Chapter 1 Extras More on Simulations and surveys

Another Simulation What if Wheaties put pictures of athletes on trading cards in their cereal boxes. Imagine if they put Tiger Woods in 20% of the boxes, Lance Armstrong in 30% and Serena Williams in 50% of the boxes. How could we run a simulation (using cards) to predict how many boxes we would likely need to buy to end up with the complete set?

When doing a simulation 1.Identify the component (the basic event that is to be repeated) 2.Identify how you will model the outcomes. 3.Explain how you will simulate the trial. 4.State clearly what the response variable is. 5.Run several trials. 6.Analyze the response variable. 7.State your conclusion in the context of the problem. How many trials??

More on Sample Surveys Biased Sample – over/under emphasizes some characteristics of a population. Systematic Bias - bias as result of the system (i.e. scale that is mis-calibrated) Response Bias – anything in the way the data was collected that influences the response. Does anyone know about the Alf Landon vs. FDR and the mistake made by the Literary Digest? Response Bias: Wording of a question, order in which the choices are presented, question content, question setting, appearance of questioner…

More on Sample Surveys Parameter – a number that represents something about a Population (i.e. a Population parameter) Parameters are denoted by Greek letters ( µ, σ) Statistic – a number that represents something about a Sample (i.e. a Sample Statistic) Statistics are denoted by Latin letters (x, s)

More on Sample Surveys Sampling Frame – the list of individuals from which the sample is drawn Samples drawn at random should generally differ from one another. This sample to sample difference is called sampling variability. Multistage sampling – sampling schemes that combine several methods of sampling Interesting to note: A random sample of 100 can at times represent a large population rather well, assuming that 100 is a good representative sample of the population you are measuring.

Experiments and Observational Studies A study where data is collected based on the past is called a retrospective study. Imagine a study which tries to tie music study with scholastic performance. In an experiment, the assigned treatment can be applied in a variety of ways, called levels. The treatment is the combination of all levels of application.

Experiments and Observational Studies The four principles of Experimental Design are a)Control (making conditions as similar as possible) b)Randomize (so effects of unknown or uncontrollable bias are equalized) c)Replicate (an experiment on a single subject is not data) d)Block (randomizing to equalize variation across all treatment groups) – Imagine testing fertilizer on plants from two different greenhouses… By blocking each source of plants and applying the treatments in the same way, the differences caused by the treatment can be seen more easily. Matching subjects… Blocking for Experiments is the same idea as stratifying for sampling