[Blindmath] statistical formulas

[Arielle Silverman]

Thanks Jonathan. I wonder if anyone has worked on scripting JAWS or
its competitors to read Greek letters?
Arielle

On 10/23/12, Jonathan Godfrey <a.j.godfrey at massey.ac.nz> wrote:
> Hi all,
>
> I've decided to jump in here as I've spotted a small (but crucial) error in
> the contributions given thus far. I'd also point out that the lecturing
> staff at most universities now have the ability to put Greek and formula
> into the text of email message in the same way they do in word documents.
> They won't be readable either if done that way.
>
>
>
> Correlation is the covariance divided by the square root of the variances.
> For a population, the variance is
>
> Var(x) = Sum[(x-mu)^2]/n
>
> where n is the population size and mu is the population mean. Note that
> sum[] means to sum over all observations.
>
> Expanding that out so that there is no squaring going on would give:
>
> Var(x) = Sum[(x-mu)(x-mu)]/n
>
> If you don't do the division by n then this is the sum of squares sometimes
> shortened to SS, or to denote the variable x, S_xx
>
>
> A covariance is found using:
>
> Cov(x,y) = Sum[(x-mu_x)(y-mu_y)]/n
>
> Where the mu is relevant to either the x or y and therefore gets given the
> subscripts.
>
>
>
> The reduction to alternate forms comes because the cross product S_xy is
> the
> numerator of the covariance. This means we can write the correlation as:
>
> Cor(x,y) = Cov(x,y)/sqrt[Var(x)Var(y)]
> Or
> Cor(x,y) = S_xy / sqrt[S_xx S_yy]
>
> Another notation uses the fact that the square root of the variance is the
> standard deviation. This means that we see the correlation expressed as the
> covariance divided by the product of the standard deviations.
>
> Mathematically it's all the same. The expression using the cross products
> (sum of squares) working is equally useful for samples and populations.
> Remember that the division is by (n-1) for samples for both covariances and
> variances.
>
>
> Hope this helps.
>
> Jonathan
>
>
>
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