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Why assume population variances are equal?
In situations when we do not know the population variances but assume the variances are the same, the pooled sample variance will be smaller than the individual sample variances. This will give more precise estimates and reduce the probability of discarding a good null.
What is equal to variance?
Equal variances (homoscedasticity) is when the variances are approximately the same across the samples. 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.
Why variance is squared?
The calculation of variance uses squares because it weighs outliers more heavily than data closer to the mean. This calculation also prevents differences above the mean from canceling out those below, which would result in a variance of zero.
What does the variance formula tell us?
The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean. Variance tells you the degree of spread in your data set. The more spread the data, the larger the variance is in relation to the mean.
Which is the correct formula for the variance?
The main formula of variance is consistent with these requirements because it sums over squared differences between each value and the mean. If all values are equal to some constant c, the mean will be equal to c as well and all squared differences will be equal to 0 (hence the variance will be 0).
Why is it important to know the variance of a sample?
Variance is important to consider before performing parametric tests. These tests require equal or similar variances, also called homogeneity of variance or homoscedasticity, when comparing different samples. Uneven variances between samples result in biased and skewed test results.
What happens to the variance if the mean is zero?
Well, if the mean is zero, by definition and the alternative formula reduces to: Actually, the main formula would reduce to the same thing as well but the point is that, if the mean is 0, the variance simply measures the expected squared deviations from 0. The farther apart the values are from 0, the bigger their spread.
Why is variance important in a parametric test?
Variance matters for two main reasons: Parametric statistical tests are sensitive to variance. Comparing the variance of samples helps you assess group differences. Homogeneity of variance in statistical tests