FP7 and looking for the truth: mathematicians have it easy!

1. FP7 and looking for the truth: mathematicians have it easy! Steve Quarrie Director KBMP /28 Mathematicians

2. Where does Okvirni Program 7 (FP7) fit in? What is its relevance to young researchers and PhD students? FP7 has a lot of opportunities for young scientists to improve their research skills. But the best FP7 money goes to only the very best quality research. So, how do you ensure that you are doing the best quality research? That’s what this talk is all about. /28 Mathematicians

3. What is the purpose of a research-based post-graduate degree, such as a PhD? WRONG!!! To do research. RIGHT!!! To learnhow to do research. How many supervisors use their PhD students as technicians? How many PhD studentsfeelas if they are used as technicians? How many supervisors abandon their post-graduate students? How many post-graduate studentsfeelas if they are abandoned? Developing effective research skills needs constant help and support to understand what to do and, more importantly, why. /28 Mathematicians

4. The purpose of the post-graduate education is to teach PhD students how toTHINK and to become RELIABLEas independent workersusing RESEARCH as the vehicle for these goals. So, what is RESEARCH all about? What is RESEARCH? /28 Mathematicians

5. Start by reading this piece of text: …… A: Znači, vi terate njega da optuži lažne ljude... B: Ko kaže? A: Pa, što mi ne odgovorite onda da li jeste ili niste? B: Ja što s njim razgovaram to vas ne treba da se tiče. A: Znači, nećete da odgovorite da li ste ga terali? B: Ne, ja vam odgovaram šta je. I slušajte me sada, ja nemam nijedan razlog da pričam i da se plašim onog što sam ja sa svojim klijentom razgovarala, uopšte ni jedan jedini razlog, … A: Pa, on je rekao da ste ga terali da lažno svedoči... B: Ma, ne interesuje me. A: Zašto nećete da odgovorite na pitanje da li ste terali vašeg klijenta da lažno... Ako niste terali, znači da X. kao svedok-saradnik laže? B: Ja ne znam šta on priča i ne interesuje me. A: Evo, to je rekao. B: Ma, mene ne interesuje šta on priča. A: Ne, ali da li to znači da on laže? So, what is the truth? /28 Mathematicians

6. A court of law looks for the truth. Research is also looking for the truth! /28 Mathematicians

7. Here’s how a court of law would find the truth: The case of the Canadian Cheese Burglar! /28 Mathematicians

8. Here is the cheese at the centre of this case: Here is the cheese at the centre of this case: Cheddar cheese Case circumstances Two suspects were caught within 12 h of a robbery and were found to be in possession of articles taken from a private residence. The suspects claimed they were innocent of any crime. /28 Mathematicians

9. Evidence showed that the suspects possessed stolen property, but there was no evidence connecting the suspects to the crime scene. With the help of the home owners, police recovered a small piece of cheddar cheese from the scene within 36 h which showed bite marks, and from which DNA was recovered. The police managed to get blood samples from the two suspects, and DNA was extracted from the blood. /28 Mathematicians

10. Here are electropherograms comparing DNA recovered from saliva on the cheese (upper traces) with DNA from a suspect (lower traces) using markers for 9 DNA loci plus Amelogenin, a gender locus probe. DNA collected from the cheese and suspect was identical at every locus: all peaks were in the same places and of very similar intensities. Calculating frequency of this genotype in Canadians gave 1 in 1.59 x 1014. /28 Mathematicians

11. So, the DNA from the cheese and suspect were identical, despite the denials by the suspects. So, here was the truth. • You should compare yourself with all the participants of a court trial. • When doing research you are: • Counsel for the prosecution • Counsel for the defence • All the expert witnesses • The judge and (in the UK) also • The jury - all at the same time! So, just like the court case of the Canadian cheese burglar, when doing research you have a lot of responsibility to get it right! - to identify the truth about what really happened. /28 Mathematicians

12. However, the truth may not always be easy to find, and the truth may not always be what you think it is! Instead of looking for the truth, a lot of research appears to be based on proving facts by doing experiments. A fact is regarded to be the result of one or more experiments. Frequently, research programmes seem to be built around the availability of facilities/equipment/chemicals without having a logical research strategy to follow. Good quality research is largely based on hypothesis testing. You set up a hypothesis and then design experiments to test it. /28 Mathematicians

13. A dictionary definition Hypothesis[n] 1. A concept that is not yet verified but that if true would explain certain facts or phenomena; 2. A proposal intended to explain certain facts or observations /28 Mathematicians

14. This is a key factor needed for good quality research: • Designing your experiments to ensure that there can beno other explanationthat would invalidate the test of your hypothesis. • Only then will you know whether your hypothesis is right or wrong! This leads to ... /28 Mathematicians

15. Formulate a new hypothesis Formulate a hypothesis Hypothesis Hypothesis Interpret the results and make conclusions Work out how to test it Deduce Design Analyse Carry out Do the experiment and collect the data Process the results The Research Cycle /28 Mathematicians

