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 ...

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/...

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 ...

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 ...

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}\...

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 ...

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 ...

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) ...

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 ...

The standard error of the regression line at point $X$ (i.e. $s_{\widehat{Y}_{X}}$) is hand calculated (Yech!) using: $s_{\widehat{Y}_{X}} = s_{Y|X}\sqrt{\frac{1}{n}+\frac{\left(X-\overline{X}\right)^{... View answer 22 votes I would recommend not performing stepwise model building, unless you are looking for biased (inflated) coefficients, biased (deflated) p-values, and inflated model fit statistics. The fundamental ... View answer 22 votes No. There are many continuous probability distributions out of all the probability distributions. There are whole books containing nothing but such things. Some of the non-normal continuous ... View answer Accepted answer 20 votes The answer will depend on your study design (e.g., cross-sectional time series? cohort time series, serial cohorts time series?). Honaker and King have developed an approach that is useful for cross-... View answer Accepted answer 19 votes A p value is the probability of observing a test statistic as or more extreme than the researcher's own test statistic, assuming the null hypothesis, and an assumed distribution model are both true. ... View answer Accepted answer 19 votes$f(x)$describes the probability density rather than a probability mass in your example. In general, for continuous distributions the events—the things we get probabilities for—are ranges of values, ... View answer Accepted answer 19 votes The output following the Kruskal-Wallis test provides all possible pairwise comparisons (six in the case of four groups). So the one on the first row compares group B with group A, the first on the ... View answer 19 votes How important are multiple comparisons when dealing with 6 groups? Well... with six groups you are dealing with a maximum of$\frac{6(6-1)}{2} = 15$possible post hoc pairwise comparisons. I will let ... View answer Accepted answer 17 votes This is a good question. Frequently, one will see smoothing regressions (e.g., splines, but also smoothing GAMs, running lines, LOWESS, etc.) described as nonparametric regression models. These models ... View answer Accepted answer 16 votes Yes. For example in the DAG below, the instrumental variable$Z$causes$X$, while the effect of$X$on$O$is confounded by unmeasured variable$U$. The instrumental variable model for this DAG ... View answer Accepted answer 16 votes No, you should not use the Mann-Whitney$U$test in this circumstance. Here's why: Dunn's test is an appropriate post hoc test* following rejection of a Kruskal-Wallis test. If one proceeds by moving ... View answer Accepted answer 15 votes Understanding how these test implementations differ requires understanding the actual test statistics themselves. For example, dunn.test provides Dunn's (1964) z test approximation to a rank sum test ... View answer 15 votes A picture is worth a thousand words. Null hypothesis: patient is not pregnant. Image via Paul Ellis. View answer Accepted answer 15 votes @Dian breathe easy, it's pretty much not too difficult. So let's work from familiar territory to false discovery rate (FDR). First, I see that you have a bunch of outcomes, with a varying number of ... View answer 13 votes The author of the article suffers from not understanding that hypothesis tests and confidence intervals serve different inferential purposes: The confidence interval (bootstrap or otherwise) serves ... View answer 13 votes It sounds like you desire to perform stepwise model building. I suggest you not do this. Here's why: Your$p$-values no longer mean “the probability of observing the test statistic given the null ... View answer 13 votes No, it is not a valid nonparametric alternative. The rank sum test (either original Wilcoxon flavor, or New Improved Mann-Whitney$U$varieties): ignore the rankings used by the Kruskal-Wallis test, ... View answer 13 votes "Nonlinear" has many meanings, only some of which are (directly) about curves. I would say that I have encountered "curvilinear" to mean smooth curves. So a parabola or a logarithmic curve are "... View answer 12 votes Here is a graph of the two days' data (Day 1, gold line with black markers, Day 2 black line with gold markers; I coded time in terms of minutes elapsed since the first measurement of the day): The ... View answer 12 votes The point of instrumental variable regression is to provide an unbiased estimate of the causal effect of exposure$X$on outcome$O$, when there is some unmeasured—possibly unmeasureable—variable$U\$ ...