# Inferential Statistics Is an Unfit Tool for Interpreting Data
## 6 An Example with Real Data  
The examples above have been on intervention studies, but there is nothing special to these kinds of study designs. Whatever the study question or design might be, researchers must measure the phenomena of interest in a way that allows them to apply their domain knowledge to understand the results. I turn now to exemplify the approach to interpreting data described above to some real data. In the interesting study by [PERSON] and colleagues [30], one thing the researchers investigated was the relationship between patient happiness and \(f_{\text{o}}\) among transwomen. My personal _prior_ guess regarding this relationship would be that transwomen who have a lower \(f_{\text{o}}\) are _generally_ less happy with their voices than transwomen with higher \(f_{\text{o}}\)'s. However, [PERSON] et al. write in their abstract, \"This study demonstrates that happiness with voice in male-to-female transgender clients is not directly related to \(F_{\text{o}}\)\". This is a somewhat surprising claim. It is especially surprising considering that they report that _in their sample_, there was a positive correlation, \(r=0.32\), between the two variables. They further use an instructive scatterplot to illustrate the inter-individual dispersion in the two variables and what, to me, looks to be a positive correlation between \(f_{\rm o}\) and \"Happiness with voice\".  
As the correlation in their sample was \(r=0.32\), the researcher must have based their claim that happiness with voice is _not_ related to \(f_{\rm o}\) on some other statistic. Indeed, their complete reporting was: \"It was not possible to demonstrate a statistically significant relationship between patient happiness and \(F_{0}\) (\(r=0.32\), \(p=0.32\))\". Thus, these researchers based their negative claim on \(p=0.32\) (which is more than 0.05, the assumed \(\alpha\) level). That is, what these researchers happened to do (and what is quite common) is that they confused the acts of _interpreting data_ and _making inferences from the data_. The _result of their study_ was that there was a positive correlation between \(f_{\rm o}\) and patient happiness with their voices (\(r=0.32\)). Whether this correlation is _large_, _important_, or _spurious_, or not is a question that requires the researchers to apply their domain knowledge, what they know about male-to-female transgender persons, what they understand of the rating scale involved, what they understand of correlation coefficients, and so on. This question cannot be resolved based on \(p\)-values, standard recommendations of effect sizes, or any other abstract statistical benchmark.  
If we turn to _making inferences from the data_, the researchers should, according to the American Statistical Association [1, 2], _not_ focus on the \(p\)-value related to their correlation coefficient but on the confidence interval around their correlation coefficient. Calculating a confidence interval for a correlation coefficient can be achieved with different degrees of sophistication, but for simplicity, we can calculate a Fisher transformed confidence interval around [30] result to be 95% CI [\(-0.31\), \(0.76\)]. This interval should be reported via something as \"The correlation _in our sample_ was \(r=0.32\), and our data are compatible with the population correlation being somewhere between \(-0.31\) and \(0.76\) (95% CI). Note that our data are equally compatible with the population correlation being as large as 0.58, as it being as small as 0.0. Our estimate is reasonably imprecise, as we had such a small sample\". Publishing small scale studies is not a bad thing. However, we must accept the uncertainty involved in small scale studies and encourage \"meta-analytic thinking\" [2]. [PERSON] and colleagues just provided one estimate on how large the population correlation might be (somewhere between \(r=-0.31\) and \(r=0.76\)), and now we should wait for more studies with perhaps more precise estimates.