16. A good research project has to take account of four key components: - the scale of the project - the cost of the project - the time available for the project - the quality of the results Each of these factors depends on the others, so they can be considered as a research pyramid ….. /28 Mathematicians

17. The Research Pyramid Scale Quality Cost You need to adjust Scale, Cost and Time to maximise Quality Time Note that the line joining Quality to Cost is dashed. In fact Quality rarely depends on Cost! /28 Mathematicians

18. Good experimental design is vitally important. How do you design your experiments to get the best test of your hypotheses? How many replicates of the tests do you need to know whether any differences are significant or not? If you are going to compare one or more treatments with a control, how do you define the control? Are they the only controls or should you have several types of control? /28 Mathematicians

19. Will you use individual samples, pooled samples or can you use paired samples? What statistical methods do you plan to use to test whether the data sets are different? Are there alternative statistical methods that would be better but possible only if you changed the experimental design (eg paired samples)? You need to think about all of this before you start any experimental work as this will determine your experimental design. So, the most critical part of the research cycle is experimental design - get this wrong and you are wasting your time! - get this wrong and you are wasting your time! /28 Mathematicians

20. Here’s an example to challenge you - it’s about plants! This example is from my research programme at Newcastle University which is looking for the truth. The hypothesis: Ozone is damaging to the yield of wheat plants, and the more ozone you give them, the lower the yield. [Note that wheat is supposed to be the most sensitive crop to ozone in the UK!] The highest ozone treatment (75 ppb) given in growth chambers to 95 wheat genotypes should have been enough to cause significant damage. /28 Mathematicians

21. 2.5 2 Note lots of genotypes with yield stimulated by ozone!! 26 genotypes > 1.1 1.5 Ratio yield/plant 75ppb/Control 1 0.5 0 Genotype This is the result of ranking wheat genotypes for yield under ozone (75 ppb) relative to control yields using the original data: Yields are expressed as the ratio: ozone-treated yield/control yield. So the hypothesis is WRONG!! Or is it? What is the truth? /28 Mathematicians

22. 2.5 Note lots of genotypes still with yield stimulated by ozone!! 25 genotypes > 1.1 2 Ratio yield/plant 75ppb/Control 1.5 1 0.5 0 Genotype Well, let’s clean up the data to remove values affected by mice eating the ears, and the bags that were spilt on the floor, etc: So the hypothesis IS STILL WRONG!! Or is it? /28 Mathematicians

23. Yield in wheat is derived by multiplying the following components: spikelets/ear x ears/plant x grains/spikelet x weight/grain (klasica/klasu x klasa/biljci x zrna/klasicu x težina/zrnu) Components are determined at different stages of development - essentially in the order shown above. OK, let’s be clever (let’s pretend we are mathematicians!) and think whether it is realistic for the hypothesis to be wrong, or could there still be mistakes in our dataset? Ozone treatment started on 20th May. Spikelet production was already completed by 20th May. Therefore spikelets/ear should be the same in both treatments. But for several genotypes there were some small spikelets/ear, particularly for control plants, as shown here: /28 Mathematicians

24. So, can we just delete the values that look small? Possibly, if we can show that they are significantly different from the rest. It looks as though the most frequent spikelet number for this line is 17. So, let’s rank all the lines for mean spikelet number, then look at only those lines with spikelet number means from 16.0 to 18.0, i.e. 17.0 plus or minus 1: [Note: data shaded yellow are for the ozone treatment] /28 Mathematicians

25. 180 160 140 120 Number per class 100 80 60 40 20 0 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Spikelet number per ear Then work out a frequency distribution for spikelet number per ear for those genotypes: 81 genotypes (across both treatments), giving in total 476 values for spikelet number per ear. The range from 15 to 19 (green bars) contains 450 values, which = 95% total values. Therefore, any values outside this range (red bars) can be regarded as significantly different. /28 Mathematicians

26. 2.5 2.5 2 Note very few genotypes now with yield stimulated by ozone!! Now only 11 genotypes > 1.1 2 1.5 Ratio yield/plant 75ppb/Control 1.5 1 1 0.5 0.5 0 0 Genotype So, let’s see what the picture looks like once we have corrected for variation in spikelets per ear (determined before ozone was given): So the hypothesis is probably RIGHT after all!! /28 Mathematicians

27. So, the truth from that experiment was that ozone did reduce wheat yields compared with the controls. But, this was confirmed only after very careful analysis and interpretation of all the data. Thus, if you havewell-designed experimentsto give yougood quality results, which are analysed and interpretedvery carefully, this gives you: - a valid test of your hypothesis - something worth writing up for one or more good quality publications - a sound basis upon which to develop ideas on what to do next: forming your next hypothesis - but crucially: access to the TRUTH /28 Mathematicians

28. Now, plants are difficult to work with because you can never predict what they will do. That’s why it takes a lot of effort to find the truth. Mathematics should be less problematic: The answer is either true or it isn’t! So, you mathematicians have it easy! /28 Mathematicians