# Non-Linear probability scale (y-axis)

Very new to stats so excuse me if my terminology is wrong.

Hi, trying to plot a log probability plot and don't know the equation to use to generate the y axis.

With 50% mean I am trying to achieve the following scale(y).

99.99 99.9 99.8 99 98 95 90 80 .. .. 10 5 2 1 0.5 0.2 .1 .05 .02 .01

## migrated from math.stackexchange.comJul 10 at 13:54

This question came from our site for people studying math at any level and professionals in related fields.

• and between 10 and 80 you want steps of size 10? Or something that is increasing in step size till 50 (like 10, 25, 50)? Or symmetric around but not including 50? – Jfischer Jul 10 at 10:01

You might want to consider a scale based on log-odds i.e. $$\log\left(\frac p{1-p}\right)$$ with $$0 \lt p \lt 1$$ sometimes called the logit function. You can then multiply by or add constants to get it to fit your graph paper. The inverse function if using natural logarithms is the logistic function $$p=\frac{1}{1-e^{-x}}$$

So as examples, you might choose one of these if you find the spacing is the kind of thing you want

percent ln(p/(1-p)) log_10(p/(1-p)) log_10(p/(1-p)) + 4
99.99    9.21024     3.99996        7.99996
99.9     6.90675     2.99957        6.99957
99.8     6.21261     2.69810        6.69810
99       4.59512     1.99564        5.99564
98       3.89182     1.69020        5.69020
95       2.94444     1.27875        5.27875
90       2.19722     0.95424        4.95424
80       1.38629     0.60206        4.60206
70       0.84730     0.36798        4.36798
60       0.40547     0.17609        4.17609
50       0.00000     0.00000        4.00000
40      -0.40547    -0.17609        3.82391
30      -0.84730    -0.36798        3.63202
20      -1.38629    -0.60206        3.39794
10      -2.19722    -0.95424        3.04576
5      -2.94444    -1.27875        2.72125
2      -3.89182    -1.69020        2.30980
1      -4.59512    -1.99564        2.00436
0.2    -6.21261    -2.69810        1.30190
0.1    -6.90675    -2.99957        1.00043
0.01   -9.21024    -3.99996        0.00004