# Questions tagged [heteroscedasticity]

Non-constant variance along some continuum in a random process.

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### What does having "constant variance" in a linear regression model mean?

What does having "constant variance" in the error term mean? As I see it, we have a data with one dependent variable and one independent variable. Constant variance is one of the assumptions of linear ...
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### Alternatives to one-way ANOVA for heteroskedastic data

I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population. One-...
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### When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?

It seems like when the assumption of homogeneity of variance is met that the results from a Welch adjusted t-test and a standard t-test are approximately the same. Why not simply always use the Welch ...
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### Why are there two spellings of "heteroskedastic" or "heteroscedastic"?

I frequently see both the spellings "heteroskedastic" and "heteroscedastic", and similarly for "homoscedastic" and "homoskedastic". There seems to be no difference in meaning between the "c" and the "...
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### What are the dangers of violating the homoscedasticity assumption for linear regression?

As an example, consider the ChickWeight data set in R. The variance obviously grows over time, so if I use a simple linear regression like: ...
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### How do you find weights for weighted least squares regression?

I am a bit lost in the process of WLS regression. I have been given dataset and my task is to test whether there is heteroscedascity, and if so I should run WLS regression. I have carried out the ...
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### Sandwich estimator intuition

Wikipedia and the R sandwich package vignette give good information about the assumptions supporting OLS coefficient standard errors and the mathematical background of the sandwich estimators. I'm ...
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### Practically speaking, how do people handle ANOVA when the data doesn't quite meet assumptions?

This isn't a strictly stats question--I can read all the textbooks about ANOVA assumptions--I'm trying to figure out how actual working analysts handle data that doesn't quite meet the assumptions. I'...
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### Best way to deal with heteroscedasticity?

I have a plot of residual values of a linear model in function of the fitted values where the heteroscedasticity is very clear. However I'm not sure how I should proceed now because as far as I ...
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### Regression modelling with unequal variance

I would like to fit a linear model (lm) where the residuals variance is clearly dependent on the explanatory variable. The way I know to do this is by using glm with the Gamma family to model the ...
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### Always Report Robust (White) Standard Errors?

It has been suggested by Angrist and Pischke that Robust (i.e. robust to heteroskedasticity or unequal variances) Standard Errors are reported as a matter of course rather than testing for it. Two ...
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### Why Levene test of equality of variances rather than F ratio?

SPSS uses the Levene test to evaluate homogeneity of variances in the independent group t-test procedure. Why is the Levene test better than a simple F ratio of the ratio of the variances of the ...
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### Transforming proportion data: when arcsin square root is not enough

Is there a (stronger?) alternative to the arcsin square root transformation for percentage/proportion data? In the data set I'm working on at the moment, marked heteroscedasticity remains after I ...
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### How to run two-way ANOVA on data with neither normality nor equality of variance in R?

I am working on my master thesis at the moment and planned on running the statistics with SigmaPlot. However, after spending some time with my data I came to the conclusion that SigmaPlot might not be ...
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### How to perform residual analysis for binary/dichotomous independent predictors in linear regression?

I am performing the multiple linear regression below in R to predict returns on fund managed. reg <- lm(formula=RET~GRI+SAT+MBA+AGE+TEN, data=rawdata) Here ...
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### Checking ANOVA assumptions

A few months ago I posted a question about homoscedasticity tests in R on SO, and Ian Fellows answered that (I'll paraphrase his answer very loosely): Homoscedasticity tests are not a good tool ...
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### How do I interpret this fitted vs residuals plot?

I don't really understand heteroscedasticity. I would like to know whether my model is appropriate or not according to this plot.
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### Measures of residuals heteroscedasticity

This wikipedia link lists a number of techniques to detect OLS residuals heteroscedasticity. I would like to learn which hands-on technique is more efficient in detecting regions affected by ...
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### Is bootstrapping standard errors and confidence intervals appropriate in regressions where homoscedasticity assumption is violated?

If in standard OLS regressions two assumptions are violated (normal distribution of errors, homoscedasticity), is bootstrapping standard errors and confidence intervals an appropriate alternative to ...
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### Explanation for non-integer degrees of freedom in t test with unequal variances

The SPSS t-Test procedure reports 2 analyses when comparing 2 independent means, one analysis with equal variances assumed and one with equal variances not assumed. The degrees of freedom (df) when ...
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### MLE vs least squares in fitting probability distributions

The impression that I got, based on several papers, books and articles that I've read, is that the recommended way of fitting a probability distribution on a set of data is by using maximum likelihood ...
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### Comparison between Newey-West (1987) and Hansen-Hodrick (1980)

Question: What are the main differences and similarities between using Newey-West (1987) and Hansen-Hodrick (1980) standard errors? In which situations should one of these be preferred over the other? ...
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### Alternative to One-way ANOVA unequal variance

I would like to compare the means across three groups of equal sizes (equal sample size is small, 21). The means of each group are normally distributed, but their variances are unequal (tested via ...
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### Why does sphericity diagnosed by Bartlett's Test mean a PCA is inappropriate?

I understand that Bartlett's Test is concerned with determining if your samples are from populations with equal variances. If the samples are from populations with equal variances, then we fail to ...
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### Visualizing many left-skewed distributions

I have a series of left-skewed/heavy tailed distributions that I would like to show. There are 42 distributions across three factors (labeled as A, ...
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