10.3 Consistency and reading output

Consistency between the RQ, hypotheses, the CI, the hypothesis test, and the results is important. For example: if the RQ is written in terms of proportions, then the hypotheses, CI and so forth should also be written in terms of proportions.

In addition: explaining exactly what the statistic and the CI are estimating (the parameter) is very important.

Suppose a researcher asked the RQ:

For Australians, are the odds of people with mosquito bites the same for people sitting near a citronella candle as for people sitting near an ordinary wax candle?

Which would be the appropriate null hypothesis?
The odds of a person being bitten by a mosquito is the same for people near citronella candles and wax candles The proportion of people being bitten by a mosquito is the same for people near citronella candles and wax candles Either of the above

Which would be the appropriate CI to produce?
A CI for the odds ratio A CI for the difference in proportions Either of the above

Which would be the appropriate hypothesis test?
A hypothesis tests for the difference between proportions A hypothesis tests for the odds ratio Either of the above

The jamovi output is shown in Fig. 10.1.

FIGURE 10.1: Mosquito bites when near different types of candles.

What is the odds ratio?
Very carefully, explain what this odds ratio means in context.
The output also shows the difference between proportions. Very carefully, explain what this difference means in context.
In the study, the odds that someone received a mosquito bite when a wax candle was being used was \(2.167\). What are the odds that someone in the study received a mosquito bite when a citronella candle was used?
The \(95\)% CI for the odds ratio is from \(0.234\) to \(1.102\). Very carefully interpret what this means in context.
Suppose the \(95\)% CI for the odds ratio was from \(0.11\) to \(0.94\). Very carefully interpret what this would mean in context.
Suppose the \(95\)% CI for the odds ratio was from \(1.28\) to \(4.13\). Very carefully interpret what this would mean in context.
Check that the CIs are statistically valid.