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| way of thinking for which math is the tool |
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| studying a portion of the population |
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| studies the whole population by surveying the entire population |
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| Convenience Sampling, Voluntary Response |
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| Interviews easiest to reach (i.e. friends) |
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| measures only strong opinions |
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| Exploratory Data Analysis |
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| discover and describe what data say by using graphs and numerical summaries |
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| measures variables, but does not attempt to influence the responses. Records values for a variable of interest. |
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| deliberately imposes some treatment on individuals to influence their response |
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effects on a response variable cannot be distinguished from another lurking variable.
Example:
Those who attend church (explanatory variable x) generally live longer (response variable y). This is a correlation. However, lurking variable z (behavior, genes, etc) might affect variable y. |
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| Simple Random Sampling (SRS) |
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| Can be chosen through TRD. Each sample has an equal and random chance of being selected. |
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| sample chosen by chance. must know which samples are possible and the probability it is. |
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for a large population spread over a wide area, sample important groups (strata) separately, then combine the results.
Congress is an example. |
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| Differences between Studies and Experiments |
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Definition
Studies: can only show a correlation, no treatments
Experiments: cost more, more time involved, can show cause, imposes treatment |
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| Undercoverage, nonresponse, response, wording of questions |
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| some parts of the population, when taking a survey, are missed |
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| (can be 30% or more) higher in urban areas |
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Telescoping - fault memory
- Bias towards interviewer's characteristics
- Respondents may lie, especially about illegal behavior |
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| word questions so they are not misleading or confusing |
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| select small samples within a larger population |
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| Divide population into clusters & randomly choose a few clusters to survey. Survey everyone in the clusters. |
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| experiment objects; cannot be human. Humans are called subjects instead. |
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| explains changes. generally the treatment. |
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| Measure of what happened (or not) |
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generally the explanatory variable.
combination of factor & level. |
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| value or amount of a factor |
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Definition
Example:
Those who do well on SAT Math (variable x) also do well on SAT Verbal (variable y). This is a correlation. However, lurking variable z (i.e. cheating, school education) can cause either of the good schools. |
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| Principles of Experimentation |
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Definition
1. Randomization (balance subject variables - chance to assign E.U. to treatments)
2. Replication (each treatment on many units - reduce chance variation)
3. Control (for lurking variables) |
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Definition
| just getting treatment, in this case - a treatment with no value, causes a change. |
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| Design an experiment to test if SAT classes really work |
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Definition
1. Label students 01-90 and use TRD to separate them into 3 treatment groups. 3 different treatments, 1 for each group with a fixed time (factor). Then compare response variables (change in test scores) .
This employs 1 factor and 3 levels. |
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Term
Design an experiment to test if SAT classes really work
(other option) |
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Definition
| 30 students from Mills with a 3.5 GPA average are to take a practice SAT test at the same time. Then, the students are divided into 2 groups at random. One group (w/ the explanatory variable) will be forced to attend 8 weeks of SAT class 4x a week. The other half will be asked to study independently. |
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Definition
| controls a single variable that we think will affect our response variable. |
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| uses experimental units that are exactly the same except for treatment (i.e. twins) |
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| the use of chance to divide experimental units into groups |
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| describes response variables, factors (explanatory), layout of treatments. Focuses on comparison. |
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| Statistically Significant |
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Definition
| hope to see a difference in response so large its unlikely just chance variation |
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| all E.U. are allocated at random among all treatments |
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| neither the subjects nor those who work with them know which treatment a subject receives. Avoids unconscious bias. |
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| subjects or treatments or setting of an experiment may not realistically duplicate the conditions we want to study |
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| 120 subjects -> block for gender = 60 men, 60 women -> split into groups of 20 (3 treatments each) |
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| Subjects (twins) -> random assignment -> each group receives separate treatment |
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| group of E.U.'s that are known before the experiment to be similar in some way that is expected to affect the response of the treatments |
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Definition
| random assignment of units to treatments is carried out separately in each group |
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Definition
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 conclusions |
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Definition
| of trials means that the results of one trial does not influence the result of the next trial (EX: toin cosses, heads on first toss does not increase the chance that the next will be a tail) |
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| Mr. Belzer wnats to get student input on a new tardy policy. He wants to be sure that he gets opinions from students in all grades. What would be the best sampling technique? |
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Definition
| Stratified Random Sampling |
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Term
| Compare and contrast Stratified Random Sampling and Cluster Sampling. |
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Definition
In stratified random sapling, a population is separated into stratas (groups). Then, a subject(s) is selected randomly be surveyed. This subject(s) is designed to represent the whole strata.
In cluster sampling, a population is also separated into groups. A cluster is randomly chosen to be surveyed. However in this case, everyone in the cluster is surveyed. |
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| He decides to choose 50 students from the student body of 800 students. |
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| Population: 800, label: 01-800. |
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