jamovi is a brilliant way to do statistics. It is open statistical software built on top of the powerful R statistical language. Moreover, it is free.
The likelihood/evidential approach is one of several approaches to making inferences from data. The best description and justification for the approach is given by Edwards, A.W.F. (1992) Likelihood, Johns Hopkins Press. Others, such as R. Royall (1997), S. Goodman (1988), Z. Dienes (2008), S. Glover & P. Dixon (2004) have subsequently made important contributions. More recently, useful contributions are by Dennis et al (2019, and Taper et al (2022)
The likelihood approach focusses on the observed data, using maximum likelihood for estimates, and calculates likelihood ratios for specific parameter values given the collected data. The log of the likelihood is known as the support. When comparing two parameter values (as might be suggested by different hypotheses), the difference in log likelihoods represents the ratio of their likelihoods. Using support has distinct advantages. It represents the weight of evidence with a scale that ranges from positive to negative (indicating support for or against a hypothetical parameter value). Support values obtained from independent studies can simply be added together to give their combined support. Unlike p values, support values are insensitive to transforms.
| S | Likelihood Ratio | Interpretation - evidence for H1 versus H2 |
|---|---|---|
| 0 | 1 | No evidence either way |
| 1 | 2.72 | Weak evidence |
| 2 | 7.39 | Moderate evidence |
| 3 | 20.10 | Strong evidence |
| 4 | 54.60 | Extremely strong evidence |
| 7 | 1097 | More than a thousand to one |
| 14 | 1.2 x 106 | More than a million to one |
Table 1: Interpretation for values of S, the support, calculated as the natural logarithm of the likelihood ratio. Negative values would represent support for hypothesis values H2 vs H1. Typically, it is sufficient to give S to one decimal place.
Support values give the relative strength of evidence for one hypothesis value versus another, see Table 1. They range from negative infinity to positive infinity. There is no specific threshold value (unlike 0.05 in frequentist testing), and values can be rounded to the nearest 1 decimal place, e.g. -2.161 ➡️ -2.2. A support of 0 shows no support for either hypothesis, while a support of 1 represents weak evidence for the first hypothesis versus the second. A support of 2 represents moderate evidence, and is roughly equivalent to the 5% significance level in the frequentist approach. A support of 3 represents strong evidence and 4 represents extremely strong evidence, and so on. Negative values represent the same strength of evidence, except for the second hypothesis value versus the first. Support values for a given likelihood function can be compared with each other simply by subtracting them.
The log likelihood ratio interval (support interval) identifies a supported range of values which are consistent with the observed statistic. In jeva it is denoted as S-X, where X can be any number between 1 and 100. The S-2 interval is commonly used since it is numerically close to the 95% confidence interval. For this interval, it means that the values within the interval have likelihood ratios with each other in the range 0.135 to 7.38, corresponding to e-2 to e2. Simply put, within an S-2 interval, no likelihoods are more than 7.38 times different from each other. Similarly for the S-3 interval, likelihood ratios will range from 0.050 to 20.09, corresponding to e-3 to e3, and no likelihoods are more than 20.09 times different from each other.
The support interval is different from the confidence interval. The latter represents the long run probability of capturing the population parameter and may need to be corrected for multiple testing, stopping rule, etc. The likelihood interval is also distinct from the Bayesian credibility interval that represents the subjective probability for a population value occurring within it.
There are few statistical packages that implement the likelihood approach and which calculate support. This jamovi module calculates support for a range of statistical analyses: t tests, ANOVA, regression, correlation and various categorical analyses.
The analyses in the module complement my recent book: Cahusac, P.M.B.
(2020) Evidence-Based Statistics, Wiley
Amazon.co.uk
In jamovi the .jmo file dropbox can be sideloaded, and the module will appear among the other modules. Example datasets from the book are provided by the jamovi Data Library (see Open file menu).
It can also be installed as a regular R package. To do this download the tar.gz file from dropbox Install the R package jmvcore and then in R:
library(jeva)
library(jmvcore)
I would be interested in feedback [email protected] or [email protected] Peter Cahusac
Below is a sample screenshot from jamovi showing the acquisition and results for an odds ratio analysis of the MRC study (1991) of neural tube defects in babies born to mothers receiving either folic acid or placebo (double-blind randomized study), see pp 146 - 151 in Cahusac (2020) book.
