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What does it means if the standard deviation is large?
that you have a large variance in the population and/or your sample size is too small
Is sigma square equal to variance?
Yes, sigma squared (σ²) represents the variance of a population in statistics. Variance measures the dispersion of a set of values around their mean, and it is calculated as the average of the squared differences from the mean. In summary, σ² is simply the symbol used to denote variance in statistical formulas.
How do you prove that the sample variance is equal to the population variance?
You cannot prove it because it is not true.The expected value of the sample variance is the population variance but that is not the same as the two measures being the same.
What does n-1 indicate in a calculation for variance?
The n-1 indicates that the calculation is being expanded from a sample of a population to the entire population. Bessel's correction(the use of n − 1 instead of n in the formula) is where n is the number of observations in a sample: it corrects the bias in the estimation of the population variance, and some (but not all) of the bias in the estimation of the population standard deviation. That is, when estimating the population variance and standard deviation from a sample when the population mean is unknown, the sample variance is a biased estimator of the population variance, and systematically underestimates it.
When the null hypothesis is true the ratio of the between groups population variance estimate to the within groups population variance estimate should be about?
1
