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Presentation at a Training
Program on Biostatistics for physician managers working in Public Health
Administration, Qassim Province on May 1, 2013 by Professor Omar Hasan Kasule
Sr MB ChB (MUK), MPH (Harvard), DrPH (Harvard). EM: omarkasule@yahoo.com
1.0 THE NULL AND THE
ALTERNATIVE HYPOTHESES
1.1 Hypotheses
and the scientific method
The scientific method consists of
hypothesis formulation, experimentation to test the hypothesis, and drawing
conclusions.
Hypotheses are statements of prior
belief. They are modified by results of experiments to give rise to new
hypotheses. The new hypotheses then in turn become the basis for new
experiments.
1.2 Null hypothesis (H0) &
alternative hypothesis (HA):
The null or research hypothesis, H0,
states that there is no difference between two comparison groups and that the
apparent difference seen is due to sampling error.
The alternative hypothesis, HA,
disagrees with the null hypothesis. H0 and HA are
complimentary and exhaustive.
A hypothesis can be rejected but cannot
be proved. A hypothesis cannot be proved in a conclusive way but an objective
measure of the probability of its truth can be given in the form of a p-value.
2.0
HYPOTHESIS TESTING AND INTERPRETATION
2.1 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).
2.2 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 significant).
2.3 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 biological difference.
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.