# Confusion about normal probability plots

Gold Member
The expositions for a normal probability plot (aka normal quantile plot) (in which observed probabilities are plotted against theoretical probabilities, or sometimes the other way around, to get a rough check as to whether a set of data is normally distributed by checking linearity) are not too clear (to me).
To make this easy to answer, I will put my doubts into four succinct questions:
First, which one standardly goes on the vertical axis: the observed or theoretical values?
Secondly, does one put probabilities, or the values, on the axes? If probabilities, are the observed probabilities just calculated as per a frequency table?
Thirdly (and this depends on the answer to the previous question), are the scales linear, a concatenation of logarithmic scales, or what?
Fourthly, how does one calculate the theoretical value that goes to a given observed value?
Thanks for answering any (or all) of these.

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Simon Bridge
Homework Helper
http://analyse-it.com/blog/2008/11/normal-quantile-probability-plots
First, which one standardly goes on the vertical axis: the observed or theoretical values?
Doesn't matter. I haven't heard of a standard. Use the one that makes the math easiest.

Secondly, does one put probabilities, or the values, on the axes? If probabilities, are the observed probabilities just calculated as per a frequency table?
All the ones I've seen are from frequency data.
The idea is to use the theoretical distribution to generate a theoretical data set which you compare with the actual data set. So you use whatever the data says it is.

Thirdly (and this depends on the answer to the previous question), are the scales linear, a concatenation of logarithmic scales, or what?
They are usually linear.

Fourthly, how does one calculate the theoretical value that goes to a given observed value?
You use the theory of probabilities. You know how a normal distribution works right?

Gold Member
Thanks, Stephen Bridge. So, following your answers and the link you sent, I would proceed as follows:
put the observed values on one axis (say, the horizontal one)
Then for each observed value v, I find Prob(X< v), and plot that on the other axis.
Right?

Gold Member
Thanks, Stephen Bridge. So, following your answers and the link you sent, I would proceed as follows:
put the observed values on one axis :say, the horizontal one.
Then for each observed value v, I find Prob(X< v) from the normal curve, and plot (v, Prob(X< v)) .
Right?

Gold Member
Thanks, of course I would calculate the z-score in order to find the probability, but I don't think you mean that the points are (v, z-score of v), because that will always give you a straight line
y=(1/σ)x - (μ/σ),
regardless of whether your data is normally distributed or not.

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