Cross Validated Community Digest

Top new questions this week:

Examples of distributions with easily solvable quantile functions but hard to solve CDFs

I'm interested in examples of probability distributions where the quantile function $F^{-1}(p)$ exists in closed form or is easy to calculate but where the cumulative distribution function (CDF) $F(x)$...

quantiles cumulative-distribution-function  
user avatar asked by spencergw Score of 8
user avatar answered by kjetil b halvorsen Score of 9

I think standard deviation of y is related to size of x. How do I create a model for this / test this?

I have a sample of data $(x_i, y_i)$. I hypothesize that $y_i$ is not dependent on $x_i$, but the standard deviation of $y_i$ depends on $x_i$ More concretely, say I assume $\textrm{Var}(y_i | x_i) = ...

regression data-visualization standard-deviation heteroscedasticity  
user avatar asked by Lost1 Score of 6
user avatar answered by Frans Rodenburg Score of 6

ANOVA with unreliable measure

I’m doing some literature review on sports science, in particular the effect of training on endurance. There is no standard endurance tests. Some consist in intermittent contractions until exhaustion ...

statistical-significance anova group-differences reliability intraclass-correlation  
user avatar asked by Experience111 Score of 5
user avatar answered by Eoin Score of 4

Standard negative binomial regression when counts are mainly zeros?

This question must have been asked many times before but I can't find an answer. I'm getting very confused about when to use a zero-inflated negative binomial regression vs standard negative binomial ...

regression count-data negative-binomial-distribution zero-inflation structural-zero  
user avatar asked by Picapica Score of 5
user avatar answered by Stephan Kolassa Score of 9

Interpreting complex roots of $R^2$

This is a common way to define $R^2$ in a regression problem. $$ R^2=1-\left(\dfrac{ \overset{N}{\underset{i=1}{\sum}}\left( y_i-\hat y_i \right)^2 }{ \overset{N}{\underset{i=1}{\sum}}\left( y_i-\bar ...

regression r-squared complex-numbers negative-r-squared  
user avatar asked by Dave Score of 4

I have count data, but it does not follow a Poisson distribution, what to do?

My data consists of 3 variables, one is a numerical variable of the number of flower visits that I have counted on certain locations and on certain shrub species. My other 2 variables are categorical ...

chi-squared-test poisson-distribution  
user avatar asked by Geertje Score of 4
user avatar answered by Nick Cox Score of 2

Welch t-test p-values are poorly calibrated for $N=2$ samples

I am performing a large number of Welch's t-tests (t-test with unequal variance) on very small sample sizes, often with only two samples per condition. I am finding the p-values are poorly calibrated: ...

t-test p-value calibration  
user avatar asked by emarti Score of 4
user avatar answered by Sextus Empiricus Score of 3

Greatest hits from previous weeks:

Famous statistical quotations

What is your favorite statistical quote? This is community wiki, so please one quote per answer.

references history  
user avatar asked by robin girard Score of 282
user avatar answered by Rob Hyndman Score of 279

What are the differences between Factor Analysis and Principal Component Analysis?

It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use ...

pca factor-analysis  
user avatar asked by Brandon Bertelsen Score of 267
user avatar answered by Jeromy Anglim Score of 186

Difference between confidence intervals and prediction intervals

For a prediction interval in linear regression you still use $\hat{E}[Y|x] = \hat{\beta_0}+\hat{\beta}_{1}x$ to generate the interval. You also use this to generate a confidence interval of $E[Y|x_0]$....

regression confidence-interval predictive-models prediction-interval faq  
user avatar asked by question Score of 133
user avatar answered by Charlie Score of 137

Percentile vs quantile vs quartile

What is the difference between the three terms below? percentile quantile quartile

descriptive-statistics quantiles median percentage  
user avatar asked by luciano Score of 171
user avatar answered by stochazesthai Score of 201

How to determine which variable goes on the X & Y axes in a scatterplot?

I am trying to do a scatterplot to see the relationship between literacy and baby mortality. How do I know if literacy is my X axis and baby mortality is my Y axis, or the reverse? How do I ...

data-visualization scatterplot  
user avatar asked by Beth Score of 10
user avatar answered by Glen_b Score of 17

Why square the difference instead of taking the absolute value in standard deviation?

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...

standard-deviation definition absolute-value faq  
user avatar asked by c4il Score of 562
user avatar answered by Tony Breyal Score of 257

What is the difference between fixed effect, random effect in mixed effect models?

In simple terms, how would you explain (perhaps with simple examples) the difference between fixed effect, random effect in mixed effect models?

mixed-model fixed-effects-model definition  
user avatar asked by Andrew Score of 436
user avatar answered by John Salvatier Score of 234

Can you answer these questions?

Diffusion Model consistency term derivation question

The consistency term of the diffusion model is written as: $$\mathop{\mathbb{E_{q_\phi(x_{1:T}|x_0)}}} \left[\log\prod_{t=2}^T \frac{p(x_{t-1} | x_t)}{q_\phi(x_{t-1}|x_t, x_0)}\right]$$ $$= \sum_{t=2}^...

conditional-expectation kullback-leibler generative-models  
user avatar asked by Shawn_this_is Score of 1
user avatar answered by cinch Score of 0

Why is the threshold term incorporated into the weight vector in linear classifiers?

In the context of linear classifiers, such as the perceptron or logistic regression, I understand that the decision boundary is defined by a linear combination of input features and weights, plus a ...

regression machine-learning neural-networks bias perceptron  
user avatar asked by Narges Ghanbari Score of 1

Rescale measures of association for meta-analysis (e.g., log-transformed independent variables)

I am carrying out a meta-analysis of studies evaluating the association between blood levels of specific environmental pollutants and health outcomes (binary). Some studies reported OR/RR/HR for ...

logistic data-transformation meta-analysis logarithm  
user avatar asked by msas Score of 1
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