130501P - HYPOTHESES

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 (H_A):

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, H_A, disagrees with the null hypothesis. H₀ and H_A 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.