Alexis
  • Member for 7 years, 9 months
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Is the COVID-19 pandemic curve a Gaussian curve?
75 votes

No. For example: Not in the sense of a Gaussian probability distribution: the bell-curve of a normal (Gaussian) distribution is a histogram (a map of probability density against values of a single ...

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Why does frequentist hypothesis testing become biased towards rejecting the null hypothesis with sufficiently large samples?
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49 votes

Answer to question 1: This occurs because the $p$-value becomes arbitrarily small as the sample size increases in frequentist tests for difference (i.e. tests with a null hypothesis of no difference/...

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What are some of the most common misconceptions about linear regression?
42 votes

False premise: A $\boldsymbol{\hat{\beta} \approx 0}$ means that there is no strong relationship between DV and IV.Non-linear functional relationships abound, and yet data produced by many such ...

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Assumptions of linear models and what to do if the residuals are not normally distributed
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41 votes

First off, I would get yourself a copy of this classic and approachable article and read it: Anscombe FJ. (1973) Graphs in statistical analysis The American Statistician. 27:17–21. On to your ...

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What's the difference between the variance and the mean squared error?
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32 votes

The mean squared error as you have written it for OLS is hiding something: $$\frac{\sum_{i}^{n}(y_i - \hat{y}_i) ^2}{n-2} = \frac{\sum_{i}^{n}\left[y_i - \left(\hat{\beta}_{0} + \hat{\beta}_{x}x_{i}\...

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What is the relationship between $Y$ and $X$ in this plot?
32 votes

Let's have some fun! First of all, I scraped the data off your graph. Then I used a running line smoother to produce the black regression line below with the dashed 95% CI bands in gray. The graph ...

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Post-hoc tests after Kruskal-Wallis: Dunn's test or Bonferroni corrected Mann-Whitney tests?
26 votes

You should use a proper post hoc pairwise test like Dunn's test.* If one proceeds by moving from a rejection of Kruskal-Wallis to performing ordinary pair-wise rank sum tests (with or without multiple ...

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Why do we need to dummy code categorical variables
26 votes

Suppose your four categories are eye colors (code): brown (1), blue (2), green (3), hazel (4)—ignoring heterochromia, violet, red, gray, etc. for the moment. In no way (that I can currently imagine) ...

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When should we discretize/bin continuous independent variables/features and when should not?
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26 votes

Aggregation is substantively meaningful (whether or not the researcher is aware of that). One should bin data, including independent variables, based on the data itself when one wants: To ...

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Why are hypothesis tests still used when we have the bootstrap and central limit theorem?
25 votes

Hypothesis tests are still used because they are motivated by a different need in statistical inference than interval estimators are motivated by. The purpose of a hypothesis test is to make a ...

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Understanding shape and calculation of confidence bands in linear regression
25 votes

The standard error of the regression line at point $X$ (i.e. $s_{\widehat{Y}_{X}}$) is hand calculated (Yech!) using: $s_{\widehat{Y}_{X}} = s_{Y|X}\sqrt{\frac{1}{n}+\frac{\left(X-\overline{X}\right)^{...

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Backward selection for Cox model using R
22 votes

I would recommend not performing stepwise model building, unless you are looking for biased (inflated) coefficients, biased (deflated) p-values, and inflated model fit statistics. The fundamental ...

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Are all continuous random variables normally distributed?
22 votes

No. There are many continuous probability distributions out of all the probability distributions. There are whole books containing nothing but such things. Some of the non-normal continuous ...

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How to fill in missing data in time series?
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20 votes

The answer will depend on your study design (e.g., cross-sectional time series? cohort time series, serial cohorts time series?). Honaker and King have developed an approach that is useful for cross-...

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Frequentist perspective of regression coefficients and significance (coming from Bayesian background)?
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19 votes

A p value is the probability of observing a test statistic as or more extreme than the researcher's own test statistic, assuming the null hypothesis, and an assumed distribution model are both true. ...

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Why is the sum of probabilities in a continuous uniform distribution not infinity?
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19 votes

$f(x)$ describes the probability density rather than a probability mass in your example. In general, for continuous distributions the events—the things we get probabilities for—are ranges of values, ...

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How to read the results of Dunn's test?
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19 votes

The output following the Kruskal-Wallis test provides all possible pairwise comparisons (six in the case of four groups). So the one on the first row compares group B with group A, the first on the ...

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Is Fisher's LSD as bad as they say it is?
19 votes

How important are multiple comparisons when dealing with 6 groups? Well... with six groups you are dealing with a maximum of $\frac{6(6-1)}{2} = 15$ possible post hoc pairwise comparisons. I will let ...

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Is a spline interpolation considered to be a nonparametric model?
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17 votes

This is a good question. Frequently, one will see smoothing regressions (e.g., splines, but also smoothing GAMs, running lines, LOWESS, etc.) described as nonparametric regression models. These models ...

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Can a instrument variable equation be written as a directed acyclic graph (DAG)?
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16 votes

Yes. For example in the DAG below, the instrumental variable $Z$ causes $X$, while the effect of $X$ on $O$ is confounded by unmeasured variable $U$. The instrumental variable model for this DAG ...

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Can Mann-Whitney test be used for post-hoc comparisons after Kruskal-Wallis?
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16 votes

No, you should not use the Mann-Whitney $U$ test in this circumstance. Here's why: Dunn's test is an appropriate post hoc test* following rejection of a Kruskal-Wallis test. If one proceeds by moving ...

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What is the difference between various Kruskal-Wallis post-hoc tests?
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15 votes

Understanding how these test implementations differ requires understanding the actual test statistics themselves. For example, dunn.test provides Dunn's (1964) z test approximation to a rank sum test ...

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Examples for Type I and Type II errors
15 votes

A picture is worth a thousand words. Null hypothesis: patient is not pregnant. Image via Paul Ellis.

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False discovery rate of multiple regressions models
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15 votes

@Dian breathe easy, it's pretty much not too difficult. So let's work from familiar territory to false discovery rate (FDR). First, I see that you have a bunch of outcomes, with a varying number of ...

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Three questions about the article "Ditch p-values. Use Bootstrap confidence intervals instead"
13 votes

The author of the article suffers from not understanding that hypothesis tests and confidence intervals serve different inferential purposes: The confidence interval (bootstrap or otherwise) serves ...

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Investigating interaction
13 votes

It sounds like you desire to perform stepwise model building. I suggest you not do this. Here's why: Your $p$-values no longer mean “the probability of observing the test statistic given the null ...

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Are pairwise Wilcoxon tests a valid non-parametric alternative to Tukey's HSD test?
13 votes

No, it is not a valid nonparametric alternative. The rank sum test (either original Wilcoxon flavor, or New Improved Mann-Whitney $U$ varieties): ignore the rankings used by the Kruskal-Wallis test, ...

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What does "curvilinear" mean?
13 votes

"Nonlinear" has many meanings, only some of which are (directly) about curves. I would say that I have encountered "curvilinear" to mean smooth curves. So a parabola or a logarithmic curve are "...

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Which stats tests to use? Bee flight activity quantified during an eclipse
12 votes

Here is a graph of the two days' data (Day 1, gold line with black markers, Day 2 black line with gold markers; I coded time in terms of minutes elapsed since the first measurement of the day): The ...

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Why not use instrumental variable directly as a covariate in the regression?
12 votes

The point of instrumental variable regression is to provide an unbiased estimate of the causal effect of exposure $X$ on outcome $O$, when there is some unmeasured—possibly unmeasureable—variable $U$ ...

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