Alternative Ratio
Introduction
The Alternative Ratio is an effect size measure if you have a single binary variable, and performed for example a one-sample binomial , score, or Wald test. It is only mentioned in the documentation of a program called PASS (NCSS, n.d.), and referred to as Relative Risk by JonB (2015).
Obtaining the Measure
with Flowgorithm
A basic implementation for the Alternative Ratio is shown in the flowchart in figure 1
Figure 1
Flowgorithm for the Alternative Ratio
It takes as input the frequency of one of the categories (k) and the sample size (n).
Flowgorithm file: ES - Alternative Ratio.fprg.
with Python
Jupyter Notebookfrom videos: ES - Alternative Ratio (P).ipynb.
with stikpetP
without stikpetP
with R
The Jupyter notebook used in the videos: ES - Alternative Ratio (R).ipynb
with stikpetR
without stikpetR
The data file used: StudentStatistics.sav
R Studio file: ES - Alternative Ratio.R
with SPSS (not directly possible)
Unfortunately I'm not aware of any method to determine the Alternative Ratio with SPSS. However, it is fairly easy to determine the frequencies for each category and use the online calculator below to determine the Alternative Ratio.
Online calculator
Enter the number of cases in the category of interest, then the total sample size, and the expected proportion (usually 0.5 for binary data):
Manually (with Formula)
Given a sample proportion (p) and the expected proportion in the population (π), the formula for the Alternative Ratio (Relative Risk) will be:
\(AR=\frac{p}{\pi}\)
In the example the sample proportion of female was 0.26 and the expected proportion in the population 0.50. Filling this in the formula yields:
\(AR=\frac{0.26}{0.5}=0.52\)
And for the male proportion, which was 0.74 in the sample, we get:
\(AR=\frac{0.74}{0.5}=1.48\)
Interpretation
It is simply the sample proportion (percentage), divided by the expected population proportion (which we set at 0.5 (50%)).
For example, if the sample proportion was 0.26, then dividing this by 0.5 gives an Alternative Ratio of 0.26 / 0.5 = 0.52. This means that the proportion was (1 – 0.52) = 48% lower than expected. Similar for the other category we get 0.74 / 0.5 = 1.48. This indicates that the other category proportion is 48% higher than expected.
Unfortunately, there is no rule to determine if 48% is high or low (although most people would find it pretty high).
Alternatives
Alternatives for the Alternative Ratio as an effect size measure are Cohen g, or Cohen h'.
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