# 2. Odds Ratios

## 2.1 Example/Provocation

Returning to the article Harrigan et al. 2017, look again at Table 2, but this time focus on the coefficients for the independent variables.

1. Is the table reporting coefficients or odds ratios? How do you know?
2. How would you explain the coefficents/odds ratios?

## 2.2 How to explain Odds Ratios

Look at the first paragraph of the ‘Discussion’ and identify the sentences where key odds ratios in Models 2 and Models 5 (of Table 2) are explained.

“Through a path analysis of quantitative surveys of 582 migrant workers, Study 1 showed that one of the primary proximate causes of risk of serious mental illness is the threat of deportation, a threat which, by definition, only migrants are vulnerable to. Controlling for all other factors, the odds of suffering from serious mental illness were 7.5 times higher (95% CI: 2.78, 20.34) for migrant workers threatened with deportation, as compared to those not threatened. The path analysis in Study 1 shows that the migrant workers at higher risk of threat of deportation, and thus higher risks of mental illness, are those in workplace conflict with their employer, i.e. those with salary or injury disputes. While an ordinary migrant worker (i.e. without an injury or salary dispute) had an 11% chance of being threatened with deportation, 64% of claimant migrant workers (i.e. with injury or salary dispute) were threatened. Using statistical modelling and controlling for other factors, the odds of being threatened with deportation were 8 times higher (95% CI: 3.39, 20.5) for migrant workers with salary disputes, and more than 12 times higher (95% CI: 6.7, 22.12) for migrant workers with injury disputes, as compared to an ordinary worker.”

Question: Based on the style of the above paragraph, what are the key phrases you need to use when explaining an odds ratio in a paper?

## 2.3 Understanding Odd Ratios

This is a fanastic guide to Odds Ratios. I have provided it so that we can read through it in class and talk through the concepts.

https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-do-i-interpret-odds-ratios-in-logistic-regression/

[If you are an external student, please review the video of the class, and read the article in the link in your own time.]

Last updated on 14 October, 2019 by Dr Nicholas Harrigan (nicholas.harrigan@mq.edu.au)