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Both CIBASIC and CIQUANTNORMAL (unlike CIQUANTDF) calculate confidence intervals based on the assumption that the data are normally distributed. Since mean and median (=50% quantile) of a normal distribution coincide, a confidence interval (CI) for the mean is also a CI for the median.
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ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. Watch this tutorial for more.