## Top new questions this week:

### Can increasing the amount of training data make overfitting worse?

Suppose I train a neural network on dataset A and evaluate on dataset B (that has a different feature distribution than dataset A). If I increase the amount of data in dataset A by a factor of 10, is ...

machine-learning neural-networks validation overfitting train

### How to calculate number of sets in Sigma Algebra

The example 1.2.2 of the book Statistical Inference by Casella and Berger states: if S has n elements, there are 2^n sets...(please see attached). Could you please explain how the authors derived ...

probability mathematical-statistics subset

### How are PQL, REML, ML, Laplace, Gauss-Hermite related to each other?

While learning about the Generalized Linear Mixed Models, I often see the above terms. Sometimes it seems to me these are separate methods of estimation of (fixed? random? both?) effects, but when I ...

mixed-model glmm glmmtmb reml laplace-approximation

### The distribution of the p-values under the null hypothesis is uniform(0, 1)

I have seen this, and this and a few YouTube videos, and I'm still stuck. I understand how the probability integral transform gives rise to the result that the CDF of the p-values will have a ...

distributions p-value

### When can't Cramer-Rao lower bound be reached?

The Cramer-Rao lower bound (CRLB) gives the minimum variance of an unbiased estimator. One sentence in the wiki page says "However, in some cases, no unbiased technique exists which achieves the ...

estimation unbiased-estimator estimators point-estimation efficiency

### Comparison of statistical tests exploring co-dependence of two binary variables

Suppose we observe data $(X_i,Y_i)_{i=1,...,n}$ on two binary variables: $X\in\{0,1\}$ and $Y\in\{0,1\}$. We would like to test if $X$ and $Y$ are co-dependent (related). Standard suggestions in ...

hypothesis-testing logistic generalized-linear-model binary-data power

### What exactly is model instability due to multicollinearity?

I've read that model parameters become unstable in case of multicollinearity. Can some one give an example situation of this behavior, and explain why this is happening? Please use the following ...

regression machine-learning multiple-regression linear-model multicollinearity

## Greatest hits from previous weeks:

### Is it possible to find the combined standard deviation?

Suppose I have 2 sets: Set A: number of items $n= 10$, $\mu = 2.4$ , $\sigma = 0.8$ Set B: number of items $n= 5$, $\mu = 2$, $\sigma = 1.2$ I can find the combined mean ($\mu$) easily, but how am ...

standard-deviation

### What is your favorite "data analysis" cartoon?

This is one of my favorites: One entry per answer. (This is in the vein of the Stack Overflow question What’s your favorite “programmer” cartoon?.) P.S. Do not hotlink the cartoon without the ...

humor

### Pearson's or Spearman's correlation with non-normal data

I get this question frequently enough in my statistics consulting work, that I thought I'd post it here. I have an answer, which is posted below, but I was keen to hear what others have to say. ...

correlation normality-assumption pearson-r spearman-rho

### How to 'sum' a standard deviation?

I have a monthly average for a value and a standard deviation corresponding to that average. I am now computing the annual average as the sum of monthly averages, how can I represent the standard ...

standard-deviation descriptive-statistics

### How to check for normal distribution using Excel for performing a t-test?

I want to know how to check a data set for normality in Excel, just to verify that the requirements for using a t-test are being met. For the right tail, is it appropriate to just calculate a mean ...

normal-distribution excel

### Statistics Jokes

Well, we've got favourite statistics quotes. What about statistics jokes?

references humor

### R vs SAS, why is SAS preferred by private companies?

I learned R but it seems that companies are much more interested in SAS experience. What are the advantages of SAS over R?

r sas

## Can you answer these questions?

### Is there any advantage to using $\chi^2$ for checking linear relationship $y(x)$?

At my university (physics major), we are often forced to use $\chi^2$ for checking if $y(x)$, where $y$ and $x$ are measured, is linear. We fit a linear regression $f(x)$ and then use \$\chi^2 = ...

chi-squared linear

### Which statistical method do I need for my research (combining correlation and independent two-samples t-test?)

I need some guidance with my model, because I believe I need both correlation as well as an independent two samples t-test for my research.. is that even a thing? My model claims that firm ...

correlation t-test predictor two-sample
 asked by Alex UM 1 vote

### Determining Sample Size When Low Probability Items Are Of Interest

Let's assume there are 10,000,000 Yankee fans and we want to analyze what else these 10 million people are fans of. A simple question is, what sample size do we need to be confident in the results? ...

confidence-interval sample survey-sampling