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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!

Plus Twenty
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Marl
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  • Maybe your calculator is like the one in this video. Your formula requires $\Phi^{-1}(j^)$, which is the inverse of the standard normal CDF, evaluated at argument $j^$. (This is the value $z$ such that $j^$ is the area below $z$ under a standard normal density, which has mean $0$ and standard deviation $1$.) The video shows how to compute this with a Casio fx-991EX, by using the appropriate inputs (i.e., in your case the mean & standard deviation are input as $\mu=0$ and $\sigma=1$, respectively, and the value of $j^$ is input as the "Area". – r.e.s. Jun 12 '19 at 00:55
  • Thank you so much! It works! – Marl Jun 12 '19 at 10:21
  • Note: You say "These [$j^$ values] are my sample quantiles, right? To get my qq-plot I now want to plot these against the theoretical quantiles.", but no, the values of $j^$ are not the sample quantiles; rather, the $j^$th sample quantile is (approximately) $x_{(j)}$, and the $j^$th theoretical (standard normal) quantile is $\Phi^{-1}(j^)$. So you want to plot $x_{(j)}$ vs. $\Phi^{-1}(j^)$, i.e., $(−1.8,−0.82,0.3,1.2,1.6)$ vs. $(−1.28,−0.52,0.00,0.52,1.28)$ and look for a linear relationship. – r.e.s. Jun 12 '19 at 20:47
  • Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, use MathJax. – dantopa Jun 13 '19 at 01:55
  • Check this link https://www.statisticshowto.com/q-q-plots/ – Matata Dec 20 '23 at 21:46

0 Answers0