Chapter Five Vocabulary

Page 1 (1) A Census of the Population This would be ideal – we would actually KNOW the values of the parameters! Really hard and expensive, so, instead, we will use …… (2) A Sample – a subset which is supposed to be representative of the entire population

Page 2 Of course, there are various ways of taking a sample – some good and some bad. (3) Voluntary Response – bad A Convenience Sample – bad (4) A Simple Random Sample (SRS) – good! * every group of size “n” has the same probability of being selected * “n” is the symbol for the sample size

Page 3 (5) When our sample design favors one part of the population over another – either on purpose or by accident – this is called bias. Our design would be said to be “biased” in favor of tall people, or Southerners, or Republicans, or students with high GPA’s, or whatever. This is BAD.

Page 4 (6) If the population was huge (like an entire country or a large school), then we might use a multi-stage sample to make the calculations easier. For example, North Carolina has 100 counties and about 8 million people. Suppose we wanted to randomly select 200 people for a health-care survey. Rather than using RandInt for all 8 million people, we could randomly select 10 counties and then randomly select 20 people from each of those 10 counties.

Page 5 (7) If different parts of the population vary significantly according to the variable we are studying, then we will use stratification to improve the accuracy of our results. When we say “accuracy,” we mean that the values of the sample statistics will more accurately estimate the values of the unknown population parameters. Stratification is a method of selecting the sample from the population. In addition to that, stratification also reduces the variability of the sample results. These two features are VERY IMPORTANT characteristics and advantages of stratification.

Page 6 Stratification, continued We will break down the population into strata -- subgroups which differ significantly with respect to the variable of interest. We will then take an SRS from each strata and then combine these SRS’s into one big sample from the population. Don’t forget the two important advantages of stratification….accuracy and reduced variability.

Page 7 (8) Experiments vs. Observations – which is which? Treatment Subjects (9) Treatment Group, Control Group, Placebo (10) Blind and Double-Blind Experiments – Why would we want this? What would be the advantages?

Page 8 (11) A Randomized Comparative Experiment – usually the best design! What three components does it need to have? Usually should be drawn in arrow format (12) X = the explanatory variable Y = the response variable If a third variable, Z, also affects Y, then this is called confounding – we won’t know whether the change in Y has been caused by X or by Z.

Page 9 (13) Causation and Association aren’t the same thing! > For example, the variables X = an individual’s height and Y = his/her armspan are highly correlated/associated with each other. > It’s not as if growing taller causes your arms to grow longer, though, or vice versa. They are both caused by variables (genetics, mostly).

Page 10 (14) As in the smoking video, sometimes an experiment isn’t possible (or ethical) to do. > A retrospective study -- a type of observation; not an experiment – looks at events that have already happened. > A prospective study – again, not an experiment – follows two or more groups of subjects without imposing treatments, recording and comparing their results.

Page 11 (15) If you divide up the population into different groups and then sample from each of these groups, it’s called stratification. * If you first take the sample (randomly, I hope) and then divide up the sample into different groups, it’s called blocking. Blocking is a method for assigning the treatments to the subjects, which have already been chosen.

(15) (Blocking, continued) For example: I have a subject group of mosquitoes, which have been screened for abnormalities, diseases, etc, and I want to study the effectiveness of a new brand of Off. I’m concerned, though, that European mosquitoes and African mosquitoes might react differently to the Off. So I will first divide up my subject group into these two nationalities of mosquito, and then assign treatments and placebos to each nationality, doing my final comparisons within each block. Page 12

Page 13 – Special Vocab! Sometimes, an experiment or a survey is just too difficult/expensive/time-consuming to do! In this case, maybe we can run a simulation instead. A simulation often involves using random integers to simulate outcomes.

Page 14 – Special Vocab! (Simulations, continued) Things to Include when Designing a Simulation (1) How you will assign random digits to represent each outcome (2) How you will move through the integer table (3) How duplicates will be handed (4) Your stopping rule for ending a particular sequence (5) Your final result should be reported as a statistic