search this site.

220113P - HYPOTHESES

Copyright 1995-2023 © by Prof Omar Hasan Kasule - Admin
Category:
Print Friendly and PDFPrint Friendly

Presented at the Research Methodology Winter Camp of AlMaarefa University on January 11, 2022 at 10.30-11.00 by Omar Hasan Kasule MB ChB (MUK), MPH (Harvard), DrPH (Harvard) Professor of Epidemiology and Bioethics

 

1.0 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 the results of experiments to give rise to new hypotheses.
  • The new hypotheses than 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.

 

2.0 NULL HYPOTHESIS (H0) & ALTERNATIVE HYPOTHESIS (HA):

  • The null or research hypothesis, H0, states that there is no difference between the 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.

 

3.0 DIRECTION OF THE DIFFERENCE WHEN COMPARING 2 GROUPS

  • The null hypothesis to be tested: there is no difference in height between males and females.
  • 1-tail test = interested in either more or less.
  • 2-tail test = interested in both more and less.

 

4.0 REJECTION/NON-REJECTION OF A HYPOTHESIS

  • 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.
  • P-value <0.05 = reject the null hypothesis = statistically significant difference.
  • P-value >0.05 = do not reject the null hypothesis = statistically non significant difference.
  • We never talk about accepting a hypothesis.

 

5.0 ERRORS IN HYPOTHESIS TESTING

  • Type 1 error = a error = Probability of rejecting a true H0
  • Type 2 error = b error = Probability of not rejecting a false H0
  • The confidence level (1 - a) = Pr (not rejecting H0 | H0 is true).
  • Power (1-b) = True negative = Pr (rejecting H0 | H0 is false).

 

6.0 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. This is due to other factors being involved but is 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 measurements that are not discriminating enough.