Chapter 5 Data Production AP Statistics Chapter 5 Data Production

5.1 Designing Samples 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)

Population and Sample 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

Methods of (bad) Sampling 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

Simple Random Samples (SRS) 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

Random digits 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!

Calculator Random #’s Math, prb, randint(lowest #, highest #, # of people you want in your sample) If you use ctlghlp: instead of hitting enter when randint( is highlighted in the prb menu, hit “+” and it will tell you what goes in parens. You can store your random numbers in a list: Randint(1,150,25) sto-> L1

(good) Types of sampling Probability sample: 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 Multistage samples

Caution about Sample Surveys 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.

More causes of bias 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

5.2 Designing Experiments 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 & levels Factors: number of variables interested in (The explanatory variable, causes the change in other variables) Levels: number of ‘categories’ for each: Example: use 2 pain relievers at 3 different doses. This is an example of a 2x3 study

Control When designing an experiment we want to minimize the effect of lurking variables so that our results are not biased. It is essential to use a control group The control gets a fake treatment to counter the placebo effect and other lurking variables

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

Randomized Comparative Experiments

Experimental Design Step 1: Choose treatment Identify factors and levels Control group Step 2: Assign the experimental units to the treatment Matching (place similar units in each treatment group) Randomization (randomly assign units to each treatment group)

Remember if we want to examine a cause and effect relationship, we conduct an experiment If an experiment is well-designed, a strong association in the data does imply causation, since any possible lurking variables are controlled.

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

Statistical Significance 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

Types of Experiment Design In a completely randomized design, all subjects are randomly assigned to treatment groups. In a block design, subjects are first split into groups called blocks In a matched-pair design, there are only two treatments.

Blocking/block design 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 Separate into “blocks” of similar subjects to reduce the effect of variation

Matched Pairs Design Matching the subjects in various ways can produce more precise results than simple randomization Matched pairs design compares 2 treatments. Subjects matched in pairs. a single subject receives both treatments or a pair of subjects, each receiving a different treatment

Cautions about experimentation Even well- designed experiments can contain hidden bias Double-blind: neither subject nor experimenter knows which treatment is assigned May be other hidden lurking variables that are not considered in the experiment

Simulation Five steps of simulation 1. State the problem or describe the experiment 2. State the assumptions 3. Assign digits to represent outcomes 4. Simulate many repetitions 5. State your conclusion