Let's say we have the following data:
$-1.8, -0.82, 0.3, 1.2, 1.6$
Now I want to make a qq-plot out of it by hand, just with a calculator (Casio fc 991).
I start by sorting the values in ranks j and calculate how many observations are less than or equal to $x(j)$ by $j* = \frac{j-0.5}n$.
This brings us following values $j*$:
$0.1, 0.3, 0.5, 0.7, 0.9$
These are my sample quantiles, right? To get my qq-plot I now want to plot these against the theoretical quantiles. But here I stuck.
The theoretical quantiles are: $-1.28, -0.52, 0.00, 0.52, 1.28$
But how do I calculate these values without R or any software but just with a calculator?
I got the following formula: $(\phi^{-1})(j*)$ but I simply do not understand how I should come up with those values.
Cheers and thanks for your effort!