Importance of homogenity of variance

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In summary, the homogeneity of variances is important in parametric statistical tests, such as t tests and ANOVA, because the formulas and distributions of estimates and test statistics are based on this assumption. Without homogeneity of variances, the results of these tests may not be reliable. This is especially important in cases where there are more than two samples, such as in ANOVA.
  • #1
thrillhouse86
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Hey all,

When performing parametric statistical tests (especially t tests and ANOVA), why is the homogenity of variance important ?

I mean why do these tests care if the samples have significantly different variance ? Is it because the methods used to determine the test statistics require the same variances, or to interpret the results of these test statistics you need to assume the same variance for samples ?

Regards,
Thrillhouse
 
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  • #2
The formulas for the estimates, margins of error, and distributions of estimates and test statistics are based on the homogeneity of variances. Think about the two-sample mean problem, when we assume normality but different variances. The t-statistic is still used, with an awkward formula for df, but that's just an empirical approximation. things are more involved for more than two samples (ANOVA setting). same idea for regression.
 
  • #3
Thanks Statdad
 

What is homogeneity of variance?

Homogeneity of variance, also known as homoscedasticity, refers to the assumption that the variability of scores in a population is equal across different groups or conditions. In other words, the variance of scores is consistent and does not differ significantly between groups.

Why is homogeneity of variance important?

Homogeneity of variance is important because it is a crucial assumption in many statistical tests, such as t-tests and ANOVA. Violation of this assumption can lead to incorrect conclusions and inflated Type I error rates. Ensuring homogeneity of variance allows for more accurate and reliable results.

How can homogeneity of variance be assessed?

There are several methods for assessing homogeneity of variance, including visual inspection of data plots, Levene's test, and Bartlett's test. These tests compare the variances of scores between groups and determine if there is a significant difference. Additionally, the use of Box-Cox transformations can also be used to address issues with heteroscedasticity.

What are the consequences of violating the assumption of homogeneity of variance?

Violating the assumption of homogeneity of variance can lead to biased results and incorrect conclusions. When the variances between groups are significantly different, it can affect the accuracy and reliability of statistical tests. It can also lead to increased Type I error rates, which means the likelihood of falsely rejecting the null hypothesis.

How can homogeneity of variance be achieved?

There are a few ways to achieve homogeneity of variance, including using equal sample sizes in each group, using random assignment to groups, and using statistical techniques such as Welch's t-test or the Brown-Forsythe test, which do not require equal variances. Additionally, data transformations can also be used to achieve homogeneity of variance in some cases.

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