HYPOTHESIS TESTING USING P-VALUES
We start by stating the null and alternative hypotheses. We then collect data and using the computer
and complicated statistical procedures not covered here we derive a number called the p-value. The decision rules are: If
the p < 0.05, H0 is rejected (test statistically significant). If the p>0.05 H0 is not rejected
(test not statistically significant).
HYPOTHESIS TESTING USING CONFIDENCE INTERVALS
The 95% confidence interval is more informative than the p-value approach because it indicates precision.
The 95% CIs are computed by the computer using complicated statistical programs not covered here.
For example the difference in height between boys and girls can be given as 3.0 (2.5cm – 4.0cm)
where 3.0 = mean difference and 2.5 = lower bound and 4.0 = higher bound.
The 95% CI for the ratio of boy to girl heights can be given as 2.0 (1.5-3.0) where RR=2.0, 1.5 = lower
bound and 3.0 = higher bound.
Under H0 the null value is defined as 0 (when the difference between comparison groups=0)
or as 1.0 (when the ratio between comparison groups=1).
The decision rules are: if the CI contains the null value, H0 is not rejected (test not
statistically significant). When the interval does not contain the null value, H0 is rejected (test statistically
CONCLUSIONS and INTERPRETATIONS
A statistically significant test implies that the following are
true: H0 is false, H0 is rejected, data is not compatible with H0, and the data shows real/true
A statistically non significant test implies the following are true:
H0 is not false (we do not say true/accepted), H0 is not rejected, data is compatible with H0,
differences seen are due to sampling variation or random errors of measurement and not real biological difference.
Statistical significance may have no clinical/practical significance/importance.
This is due to other factors being involved but are not studied. It may also be due to invalid measurements.
Clinically important differences may not reach statistical significance
due to small sample size or due to measurement that are not discriminating enough. Hypothesis testing may be 1-sided or 2-sided.
The 1-sided test is rarely used. The 2-sided test is a more popular conservative test. We however are not covering the differences
between the 2 tests in detail here.