1 Maximum Likelihood L[hypothesis | data] = Pr[data | hypothesis] Allows you to solve problems and test hypotheses that would be extremely difficult in any other way

2 Example What proportion of this class has shoplifted an item worth more than $10? Flip a coin Don’t tell ANYONE the result –If “heads,” answer “heads” –If “tails,” answer “heads” if you’ve shoplifted something, “tails” otherwise

3 Pseudoreplication The error that occurs when samples are not independent, but are treated as though they are

4 Example: “The transylvania effect” A study of 130,000 calls for police assistance in 1980 found that they were more likely than chance to occur during a full moon.

5 Example: “The transylvania effect” A study of 130,000 calls for police assistance in 1980 found that they were more likely than chance to occur during a full moon. Problem: There may have been 130,000 calls in the data set, but there were only 13 full moons in These data are not independent.

6 Pseudoreplication We are making a false claim about the number of independent samples in our data Very common mistake in biology Easiest solution: use the average of all the pseudoreplicates

7 Very small samples and assumptions Question from the class: “ Say there's a test which you desire to carry out which is expensive and therefore you can afford only 2 treatments, each with two replicates. How would we go about analysing any difference, because are sample would be so small that we wouldn't be able to know if our data followed a normal distribution, right? and would these tests be worth carrying out since they would have pretty low power?” Answer: most scientists will just proceed with the test Interpret the results as “if our assumptions are true (and we have no idea), then…”

8 Very small samples and assumptions Example: does the Earth have more species of living things than other planets in the solar system? Data: Earth=10,000, ,000,000 Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune=0 (as far as we know)

9 Hypothesis testing Null hypothesis are usually very simple, and often known beforehand to be false You will eventually reject them if you have a big enough sample size

10 Example Study on logging H o : The density of large trees is greater in unlogged versus logged areas

11 Fewer trees

12 Statistical significance ≠ Biological importance “Statistically significant” means P < 0.05 But it does not necessarily mean important! Likewise, nonsignificant results can be biologically important It’s always useful to estimate a parameter or effect size, with a confidence interval

13 Examples Some studies of thousands of children have found statistically significant associations of IQ with birth order These differences are on the order of 1-2 IQ points Such differences are not biologically important for individuals, and can’t explain why your sister is smarter than you!

14 Examples Large study of hormone replacement therapy showed no significant benefit of HRT to post-menopausal women Confidence interval for the effect size suggested that any possible undetected effect is likely to be extremely small

15 Correlation does not require causation

16 Correlation and Causation Hot weather Ice cream Violent crime

17 Data for many countries:

18 Confounding variables Variables that mask or distort the association between measured variables in a study Two approaches: –Try to measure them all –Do an experiment

19 Make a Plan Develop a clear statement of the question List possible outcomes Develop an experimental plan Keep the design as simple as possible Check for common design problems Is sample size big enough? Discuss with other people!

20 The importance of controls Placebo effect - an improvement in a medical condition that results from the psychological effects of medical treatment –Most people get better over time –Humans like to please others, including their doctors –Benefits of doctors beyond drugs –Direct psychological effects on health

21 The importance of controls Well-documented for pain relief Up to 40% of people report improvement in pain when given sugar pills Drugs and treatments must be analyzed in this context

22 Head On = stick of wax

23 “I’m addicted to placebos. I could quit but it wouldn’t matter.” Steven Wright

24 Mistakes Two types of mistakes: –Experimental mistakes –Statistical mistakes (“Type III error”)

25 Mistakes Two types of mistakes: –Experimental mistakes –Statistical mistakes (“Type III error”)

26 Experimental Mistakes

27 Mistakes Two types of mistakes: –Experimental mistakes –Statistical mistakes (“Type III error”)

28 Statistical Mistakes 1/3 to 1/2 of scientific papers that use statistics make at lease minor mistakes ~ 8% major mistakes - enough to alter the conclusions of the paper Be careful when reading papers Be careful with your own work!

29 Data dredging The process of carrying out statistical tests on your data until you come up with a statistically significant result.

30 P = second digit

31

32 Beware multiple comparisons Probability of a Type I error in N tests = 1-(1-  ) N For 20 tests, the probability of at least one Type I error is ~65%.

33 Example - ESP

34 Six or more correct answers: you have ESP!

35 Bonferroni correction Anyone in the class have 8 or more correct?

36 Garbage-in, garbage-out Small P-values do not rescue a poor measurement Example: IQ test bias

37 Aboriginal-based IQ Test 1.What number comes next in the sequence, one, two, three, __________? MANY

38 Aboriginal-based IQ Test 2. As wallaby is to animal so cigarette is to __________ TREE

39 Aboriginal-based IQ Test 3. Three of the following items may be classified with salt-water crocodile. Which are they? marine turtle brolga frilled lizard black snake

40 Fraud happens Original Haeckel's copy (echidna embryos)

41 Recent Fraud Example Woo Sek Hwang, human cloning Much of the data suspected to be fabricated

42 Regression to the mean When repeated measurements are taken over time… Individuals with extreme values for the first measurement tend to be nearer to the mean for the second measurement

43 Regression to the Mean

44 Regression to the Mean The “sophomore slump”

45 Publication bias Papers are more likely to be published if P<0.05 This causes a bias in the science reported in the literature.

46 Meta-analysis Compiles all known scientific studies testing the same null hypothesis and quantitavely combines them to give an overall estimate of the effect and its statistical properties This is a GREAT honours project…