# Questions tagged [heteroscedasticity]

Non-constant variance along some continuum in a random process, or varying between discrete groups

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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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### 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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### What does the notation like 8.6e-28 mean? What is the 'e' for?

I have a problem with the interpretation of a test result in which the p-value is 8.6e-28. How should it be interpreted? What is the ...
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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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### 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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### Unequal variance in randomized experiments to compare treatment with control?

Consider a randomized experiment to compare (one or more) treatment(s) with a control. Since groups are defined by random assignment, we should expect equal variances for a null-experiment (that is, ...
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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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### 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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### 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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### 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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### Does homoscedasticity imply that the regressor variables and the errors are uncorrelated?

By OLS regression equation: $$Y = a + bX + e$$ My thoughts are that homoscedasticity by definition imply that $Var(Y|X) = Var(e|X)=$ constant, then this would imply that $Var(e|X) = Var(e)$ which ...
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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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### 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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### 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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### heteroskedasticity and logistic regression

I have cross sectional data and am using logistic regression. My question is how do I check my data for heteroskedasticity and in case it is present, then how to deal with it in Stata. I have come ...
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### Questions on standard deviation of a time series

If the standard deviation of a economic time series is approximately proportional to its level, that is, the standard deviation is well expressed as a percentage of the level of the series, then 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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### 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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### 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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### 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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### 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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### Simulate linear regression with heteroscedasticity

I am trying to simulate a dataset that matches empirical data that I have, but am unsure how to estimate the errors in the original data. The empirical data includes heteroscedasticity, but I am not ...
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### Resolving heteroscedasticity in Poisson GLMM

I have long-term collection data, and I'd like to test, whether the number of animals collected is influenced by weather effects. My model looks like below: ...
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### Accounting for heteroskedasticity in lme linear mixed model?

I have a data set where I measured the number of molecules (M) present in cells as a function of drug (with or without) and days of treatment (5 timepoints). I repeated the experiment 3 times, with ...
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### Kruskal-Wallis or Fligner test to check homogeneity of variances?

I need to check the homogeneity of variances on the residuals of a linear regression. I read that Kruskal is also good without assuming a normal-distribution. But I don't know if it's good in my case. ...
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### Efficiency of beta estimates with heteroscedasticity

I need something clarified and that is when you have non-constant variance, estimates won't be biased but will be a problem when it comes to the S.E. formulas and efficiency. Therefore OLS estimates ...
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### What are the assumptions of a Gamma GLM or GLMM for hypothesis testing?

What are the assumptions when doing hypothesis testing using a Gamma GLM or GLMM? Are the residuals suppose to be normally distributed and is heteroscedasticity a concern like the Gaussian (normal) ...
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### Mann Whitney test with unequal variances [duplicate]

I am confused on what I have read about the Mann whitney test. We are testing whether our actual data is the same as our projected data. We had been using the t-test until we realized the data might ...
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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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### 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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### 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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### Spearman's or Pearson's correlation with Likert scales where linearity and homoscedasticity may be violated

I am wanting to run correlations on a number of measurements where Likert scales were used. Looking at the scatterplots it appears the assumptions of linearity and homoscedasticity may have been ...
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### When to use (non)parametric test of homoscedasticity assumption?

If one is testing assumption of homoscedasticity, parametric (Bartlett Test of Homogeneity of Variances, bartlett.test) and non-parametric (Figner-Killeen Test of ...
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### Advice on explaining heterogeneity / heteroscedasticty

I am looking for any help, advice or tips in how to explain heterogeneity / heteroscedasticity to biologists in my department. In particular I want to explain why its important to look for it and deal ...
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### Conditionally heteroskedastic linear regression: How can I model variance from given predictors?

As a motivating example, consider this hypothesis: A friend and I were discussing how it might be the case that, the more one person is given control in the process of making a movie, the higher the ...
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### Breusch–Pagan test for heteroscedasticity contradicts White's test?

Testing for heteroscedasticity I get these results: Breusch–Pagan / Cook–Weisberg test for heteroskedasticity $H_0$: Constant variance $H_a$: Heteroskedasticity ...
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### Why is homogeneity of variance so important?

I do not know why testing homogeneity of variance is so important. What are the examples that require homogeneity of variance?
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### Weighted normal errors regression with censoring

I have some data which I would model via standard multiple regression except: There is censoring (left-censored, fixed but varying censoring points which are known) The errors are assumed independent ...
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### How to get ANOVA table with robust standard errors?

I am running a pooled OLS regression using the plm package in R. Though, my question is more about basic statistics, so I try posting it here first ;) Since my regression results yield ...
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### What is the difference between these two Breusch-Pagan Tests?

Using R on some data and trying to see whether or not my data is heteroscedastic, I've found two implementations of the Breusch-Pagan test, bptest (package lmtest) and ncvTest (package car). However, ...
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### Homoscedasticity Assumption in Linear Regression vs. Concept of Studentized Residuals

Having read about studentized residuals I do not understand how the idea of different residual variances conditional on certain values of a predictor $X$ (as implied by the concept of studentized ...
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### Heteroskedasticity - residual plot interpretation

I am plotting a residual plot to test for heteroskedasticity. The Breusch-Pagan test is significant and therefore I am suspecting there is evidence on heteroskedasticity. The question is: (a) How ...
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### How can you test homogeneity of variance of two groups with different sample sizes?

I have two groups of data that have different sample sizes and in order to be able to analyze both sets they must have the same variance. I was told I should use Bartlett's to test the homogeneity of ...
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### Linear regression with changing variance

I want to perform linear regression on some data. For every value of x, the data values are distributed normally across y, around some mean. However, the variance increases linearly as x increases. I ...
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### Prediction Intervals with Heteroscedasticity

I am using R to perform linear regression. I have seen ways to calculate prediction intervals, but these depend on homoscedastic data. Is there a way to calculate prediction intervals with ...
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### Terminology: unconditional heteroskedasticity

I have seen mentions of both unconditional and conditional heteroskedasticity. The latter is fine with me but I am struggling to uderstand the former. It appears I am not the only one to question ...
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### Parallel straight Lines on Residuals vs. Predicted Values Plot

In a data set I have, all of the results of the residual vs. predicted values appear as parallel lines as pictured below. I interpret this according to my training as a violation of homoscedasticity ...
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### What to do with non-normality and heterogeneous variances in two-way ANOVA when transformations do not work?

I'm conducting a Two-Way ANOVA with my two factors being Sex and Cohort. I have data from two cohorts of subjects, with each cohort consisting of males and females that were measured on one response ...
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### How to handle bounded [0,1] dependent variable that causes one to fail heteroscedasticity

In my particular situation, our outcome variable is recall (bounded between 0 and 1 inclusive), and we are building a linear mixed effects model in R. We end up with a qq plot like the one below: Is ...
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