# AP Statistics.  Observational study: We observe individuals and measure variables of interest but do not attempt to influence responses.  Experiment:

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AP Statistics

 Observational study: We observe individuals and measure variables of interest but do not attempt to influence responses.  Experiment: We deliberately impose some treatment on individuals in order to observe their responses.  Pros vs. Cons of each? (control etc…experiment better)

 Pop: the entire group of individuals that we want information about  Sample: a part of the population that we actually examine in order to gather info  Sampling vs. Census: Sampling studies a part in order to gain info about the whole, census attempts to contact every individual in the pop

 Voluntary response: People choose themselves by responding  Convenience sampling: Choosing individuals who are easiest to reach  Bias: The sampling method is biased if it systematically favors certain outcomes

 The simplest way to use chance to select a sample is to place names in a hat (the population) and draw out a handful (the sample).  SRS: every individual has = chance of getting picked, every sample of the size you are drawing has = chance of getting picked

 Table B: long string of digits 0-9, each entry in table is equally likely to be any of the 1- digits  Choosing SRS with table:  1. Label: Assign a # label to every individual in the pop (example: 01-50 for each senior girl @ CSH)  2. Table: use table B to select random labels  3. Stop: indicate when you should stop sampling (toss out repeated numbers, or numbers out of your range)  4. Identify sample: use the random #’s to identify subjects to be selected from your pop. This is your sample!

 Math, prb, randint(lowest #, highest #, # of people you want in your sample)

 SRS: samples chosen by chance  Stratified random sample: divide population into groups (aka strata) that are similar in some way, then choose a separate SRS in each stratum, then combine these SRS’s to form the full sample  Cluster sampling: divide population into groups (aka clusters). Some of these clusters are randomly selected. Then all individuals in chosen clusters are selected to be in the sample

 Undercoverage: occurs when some groups in the population are left out in the process of choosing the sample (hard to get an accurate and complete list of the population. Most samples suffer from some degree of this)  Nonresponse: occurs when an individual chosen for the sample can’t be contacted or does not cooperate.

 The behavior of the respondent or interviewer can cause response bias in sample results  Wording of questions can influence answers  We can improve our results by knowing that larger random samples give more accurate results than smaller samples

 The individuals on which the experiment is done are the experimental units.  If units are humans, they are called subjects.  The experimental condition applied to the units (aka the thing we ‘do’ to the people participating) is called a treatment.  Goal of research is to establish a causal link between a particular treatment and a response.

 Factors: number of variables interested in (example: Study differences of gender and alcohol preference. 2 factors: Gender, alcohol preference)  Levels: number of ‘categories’ for each: (gender has 2 levels…M/F, Alcohol lets say has 3 levels…hard liquor/beer/wine)  This is an example of a 2x3 study

 Control for lurking variables as much as possible.

 Comparison of the effects of several treatments is valid only when all treatments are applied to similar groups of experimental units.

 Even w/control, natural variability occurs among experimental units.  We would like to see units within a treatment group responding similarly to one another, but differently from units in other treatment groups (then we can be sure that the treatment is responsible for the differences).  If we assign many individuals to each treatment group, the effects of chance (and individual differences) will average out.

 Randomization produces 2 groups of subjects we expect to be similar in all respects before treatment is applied  Comparative design insures that influences other than what is being studied operate equally on both groups  Therefore, measured differences must be due either to treatment or play of chance in the random assignment of subjects to 2 groups

 1. Control the effects of lurking variables on the response, most simply by comparing 2 or more treatments  2. Replicate each treatment on many units to reduce chance variation in results  3. Randomize – use impersonal chance to assign experimental units to treatments

 We hope to see big differences (differences so large they are not likely just due to chance or individual differences).  If we do have an observed effect so large that it would rarely occur by chance, we call our result Statistically Significant

 A block is a group of experimental units that are known before the experiment to be similar in some way that is expected to systematically affect the response to treatments (ex: Testing the effect of weight lifting on a group of people- men/women will have obvious differences).  Separate into “blocks” of similar subjects to reduce the effect of variation

 Matching the subjects in various ways can produce more precise results than simple randomization  Matched pairs design compares 2 treatments. Subjects matched in pairs.  Fitness example: Pair females with each other, males with each other, one person in each pair goes to one treatment group (weights), the other person goes to the other treatment group (pilates)

 Double-blind: neither subject nor experimenter knows which treatment is assigned  Lack of realism: subjects or treatments of an experiment may not realistically duplicate the conditions we really want to study.

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