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Chapter 13

STAB22 - Highly detailed Chapter 13 Notes, Summer 2012, Ken Butler

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Department
Statistics
Course
STAB22H3
Professor
Ken Butler
Semester
Summer

Description
CHAPTER 13 – EXPERIMENTS AND OBSERVATIONAL STUDIES WHERE ARE WE GOING? – 4 principles of experimental design – 1. control – 2. randomize – 3. replicate – 4. block if appropriate – together these 4 principles depict the ideal experiment & how to understand results that come from it – much of knowledge that is known about social sciences, & natural sciences derive from carefully designed expts MAIN BODY Example (Music) – study wants to look at who gets better grade: students who play musical instruments or those who do not – found that, by comparing the performance of those who play and those who do not, the ones that play have higher overall GPA – 3.59 vs. 2.91 – 16% of music students had As, while only 5% for non-music OBSERVATIONAL STUDIES [1] Example (Music) – study attempted to show assoc. b/ween music edu. & grades – simply observed students in their envirnmt, recorded the choices they made (music or non-music) and then outcome (GPA) OBSERVATIONAL STUDIES - ex. is Example (Music) - no assigning of choices is done - merely observing RETROSPECTIVE STUDY - observational study that involves - identifying subj's from records - looking at subjs' past results - Example (Music) - collected data about students' past grades, and saw whether or not they played music [2] Why can we not conclude that music education CAUSES good grades? - for music education to cause good grades, this requires that there are no other diff's b/ween the two groups being looked at that can account for the diff's in the grades. - for this Ex., cannot conclude causation b/c whether or not they studied music was NOT the only diff. b/ween the 2 groups [3] Consider lurking variables - Example (Music) - var's that are we have not taken into acc't may have caused groups to perform diffntly - ex. work ethic - ex. parental support - ex. wealth - ex. level of intelligence (prior to music education) ^- these are ex's of var's that could have caused diff's b/ween the performances of the two groups [4] RETROSPECTIVE STUDIES - restrospective records can potentially have errors, b/c its based on historical data - often are used to discover var's related to rare outcomes (Ex. specific diesases) - first identify ppl w/ disease - then look into history & heritage to find things related to this diseased condition - have restricted view of world b/c typically are restricted to small part of popn - ex. identifying ppl w/ that specific disease; only minority may even have it in the first plac e [5] PROSPECTIVE STUDIES - observational study that involves - identifying subj's in advance - collecting data as events occur - observes subj's over time - record var's of interest, and see what is outcome as it occurs - Example - Music - select students who are going to join music lessons but have not do so yet - track their academic performance over several yrs - compare these music students' results to another group of subj's that we track which aren't taking music lessons [6] OBSERVATIONAL STUDIES - CANNOT POSSIBLY DETERMINE CAUSATION - regardless of if PROSPECTIVE, or RETROSPECTIVE - doesn't guarantee that impt, related var's to the outcome are the most impt, or even CORRECT - Example - Music - non-music vs. music might still differ in an IMPT way that was failed to be observed - could be this unobserved var. that caused good grades, instead of music per se RANDOMIZED, COMPARATIVE EXPERIMENTS [1] EXPERIMENT - Example - Music - take a group of students - randomly assign half to take music lessons, and the other half never - then, compare their grades several yrs after [2] EXPERIMENT - REQ. random assignment of subj's to treatments - Examples of questions that a designed experiment can justify - does music lessons cause good grades? - does taking Vitamin C decrease the chance of getting a cold? - does working with computers improves performance in STAB22? - is this drug a safe, health-conscious treatment for this disease? [3] EXPERIMENT - studies relationship b/ween 2/more var's - must identify at least 1: - FACTOR - name for EXPLANATORY VARIABLE in expts - RESPONSE VARIABLE How does experiment differ from other forms of investigation? - expter.. - actively & intentionally manipulates factors to control details of possible treatments - randomly assigns subj's to treatments - then observes response var. & compares responses for diff groups of subj's who were treated diffntly (ie. were under diff. treatments) - ex. compare treatment A subj's response to treatment B's subj's Example - Sleep - design expt to see if amount of sleep & exercise affects performance => factors = sleep, exercise => response var = performance [4] EXPERIMENT What do we call the individuals we experiment on? = EXPERIMENTAL UNITS What is the alternative term to the above used when working with humans? = PARTICIPANTS or SUBJECTS - more likely to attract them as prospective individuals to expt on if we call them by this instead of calling them EXPERIMENTAL UNITS [5] EXPERIMENT - LEVELS = specific val's for the factor that are chosen by expter - each individual is assigned a level Example - Sleep - participants are assigned to either 4, 6, or 8 hours => 3 lvls in total, and each participant is assigned one of them Levels (con.) - often times there are several factors at variety of lvls - ex. factor 1 = sleep time - lvls = 4, 6, or 8 hours - ex. factor 2 = treadmill time - lvls = treadmill, no treadmill - TREATMENT = combination of specific lvls from all factors that an experiment al unit (aka subj. or participant) receives Example - Sleep - 6 possible treatments - 4 hrs, treadmill - 6 hrs, treadmill - 8 hrs, treadmill - 4 hrs, no treadmill - 6 hrs, no treadmill - 8 hrs, no treadmill [1], 344 How to assign subj's to treatments? - to derive a fair conclusion from expt, must assign participants to treatments RANDOMLY [2] Why random? - to ensure that results of experiment are valid AN EXPERIMENT (GREEN BOX) - MANIPULATEs factor lvls to create treatments - RANDOMLY ASSIGNs subj's to treatments - COMPAREs responses of subj groups across treatments - ex. compare Treatment A (4 hrs, treadmill) vs Treatment B (6 hrs, treadmill) BLUE BOX - clinical trials = randomized health experiments - ex. randomly assigned postmenopausal women to take either - a) hormone replacement therapy - b) inactive pill => they are either treated to therapy or no therapy (lvls of factor) - concluded that hormone replacement w/ estrogen INCR'ed stroke risk THE FOUR PRINCIPLES OF EXPERIMENTAL DESIGN [1], 345 Design of Experiments (1935) - depicts methodology for designing expts - by Sir R.A. Fisher - his ideas are summarized in 4 principles - 1. Control - 2. Randomize - 3. Replicate - 4. Block 1. Control - control sources of variation other than factors being tested by making conditions similar as possible for ALL treatment groups - controlling unrelated sources of variation decr's variability in response => makes it easier to detect diff's among treatment groups [?] [2] - it is risky to make generalizations from experiment to other lvls of a CONTROLLED FACTOR (ex) - we test 2 diff. laundry detergents and carefully control water temp at 82 Centigrade - => control means that we keep it constant - by doing this, it reduces variation in our results that is DUE to the controlled var. (ie. water temp in this case) - cannot also justify that b/c of keeping at this temp, if you keep at any other temp (ex. colder temp's), it will also reduce variation in results due to this controlled var. [3] We control two things, but for diff. reasons and ways: Control: factors - How: by assigning usbj's to diff. factor lvls - Why: to see how does response var. comparing one factor lvl to another Control: other sources of variation - How: ex. keep them constant across all treatments - Why: prevent them from changing & impacting response var. 2. Randomize [4] Randomization - permits us to equalize effects of unknown or uncontrollable sources of variation - doesn't eliminate these sources - what it does do is spread them out across all treatment groups evenly - cannot use statistics to draw conclusions from experiment IF - experimental units were NOT assigned to treatments at random - what is benefit of assigning at ran
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