## 28.8 About practical importance and statistical significance

Hypothesis tests assess
*statistical significance*,
which answers the question:
‘Is there evidence of a difference between
the value of the statistic and the value of the assumed parameter?’
Even very small differences
between the sample statistic and the population parameter
can be *statistically* different if the sample size is large enough.

In contrast,
*practical importance*
asks the question:

Is the difference between the value of the statistic and the value of the assumed parameter of any

practicalimportance?

‘Practical importance’ and ‘statistical significance’ are two separate (but both important) issues. Whether a results is of practical importance depends upon the context: what the data are being used for, by whom, and for what purpose.

**Example 28.2 (Practical importance) **In the body-temperature study,
very strong evidence exists that the mean body temperature had changed
(‘statistical significance’).

*does*have practical importance however.)

*Practical importance*depends on the context in which the results will be used.

**Example 28.3 (Practical importance) **A study of some herbal medicines (Maunder et al. 2020)
for weight loss found:

Phaseolus vulgarisresulted in a statistically significant weight loss compared to placebo, although this was not considered clinically significant.

In other words,
although the difference in weight loss between placebo and *Phaseolus vulgaris*
was unikely to be explained by chance (\(P<0.001\), which is ‘statistical significant’),
the difference was so small in size (a mean weight loss of just 1.61 kg)
that it was unlikely to be of any use in practice
(‘practical importance’).