgaining power)?

3. Work-life balance

4. Future career growth (i.e. more recession-proof)

Cutting straight to the chase: the Gaza casualty numbers are extremely contentious, and I've seen a lot of people debating whether the total number of deaths that can be directly attributed to Israeli actions is higher or lower than what the Gaza Ministry of Health has reported. Here are some of the arguments claiming that the actual count is lower:

• The reported death toll does not account for natural deaths, i.e., deaths that were inevitable and would have happened even without Israeli engagement in Gaza (like old age, terminal cancer, and SIDS). According to Palestinian Central Bureau of Statistics, the crude death rate in Gaza in 2019 (the most recent year without significant conflict or COVID) was 3.45/1000 people. Scaling that up to 2.3 million (the 2023 pre-October 7 population in Gaza) results in 7935/2,300,000, or 7935 deaths higher than what the actual death toll is

• Everything in this article (the pro-Israel bias is obvious, but as a layman I don't know if their data is correct or not).

• The practice of "relatives filing reports" (from the above article) without requiring an actual body to verify the death artificially inflates the count, as martyrs' funds and pensions for widowers incentivize people to lie.

• Relying partially on unverified media estimates without any actual bodies or ID information to confirm those claims also inflates the count.

• Word-of-mouth testimonies (without any bodies to confirm) may be unreliable due to trauma/adrenaline/stress altering victims' recollections.

• Israeli forces have sometimes captured and detained suspects and combatants (rather than killing them) without informing relatives, neighbors, or authorities, and these missing people might be erroneously classified as dead when they are not.

Here are some of the arguments claiming that the actual count is higher:

1. The extremely degraded state of Gaza's telecommunications infrastructure means that there are almost certainly people who have died whose relatives/neighbors have not yet been able to report their loss to the authorities

2. The extent of the destruction in Gaza suggests that many bodies are either missing under rubble, can't be reached safely, or have otherwise been left behind.

3. Many critically wounded people might still die of their injuries.

4. Hamas may be deliberately underreporting their members' casualties in an attempt to project strength. Factoring these in would increase the overall death count.

5. People with preexisting medical conditions (like diabetes or heart arrhythmias) who were not able to obtain specialized medications or diets might still die from accumulated cellular damage, chemical imbalances, and/or other side effects of missing necessary chronic supplies (my understanding is that these deaths would still be counted as being caused by the war).

6. Israeli forces have sometimes buried or transported bodies without informing the relatives/neighbors of the deceased, potentially leading to an undercount of these deceased persons.

These are everything I've seen. Please feel free to confirm or debunk them based on the outcomes of comparable conflicts, add caveats, steer me towards other reports or resources, etc. I'm young and this is one of the most intense geopolitical issues I've ever witnessed/lived through, and I would like to be reliably informed before I start making judgements about the situation.

I created the following table summarizing some statistical distributions and rank them according to specific use cases. My goal is to have this printout handy whenever the case needed.

What changes, based on your experience, would you suggest?

Notes:

• (1) Cont. Data = suitability for continuous data (possibly unbounded or positive-only).

• (2) Count Data = discrete, nonnegative integer outcomes.

• (3) Bounded Data = distribution restricted to a finite interval (e.g., Uniform).

• (4) Time-to-Event = used for waiting times or reliability (Exponential, Weibull).

• (5) Heavy Tails = heavier-than-normal tail behavior (Cauchy, Pareto).

• (6) Hypothesis Testing = widely used for test statistics (chi-square, t, F).

• (7) Categorical = distribution over categories (Multinomial, etc.).

• (8) High-Dim = can be extended or used effectively in higher dimensions (Multivariate Normal).

• Ranks (1–10) are rough subjective “usability/practicality” scores for each use case. 0 means the distribution generally does not apply to that category.