Neither correlation showed. Not even the square root of the product of the two features was correlated with responses to our prompts.… But the results are probably more likely to be meaningless.
There are two things that “no correlation” might mean: first, that there is actually no correlation, or second, that you didn’t have enough statistical power to detect a correlation. Only in the second case is the result meaningless. You can distinguish between these by providing not just the p-value of the correlation, but the confidence interval on the correlation statistic.
Yep, I should’ve done that. See below. Insofar as we can take these numbers at face value, I think they show that we can be fairly confident that there’s no correlation.
But correct me if I’m wrong, but for a null result to not be meaningless the study would have to be methodologically excellent. I don’t trust our first foray into surveys too far. That’s what I meant in the section you quoted.
Many thanks for all your comments! (I found this one to be easiest to respond to, but I’ll get to the others next.)
Correlation between prompts and rationality:
> bayes.cor.test(
+ formula = ~ all.mean + rationality.mean,
+ data = results[!is.na(results$all.mean), ])
|**************************************************| 100%
Bayesian First Aid Pearson's Correlation Coefficient Test
data: all.mean and rationality.mean (n = 167)
Estimated correlation:
-0.054
95% credible interval:
-0.21 0.10
The correlation is more than 0 by a probability of 0.256
and less than 0 by a probability of 0.744
Correlation between prompts and altruism:
> bayes.cor.test(
+ formula = ~ all.mean + altruism.mean,
+ data = results[!is.na(results$all.mean), ])
|**************************************************| 100%
Bayesian First Aid Pearson's Correlation Coefficient Test
data: all.mean and altruism.mean (n = 167)
Estimated correlation:
-0.026
95% credible interval:
-0.18 0.13
The correlation is more than 0 by a probability of 0.379
and less than 0 by a probability of 0.621
There are two things that “no correlation” might mean: first, that there is actually no correlation, or second, that you didn’t have enough statistical power to detect a correlation. Only in the second case is the result meaningless. You can distinguish between these by providing not just the p-value of the correlation, but the confidence interval on the correlation statistic.
Yep, I should’ve done that. See below. Insofar as we can take these numbers at face value, I think they show that we can be fairly confident that there’s no correlation.
But correct me if I’m wrong, but for a null result to not be meaningless the study would have to be methodologically excellent. I don’t trust our first foray into surveys too far. That’s what I meant in the section you quoted.
Many thanks for all your comments! (I found this one to be easiest to respond to, but I’ll get to the others next.)
Correlation between prompts and rationality:
Correlation between prompts and altruism: