What does equal variance mean in t-test?
What does equal variance mean in t-test?
When running a two-sample equal-variance t-test, the basic assumptions are that the distributions of the two populations are normal, and that the variances of the two distributions are the same.
How do you know if you have equal variance?
If the variances are relatively equal, that is one sample variance is no larger than twice the size of the other, then you can assume equal variances.
Why is it important to have equal variances?
It is important because it is a formal requirement for statistical analyses such as ANOVA or the Student’s t-test. The unequal variance doesn’t have much impact on ANOVA if the data sets have equal sample sizes.
How do you know if variance is equal or UNequal?
There are two ways to do so:
- Use the Variance Rule of Thumb. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4 then we can assume the variances are approximately equal and use the Student’s t-test.
- Perform an F-test.
How do you test for UNequal variances?
How the unequal variance t test is computed
- Calculation of the standard error of the difference between means. The t ratio is computed by dividing the difference between the two sample means by the standard error of the difference between the two means.
- Calculation of the df.
What is Levene’s test used for?
Levene’s test ( Levene 1960) is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The Levene test can be used to verify that assumption.
What does it mean to have unequal variance?
For the unequal variance t test, the null hypothesis is that the two population means are the same but the two population variances may differ. The unequal variance t test reports a confidence interval for the difference between two means that is usable even if the standard deviations differ.
What does it mean when variances are not equal?
Unequal variances (heteroscedasticity) can affect the Type I error rate and lead to false positives. If you are comparing two or more sample means, as in the 2-Sample t-test and ANOVA, a significantly different variance could overshadow the differences between means and lead to incorrect conclusions.
What is an equal variance assumption?
The assumption of equal variances (i.e. assumption of homoscedasticity ) assumes that different samples have the same variance, even if they came from different populations. The assumption is found in many statistical tests, including Analysis of Variance (ANOVA) and Student’s T-Test.
What does it mean for variances to be equal?
Statistical tests, such as analysis of variance ( ANOVA ), assume that although different samples can come from populations with different means, they have the same variance. Equal variances (homoscedasticity) is when the variances are approximately the same across the samples.
What is equality of variance?
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance. Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations,…
What is a variance test?
Variance Tests. The variance of a data set is the standard deviation squared (σ2). The F Test and Bartlett’s test compare the variance between sample sets to determine if they are statistically different.