After z-score transform, shape of distribution changes?

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by cperdue » Wed Feb 19, 2020 3:12 am

I was doing a tutorial on jamovi in my undergrad statistics class, and was showing my students how to use the Compute option to create a new variable. I used the Z function to turn an existing variable into a new column of z-scores.

I ran Descriptives on the new z-scores to remind the students that they now had a mean of zero and an SD of one, and as a further demo I requested a histogram to illustrate that the shape of the distribution was unchanged from the original data.

Except... the new histogram HAD changed from the original shape. The original was a normal distribution, but the new histogram of z-scores appeared to be positively skewed. I tried this with other data sets, and got the same result: the histogram of z-scores appeared to be a different shape than for the original data.

i'm not sure if I'm missing something obvious here... Any ideas?
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by jonathon » Wed Feb 19, 2020 6:57 am

hi,

i just took a look at this and went "Wowsers, what have we done wrong here?!" ... but its all correct, and what looks to be a change in distribution, is just an artifact of histogram binning. if you turn on the density plot, you'll see that it's unchanged.

cheers

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by cperdue » Wed Feb 19, 2020 2:15 pm

Still, it's disconcerting to see a variable known to be perfectly normally distributed (skewness = zero) graphically displayed as if it were skewed.... I'm always uncomfortable in situations where I have to tell my students to "ignore that part of the output" or not to request it at all.

Otherwise, my first semester of using jamovi with my stats class has been very successful.
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by jonathon » Wed Feb 19, 2020 2:49 pm

Still, it's disconcerting to see a variable known to be perfectly normally distributed (skewness = zero) graphically displayed as if it were skewed....


yup, that's just how histograms behave unfortunately.

if you change their range of values, the start and end points will change too, which in turn changes their shape.

the density curve is a more honest indicator of a distribution than a histogram imho (perfect illustration here).

cheers

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