The Scientific Method

1. The Scientific Method

2. probability

3. Probability Probability is a measure of how likely something is to happen.

4. Probability If you flip a coin, the probability of the coin landing heads is 50%, meaning that you expect it to land heads 50 times out of every 100 flips.

5. Probability If you roll a die, the probability of the die landing on 4 is 1/6 (because a die has 6 faces), meaning that on average, you would roll a 4 once every 6 rolls.

6. Conditional Probability Sometimes the probability of an event is increased or decreased by other events. The probability that there is no final for this class is very low. But IF I die, the probability is much higher. And IF Lingnan closes, the probability is much much higher. We say that the probability of P IF Q is the probability of P conditional on Q.

7. Representing Probabilities We can represent probabilities using the symbol P(-). For example: P(H) = 50% This might mean “the probability of the coin landing heads is 50%.”

8. So for example, before we learned that the probability of A happening is always greater than or equal to the probability of A and B happening. We can represent this truth as follows: P(A) ≥ P(A & B)

9. Conditional Probabilities We also have a way of representing conditional probabilities: P(A/B) means “the probability of A conditional on B” or “the probability that A will happen IF B happens.” P(~F/C) > P(~F) The probability that there will be no final conditional on Lingnan closing is greater than the probability that there will be no final.

10. Review: Which of the following two statements is true? 1. P(Fido is an animal/ Fido is a dog) = 100%. 2. P(Fido is a dog/ Fido is an animal) = 100%.

11. The scientific method

12. Scientific Method Science proceeds by the hypothetico-deductive method, which consists of four steps: • Formulate a hypothesis • Generate testable predictions • Gather data • Check predictions against observations

13. Hypotheses A hypothesis is a proposed explanation for something we’ve observed. Generally, this hypothesis is a component of a theory which we are trying to test. But it can also be a proposed explanation that isn’t part of a bigger theory.

14. Hypotheses Observation: many countries that eat a lot of chocolate win Nobel prizes when compared to other countries. Hypothesis: chocolate makes you smarter.

15. Generate Testable Predictions Our goal is now to come up with something we can check in the world to see whether our hypothesis is correct.

16. People Will Score Higher on Tests If They’ve Eaten Chocolate

17. Gather Data Now we need to see if our predictions were right. How do we do that?

18. Experiments Today we’re going to talk about experiments and good experimental design. How do we design experiments that can test our hypotheses? Experiments that can generate data that are relevant to our predictions?

19. Causal structure

20. Causation Much of science is concerned with discovering the causal structure of the world. We want to understand what causes what so we can predict, explain, and control the events around us.

21. Prediction For example, if we know that rain is caused by cool, dry air meeting warm, wet air then we can predict when and where it will rain, by tracking air currents, temperature, and moisture.

22. Prediction This is important because rain affects our ability to engage in everyday activities, like traveling or exercising. Knowledge of causation lets us make predictions, which helps us make plans

23. Explanation One way to explain something is to determine what causes it. For example, if you find out that a certain virus causes a disease among bears, then you have explained why the animals are getting sick.

24. Explanation This is important because once you know an explanation for a disease (what causes it), you can begin treating it– for example, with antiviral drugs.

25. Control Finally, if we know what causes some effect, then we can control nature to our advantage. For example, if you don’t know what causes diamonds, you have to look through mines to find some.

26. Control But when we know that diamonds are caused by carbon under high pressure, high temperature conditions, we can simply re-create those conditions to grow as many diamonds as we want.

27. Causation vs. correlation

28. Independence In statistics, we say that two variables are independent when the value of one variable is completely unrelated to the other: P(A/ B) = P(A) and P(B/ A) = P(B) B happening does not make A any more likely to happen. (If that’s true, so is the reverse.)

29. Example For example, here’s a non-random sequences of coin flips: XOXXOXOXOOXXOXOOXOXO How do we know that this sequence was non-random? Because whether the coin lands X or O is not independent of the other tosses.

30. Example For example, here’s a non-random sequences of coin flips: XOXXOXOXOOXXOXOOXOXO How do we know that this sequence was non-random? Because whether the coin lands X or O is not independent of the other tosses.

31. Example For example, here’s a non-random sequences of coin flips: XOXXOXOXOOXXOXOOXOXO P(X/ O) = 7/9, P(X) = 10/20 P(O/ X) = 8/10, P(O) = 10/20

32. Correlation Two variables A, B that are not independent are said to be correlated. A and B are positively correlated when P(A/ B) > P(A). If B happens, A is more likely to happen. A and B are negatively correlated when P(A/ B) < P(A). If B happens, A is less likely to happen.

33. Correlation Other relationships between variables are often called correlation as well. A and B are positively correlated when increases in A correspond to increases in B. A and B are negatively correlated when increases in A correspond to decreases in B.

34. Positive Correlation Example For example, demand and price are positively correlated. If demand increases for a certain product, then the price of that product increases. If demand decreases, price decreases.

35. $250,000 for 1 Rhino Horn A greatly increased demand for rhino horn in traditional Chinese medicine has led to a tremendous price increase for the horns. They are worth so much now that all 5 species of rhino are close to extinction.

36. Negative Correlation Example On the other hand, supply and price are negatively correlated. If supply increases for a certain product, then the price of that product decreases. If supply decreases, price increases.

37. Pork Prices Predicted to Soar So recently, higher corn prices have made pig-farming less profitable, leading to a decreased supply of pigs. Experts are predicting that there will be an increase in pork prices next year.

38. Causation and Correlation One thing that can lead two variables A and B to be correlated is when A causes B. For example, if having a cold causes a runny nose, then having a cold is correlated with having a runny nose: P(cold/ runny nose) > P(cold)

39. Causation and Correlation Similarly, the number of cars on the road is correlated with the number of accidents: if there is an increase in the number of people driving, there will be an increase in the number of car accidents. This is because a larger number of cars causes a larger number of accidents.

40. Causation ≠ Correlation But causation does not imply correlation. If A and B are correlated there are several possibilities: • A causes B • B causes A • C causes A and C causes B • A and B are only accidentally correlated

41. Correlation

42. http://www.youtube.com/watch?v=-_0_suZntks

43. B causes A Whenever there are lots of police at a location, the chance that there is a criminal there goes up. So do police cause crime? No, exactly the opposite: crime causes the police to show up!

44. B causes A Here’s a somewhat more realistic example. It has been observed that democracies tend to get in fewer wars than non-democratic countries. A plausible inference would be that the negative correlation between democracy and war is due to the fact that democracy causes peace.

45. B causes A But there’s another explanation, and some studies have suggested that it’s the right one. Frequent wars cause a country to not be democratic. Countries that get in a lot of wars don’t have the stability that’s necessary for democracy to flourish.

46. Common Cause Sometimes A and B are correlated, not because A causes B and B causes A, but instead because a third variable C, the common cause, causes both A and B.

47. Porn and Rape A study of U.S. prison inmates found that prisoners who had been exposed to pornography earlier in life were less likely to be in prison for rape, compared with those exposed to porn later in life.

48. Porn and Rape Does this mean that exposure to porn early in life prevents men from becoming rapists? Should you give your children porn? No. Inmates who had been exposed to porn later were more likely to have had a religious fundamentalist upbringing.

49. Porn and Rape And a religious fundamentalist upbringing was correlated with higher rates of sexual deviancy (and rape). Fundamentalist upbringing caused both late exposure to porn and higher chances of sexual crimes.

50. Coincidence