1. University of Ottawa - Bio 4158 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 1 Epistemology, scientific method, and statistics Objectives Understand the logical foundations of scientific inference Be able to distinguish theory (or model or hypothesis) from prediction Be able to distinguish between induction and deduction Be able to state a null hypothesis corresponding to a biological hypothesis

2. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 2 -45°00' -45°05' D13 D8 D15 D1 D4 D3 D10 D5 D16 D9 D12 U17 Cornwall D11 D6 STP 74°45'74°30' 1:204 000 D2 STP Courtaulds Domtar GM Reynolds Moses-Saunders Dam Cornwall Island ALCOA D14 8 km Lac Saint-François Impact of industrial effluents on heavy metal contamination of benthic invertebrates Are invertebrates contaminated by industrial effluents?

3. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 3 The hypothetico-deductive method Hypothesis Predictions Observations Conclusions InductionDeduction Experiment Inference Question Ecological knowledge Statistics Logic Ecological techniques Statistics Logic Ecological knowledge

4. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 4 Hypothesis Invertebrates contaminated by local effluent from industrial outfall. Distance from outfall [Metal] water Impacted zone

5. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 5 Deduction If local effluents contaminate invertebrates … … then invertebrate metal burden will be higher in impacted zone than elsewhere. Distance from outfall [Metal] inv Impacted zone

6. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 6 Prediction Average metal concentrations in invertebrates will be higher in areas closer to the outfall than in areas further upstream or downstream. Distance [Metal] inv Impacted zone

7. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 7 Experiment Measure metal concentration in invertebrates collected upstream, within, and downstream of the impacted zone.

8. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 8 Results Falsifying hypothesis Concentrations in impacted zone are not higher than elsewhere… … which is NOT consistent with the hypothesis. Therefore the hypothesis is rejected (falsified)

9. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 9 Results Supporting hypothesis Average metal concentrations is higher in impacted zone compared to areas further upstream or downstream… … results consistent with the hypothesis. Therefore the hypothesis is supported (NOT proven!)

10. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 10 Inference and conclusion If the hypothesis is falsified, it must be false If the hypothesis is supported, it may be true (it is necessary but not sufficient)

11. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 11 The null hypothesis Since we can’t prove than an hypothesis is true…. But we can prove that an hypothesis is false…. ….the trick is to prove that the opposite of our prediction is false! That is, falsify the null hypothesis

12. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 12 Null hypothesis (H 0 ) Prediction –Invertebrate metal concentration is elevated in the impacted zone. H 0: –Invertebrate metal concentrations are NOT elevated in the impacted zone, or equivalently… –Invertebrate concentrations are no higher in the impacted zone than anywhere else.

13. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 13 Inferential statistics Statistical tests (t, regression, chi- square…..) Give the “probability that the null hypothesis is true” (more or less) P > 0.05 accept H 0 P < 0.05 reject H 0 accept H A

14. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 14 Summary Hypothesis –Invertebrates contaminated by local sources. Deduction –If local sources are important, then invertebrates in the impacted zone will be the most contaminated. Prediction –Contamination will be higher in impacted zone than upstream or downstream this zone. H 0 –Contamination is lower or equal in the impacted zone.

15. University of Ottawa - Bio 4118 – Applied Biostatistics © Antoine Morin and Scott Findlay 21/04/2015 11:25 AM 15 Exercise For each observed pattern, generate 3 distinct hypotheses, deduce predictions, and state the corresponding biological and null hypotheses. Incidence of breast cancer in women has increased from 1/15 in the 1960s to 1/8 today. Fecal contamination is higher near shore than offshore at Brittania beach.