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You can't simply average means of subsets if these subsets have different numbers of elements. As a simple example, suppose one subset consists of the smallest element alone, and the other subset contains all other elements. If you then average these subsets' means, the smallest element will get the same weight as all other elements together. The solution ...


2

Why not just look it up a T Table or just punch the numbers in excel? I get the elaborate explanation above and good job at it but feels a bit overkill. In excel you can use T.INV. Just that you need degrees of freedom (which for the t distribution is n-1) for the second argument in T.INV(). And then just adjust based on what test it was upper, lower, two ...


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Standardised effect sizes scale the difference between groups by the variance within each group. Cohen's $d$ is probably the simplest and most widely used. Cohen's $d$ is also sometimes called the 'standardised mean difference'. To calculate it simply divide the difference in means between the groups by the pooled standard deviation estimated within the ...


1

A good but complicated way to find out if the data point is outlier or not is to conduct a diagnostic for leverage and influence of this point. Some examples and explanation can be found here: https://online.stat.psu.edu/stat462/node/87/


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This really comes down to an issue of "dimensionality". Imagine that each of the five "difference" values is a vector (i.e., a line pointing positively or negatively with length equal to the difference value). Geometrically, the mean (of) difference value is obtained by putting these vectors end-to-end in a single dimension, to get the aggregate difference,...


1

Not that I know of, but there's a related concept: the Nonparametric skew. Let $\mu$ be the mean $\sigma$ the standard deviation and $\nu$ the median. The Nonparametric skew is $$S = \frac{\mu-\nu}{\sigma}$$ Yours is $$S^* = \mu/\nu=(S \sigma + \nu)/\nu=S\sigma/\nu+1$$ And also $$S = (S^*-1)/(\sigma\nu)$$


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