AP Statistics Chapter 4 Test
Describe a randomized block design and a matched pairs design for an experiment and explain the purpose of blocking in an experiment.
-a block is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments -in a randomized block design, the random assignment of experimental units to treatments is carried out separately within each block SEE PAGE 285 IN TEXTBOOK -a matched pairs design is a common experimental design for comparing two treatments that uses blocks of size 2. In some matched pairs designs, two very similar experimental units are paired and the two treatments are randomly assigned within each pair. In others, each experimental unit receives both treatments in a random order
Describe how to select a simple random sample using slips of paper, technology or a table of random digits
-a simple random sample of size n is chosen in such a way that every group of n individuals in the population has an equal chance to be selected as the sample -slips of paper: assign numbers, mix paper thoroughly and choose randomly -technology: calculator MATH, Probability, randInt(1,10) (it will give me a random number between 1 and 10) label (give each individual a distinct number), randomize, select (choose the individuals that correspond to the randomly selected integers -table of random digits: (label, randomize, select)
Identify the experimental units and treatments in an experiment
-a treatment is a specific condition applied to the individuals in an experiment -an experimental unit is the object to which a treatment is randomly assigned -when the experimental units are humans, they are often called subjects
Evaluate if a statistical study has been carried out in an ethical manner (not required for AP exam)
-all planned studies must be reviewed in advance by an institutional review board -all individuals who are subjects in a study must give their consent -all individual data must be kept confidential
Distinguish between an observational study and an experiment, and identify the explanatory and response variables in each type of study
-an observational study observes individuals and measures variables of interest but does not attempt to influence the responses -an experiment deliberately imposes treatments (conditions) on individuals to measure their responses -a response variable measures an outcome of a study -an explanatory variable may help explain or predict changes in a response variable
Explain the concept of confounding and how it limits the ability to make cause- and-effect conclusions
-confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other
Identify voluntary response sampling and convenience sampling and explain how these sampling methods can lead to bias
-convenience sampling selects individuals from the population who are easy to reach -voluntary response sampling allows people to choose to be in the sample by responding to a general invitation -an experiment has bias if it is very likely to underestimate or overestimate the value you want to know
Describe a completely randomized design for an experiment
-in a completely randomized design, the experimental units are assigned to the treatments completely at random LOOK AT PAGE 283 IN TEXTBOOK
Explain the purpose of comparison, random assignment, control, and replication in an experiment
-in an experiment, a control group is used to provide a baseline for comparing the effects of other treatments -control means keeping other variables constant for all experimental units -replication means giving each treatment to enough experimental units so that a difference in the effects of the treatments can be distinguished from chance variation due to the random assignment Basic Principles of Experimental Design: -comparison: use a design that compares two or more treatments -random assignment: use chance to assign experimental units to treatments -control: keep other variables the same for all groups, especially variables that are likely to affect the response variable. Control helps avoid confounding and reduces variability in the response variable -replication: giving each treatment to enough experimental units so that any differences in the effects of the treatments can be distinguished from chance differences between the groups
Describe how to randomly assign treatments in an experiment using slips of paper, technology, or a table of random digits
-in an experiment, random assignment means that experimental units are assigned to treatments using a chance process -label, randomize, select
Identify the population and sample in a statistical study
-population is the entire group of individuals we want information about -sample is a subset of individuals in the population from which we collect data
Identify when it is appropriate to make an inference about a population and when it is appropriate to make an inference about cause and effect
-random selection of individuals allows inference about the population from which the individuals were chosen -random assignment of individuals to groups allows inference about cause and effect
Explain the concept of sampling variability when making an inference about a population and how sample size affects sampling variability
-sampling variability refers to the fact that different random samples of the same size from the same population produce different estimates -larger random samples tend to produce estimates that are closer to the true population value than smaller random samples (estimates from larger samples are more precise)
Describe how to select a sample using stratified random sampling, cluster sampling, and systematic sampling, and explain whether a particular sampling method is appropriate in a given situation
-stratified random sampling selects a sample by choosing an SRS from each stratum and combining the SRSs into one overall sample -strata are groups of individuals in population who share characteristics thought to be associated with the variables being measures in a study -cluster sampling selects a sample by randomly choosing clusters and including each member of the selected clusters in the sample -a cluster is a group of individuals in the population that are located near each other -systematic random sampling selects a sample from an ordered arrangement of the population by randomly selecting one of the first k individuals and choosing every kth individual thereafter
When experiments are impractical or unethical, what would be necessary to establish a cause and effect relation between two variables?
-strong association between the variables -an association between the variables is observed in many different settings -the alleged cause is plausible -there is no other obvious variable whose effect is confounded with the explanatory variable in the study
Describe the placebo effect and the purpose of blinding in an experiment
-the placebo effect describes the fact that some subjects in an experiment will respond favorably to any treatment, even an inactive treatment -in a double-blind experiment, neither the subjects nor those who interact with them and measure the response variable know which treatment a subject is receiving -in a single-blind experiment, either the subjects or the people who interact with them and measure the response variable do not know which treatment a subject is receiving
Explain how undercoverage, nonresponse, question wording, and other aspects of a sample survey can lead to bias
-undercoverage occurs when some members of the population are less likely to be chosen or cannot be chosen in a sample -nonresponse occurs when an individual chosen for the sample cannot be contacted or refuses to participate -response bias occurs when there is a systematic pattern of inaccurate answers to a survey question (untruthful answers, poorly worded questions and other problems lead to response bias)
Explain the meaning of statistically significant in the context of an experiment and use simulation to determine if the results of an experiment are statistically significant
-when the observed results of a study are too unusual to be explained by chance alone, the results are called statistically significant There are two ways to explain why the mean change in pulse rate was 1.2 greater for the caffeine group: 1. Caffeine does not have an effect on pulse rates, and the difference of 1.2 happened because of chance variation in the random assignment. 2. Caffeine increases pulse rates.