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Presentation at a Course on Principles of Epidemiology Health Research Faculty of Medicine, King Fahad Medical City October 11-12, 2017 by Professor Omar Hasan Kasule Sr. MB ChB (MUK). MPH (Harvard), DrPH (Harvard) Chairman of the Institutional Review Board / Research Ethics Committee at King Fahad Medical City, Riyadh.
LECTURE # 7 INFERENTIAL STATISTICS
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.
• There are two traditions of formal hypothesis testing: the p-value approach (significance testing) and the confidence interval approach (Neyman-Pearson testing). The two approaches are mathematically and conceptually related.
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.
• They both cover all the possibilities.
• A hypothesis can be rejected but cannot be proved.
HYPOTHESIS TESTING USING P-VALUES:
• P value can be defined in a commonsense way as the probability of rejecting a true hypothesis by mistake.
• P values for large samples that are normally distributed is derived from 4 test statistics that are computed from the data: t, F, , and β.
• P values for small samples that are not normally distributed are computed directly from the data using exact methods based on the binomial distribution.
• 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.
• 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 95% CIs can be computed from the data using approximate Gaussian (for large samples) or exact binomial methods (for small samples).
• The decision rule are: if the CI contains the null value, H0 is not rejected. If the CI When the interval does not contain the null value, H0 is rejected.
CONCLUSIONS and INTERPRETATIONS:
• A statistically significant test implies that the following are true: H0 is false, H0 is rejected, observations are not compatible with H0, observations are not due to sampling variation, and observations are real/true biological phenomena.
• A statistically non-significant test implies the following are true: H0 is not false (we do not say true), H0 is not rejected, observations are compatible with H0, observations are due to sampling variation or random errors of measurement, and observations are artificial, apparent and not real biological phenomena.
• Statistical significance may have no clinical/practical significance/importance.