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lab exam

lab exam. when: Nov 27 - Dec 1 length = 1 hour each lab section divided in two register for the exam in your section so there is a computer reserved for you If you write in the 1st hour, you can’t leave early! If you write in the second hour, you can’t arrive late!. lab exam. format:

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lab exam

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  1. lab exam • when: Nov 27 - Dec 1 • length = 1 hour • each lab section divided in two • register for the exam in your section so there is a computer reserved for you • If you write in the 1st hour, you can’t leave early! If you write in the second hour, you can’t arrive late!

  2. lab exam • format: • open book! • similar to questions in lab manual • last section in the lab manual has review questions • show all your work: hypotheses, tests of assumptions, test statistics, p-values and conclusions

  3. Experimental Design

  4. Experimental Design • Experimental design is the part of statistics that happens before you carry out an experiment • Proper planning can save many headaches • You should design your experiments with a particular statistical test in mind

  5. Why do experiments? • Contrast: observational study vs. experiments • Example: • Observational studies show a positive association between ice cream sales and levels of violent crime • What does this mean?

  6. Why do experiments? • Contrast: observational study vs. experiments • Example: • Observational studies show a positive association between ice cream sales and levels of violent crime • What does this mean?

  7. Alternative explanation Ice cream Violent crime Hot weather

  8. Alternative explanation Ice cream Correlation is not causation Violent crime Hot weather

  9. Why do experiments? • Observational studies are prone to confounding variables: Variables that mask or distort the association between measured variables in a study • Example: hot weather • In an experiment, you can use random assignments of treatments to individuals to avoid confounding variables

  10. Goals of Experimental Design • Avoid experimental artifacts • Eliminate bias • Use a simultaneous control group • Randomization • Blinding • Reduce sampling error • Replication • Balance • Blocking

  11. Goals of Experimental Design • Avoid experimental artifacts • Eliminate bias • Use a simultaneous control group • Randomization • Blinding • Reduce sampling error • Replication • Balance • Blocking

  12. Experimental Artifacts • Experimental artifacts: a bias in a measurement produced by unintended consequences of experimental procedures • Conduct your experiments under as natural of conditions as possible to avoid artifacts

  13. Experimental Artifacts • Example: diving birds

  14. Goals of Experimental Design • Avoid experimental artifacts • Eliminate bias • Use a simultaneous control group • Randomization • Blinding • Reduce sampling error • Replication • Balance • Blocking

  15. Control Group • A control group is a group of subjects left untreated for the treatment of interest but otherwise experiencing the same conditions as the treated subjects • Example: one group of patients is given an inert placebo

  16. The Placebo Effect • Patients treated with placebos, including sugar pills, often report improvement • Example: up to 40% of patients with chronic back pain report improvement when treated with a placebo • Even “sham surgeries” can have a positive effect • This is why you need a control group!

  17. Randomization • Randomization is the random assignment of treatments to units in an experimental study • Breaks the association between potential confounding variables and the explanatory variables

  18. Experimental units Confounding variable

  19. Experimental units Treatments Confounding variable

  20. Experimental units Treatments Without randomization, the confounding variable differs among treatments Confounding variable

  21. Experimental units Treatments Confounding variable

  22. Experimental units Treatments With randomization, the confounding variable does not differ among treatments Confounding variable

  23. Blinding • Blinding is the concealment of information from the participants and/or researchers about which subjects are receiving which treatments • Single blind: subjects are unaware of treatments • Double blind: subjects and researchers are unaware of treatments

  24. Blinding • Example: testing heart medication • Two treatments: drug and placebo • Single blind: the patients don’t know which group they are in, but the doctors do • Double blind: neither the patients nor the doctors administering the drug know which group the patients are in

  25. Goals of Experimental Design • Avoid experimental artifacts • Eliminate bias • Use a simultaneous control group • Randomization • Blinding • Reduce sampling error • Replication • Balance • Blocking

  26. Replication • Experimental unit: the individual unit to which treatments are assigned Experiment 1 Experiment 2 Tank 1 Tank 2 Experiment 3 All separate tanks

  27. Replication • Experimental unit: the individual unit to which treatments are assigned 2 Experimental Units Experiment 1 2 Experimental Units Experiment 2 Tank 1 Tank 2 8 Experimental Units Experiment 3 All separate tanks

  28. Replication • Experimental unit: the individual unit to which treatments are assigned 2 Experimental Units Experiment 1 Pseudoreplication 2 Experimental Units Experiment 2 Tank 1 Tank 2 8 Experimental Units Experiment 3 All separate tanks

  29. Why is pseudoreplication bad? • problem with confounding and replication! • Imagine that something strange happened, by chance, to tank 2 but not to tank 1 • Example: light burns out • All four lizards in tank 2 would be smaller • You might then think that the difference was due to the treatment, but it’s actually just random chance Experiment 2 Tank 1 Tank 2

  30. Why is replication good? • Consider the formula for standard error of the mean: Larger n Smaller SE

  31. Balance • In a balanced experimental design, all treatments have equal sample size Better than Balanced Unbalanced

  32. Balance • In a balanced experimental design, all treatments have equal sample size • This maximizes power • Also makes tests more robust to violating assumptions

  33. Blocking • Blocking is the grouping of experimental units that have similar properties • Within each block, treatments are randomly assigned to experimental treatments • Randomized block design

  34. Randomized Block Design

  35. Randomized Block Design • Example: cattle tanks in a field

  36. Very sunny Not So Sunny

  37. Block 1 Block 2 Block 3 Block 4

  38. What good is blocking? • Blocking allows you to remove extraneous variation from the data • Like replicating the whole experiment multiple times, once in each block • Paired design is an example of blocking

  39. Experiments with 2 Factors • Factorial design – investigates all treatment combinations of two or more variables • Factorial design allows us to test for interactions between treatment variables

  40. Factorial Design pH Temperature

  41. Interaction Effects • An interaction between two (or more) explanatory variables means that the effect of one variable depends upon the state of the other variable

  42. Interpretations of 2-way ANOVA Terms Effect of pH and Temperature, No interaction

  43. Interpretations of 2-way ANOVA Terms Effect of pH and Temperature, with interaction

  44. Goals of Experimental Design • Avoid experimental artifacts • Eliminate bias • Use a simultaneous control group • Randomization • Blinding • Reduce sampling error • Replication • Balance • Blocking

  45. What if you can’t do experiments? • Sometimes you can’t do experiments • One strategy: • Matching • Every individual in the treatment group is matched to a control individual having the same or closely similar values for known confounding variables

  46. What if you can’t do experiments? • Example: Do species on islands change their body size compared to species in mainland habitats? • For each island species, identify a closely related species living on a nearby mainland area

  47. Power Analysis • Before carrying out an experiment you must choose a sample size • Too small: no chance to detect treatment effect • Too large: too expensive • We can use power analysis to choose our sample size

  48. Power Analysis • Example: confidence interval • For a two-sample t-test, the approximate width of a 95% confidence interval for the difference in means is: (assuming that the data are a random sample from a normal distribution) 2 n precision = 4 

  49. Power Analysis • Example: confidence interval • The sample size needed for a particular level of precision is: 2  Precision n = 32

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