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STAB22H3 (130)
Chapter 13

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University of Toronto Scarborough
Mahinda Samarakoon

Stats: Data and Models – Canadian Edition Chapter 13 – Experiments and Observational Studies Observational Studies - Studies where researchers don’t assign choices, they simply observe them - Retrospective study – subjects are identified first and then data is collected on an aspect of their past, can have errors because they are based on historical data - Used widely in public health and marketing, used for discovering trends and possible relationships - Prospective study – identifying subjects in advance and collecting data as events unfold - Observational studies cannot demonstrate causal relationships Randomized, Comparative Experiments - An experiment requires a random assignment of subjects to treatments - An experiments studies the relationship between two or more variables – at least one explanatory variable (a factor) that is manipulated, and at least one response variable to measure - The experimenter actively and deliberately manipulates the factors to control the details of the possible treatments and assigns subjects to those treatments at random - Experimental units – individuals on whom we experiment, human units are called subjects or participants - Levels of a factor – specific values of a factor that the experimenter chooses - Treatment – combination of specific levels from all factors that a unit receives The Four Principles of Experimental Design - Control: control sources of variation other than the factors we are testing by making conditions as similar as possible for all treatment groups; controlling extraneous sources of variation reduces the variability of responses, making it easier to detect differences among the treatment groups o Control a factor by assigning subjects to different factor levels to see how to response will change at different levels o Control other sources of variation to prevent them from changing and affecting the response variable - Randomize: randomization allows us to equalize the effects of unknown or uncontrollable sources of variation, assigning subjects to treatments at random reduces bias due to uncontrolled sources of variation - Replicate: each treatment should be applied to a number of subjects; the outcome of an experiment on a single subject is an anecdote, not data, replication of an entire experiment with the controlled sources of variation at different levels is essential - Blocking: compromise between randomization and control, uncontrollable attributes of experimental units (i.e. age) may affect the outcomes of an experiment so we group similar individuals together and randomize within each block to remove variability that was due to the difference amongst blocks Diagrams - A diagram of an experiment’s procedure emphasizes the random allocation of subjects to treatment groups, the separate treatments applied to these groups, and the ultimate comparison of results Does the Difference Make a Difference? - Even if the treatment made no difference, there would still be some variation between groups of an experiment - Differences are statistically significant if it can be decided that the difference is bigger than that that could be attributed to just the randomizati
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