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Statistics: Chapter 12
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Terms in this set (41)
Prospective Study
An observational study in which subjects are followed to observe future outcomes; Because no treatments are deliberatly applied, a prospective study is not an experiment; Typically focus on estimating differences among groups that might appea as the groups are follwed during the course of the study
Experiment
An experiment manipulated factor leevls to create treatments, randomly assigns subjects to these treatment levels, and then compares the responses of the subject grouos acfoss treatment levels
Random assignment
To be valid, an experiment must assign experimental units to treatment groups at random
Factor
A variable whose levels are manipulated by the experiment; experiments attempt to discover the effects that differences in factor levels may have on the responses of the experimental units
Response
A variable whose values are compared across different treatments; in a randomized experiment, large response differences can be attributed to the effect of differences in treatment level
Experimental unit
Individuals on whom an experiment is performed; usually called subjects or participants
Level
The specific values that the experimenter chooses for a factor
Treatment
The process, intervention, or other controlled circumstances applied to randomly assigned experimental units; treatments are the different levels of a single factor or are made up of combinations of levels of two or more factors
Principles of experimental design
-Control aspects of the experiment that we know may have an effect on the response, but that are not the factors being studied
-Randomize subjects to treatments to even out effects that we cannot control
-Replicate over as many subjects as possible; results for a single subject are just anecdotes; if (as often happens) the subject of the experiments are not a representative sample from the population of interest, replicate the entire study with a different group of subjects, preferably from a different part of the population
-Block to reduce the effects of identifiable attributes of the subjects that cannot be controlled
Completely randomized design
In a completely randomized design, all experimental units have an equal chance of receiving any treatment
Statistically significant
When an observed difference is too large for us to believe that it is likely to have occurred naturally, we consider the difference to be statistically significant;
Control group
The experimental units assigned to a baseline treatment level, typically ether the default treatment, which is well understood, or a null, placebo treatment; their response provides a basis for comparison
Blinding
Any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups; here are two main classes of individuals who can affect the outcome of an experiment:
-those who could influence the results
-those who evaluate the results
Single-Blind
When every individual in EITHER class is blinded
Double-blinded
When everyone in BOTH classes is blinded
Placebo
A treatment known to have no effect; administered to one group so that all groups experience the same conditions; many subjects respond to such a treatment (a response known as the placebo effect); only by comparing with a placebo can we be sure that the observed effect of a treatment is not due simply to the placebo effect
Placebo effect
The tendency of many human subjects (often 20% or more) to show a response even when administered a placebo
Blocking
When groups of experimental units are similar, it is often a good idea to gather them together into blocks; by blocking we isolate the Variability attributable to the differences between the blocks so that we can see the differences caused by the treatments more clearly
Randomized block design
In a randomized bloc design, the subjects are randomly assigned to treatments only within blocks
Matching
In retrospective or prospective study, subjects who are similar in ways not under study may be matched and then compared with each other on the variables of interest; matching, like blocking, reduces unwanted variables
Confounding
When the levels of one factor are associated with the levels of another factor in such a way that their effects cannot be separated, we say that these two factors are confounded
What are observational studies?
In observational studies, researchers don't assign choices; they simply observed them
What are randomized, comparative experiments?
An experiment requires a random assignment of subjects to treatments; an experiment led must identify at least one explanatory variable, called a factor, to manipulate and at least one response variable to measure
What are the specific values that the experimenter chooses for a factor?
Levels of factor
What are the combinations of specific levels from all the factors that an experimental unit receives?
The treatment
What are the four principles of experimental designs?
1. Control
2. Randomize ("control what you can, randomize the rest")
3. Replicate
4. Block (blocking is an important compromise between randomization and control; it's not required in an experimental design)
When is an outcome statistically significant?
An outcome is statistically significant if the probability that it happened just by chance is so low that we're convinced there must be another explanation
Difference between experiments and surveys?
Experiments can draw stronger conclusions than surveys
What are control treatments?
A baseline measurement is called a control treatment and the experimental units to whom it is applied are called a control group; another level of the facto in order to compare the treatment results to a situation in which nothing happens
What is the best defense?
The best defense is to keep anyone who could affect the outcome or the measurement of the response form knowing which subjects have been assigned to which treatment
Who can affect the outcome of the experiment?
-Those who could influence the results
-Tjose who evaluate the results
Single blinded experiment
When all individuals in either of these classes are blinded
Double blinded experiment
When everyone in both classes are nlinded
Placebos
Best way to blind subjects from knowing whether they are receiving the treatment or not
What are the best experiments?
The best experiments are usually randomized, comparative, double blind, and placebo controlled
Randomized block design
The randomization occurs only within the blocks
Blocking in experiments is the same as stratifying in sampling...
Both group together subjects that are similar and randomize within those groups to remove unwanted variation
Completely randomized two factor experiments:
Any subject could end up assigned at random to any of the treatments
What is confounding?
When the levels of one factor are associated with the levels of another factor, we say that these two factors are confounding
Lurking variable
A lurking variable creates an association between two other variables that tempt us to think one may cause the other
Confounding
Confounding can arise in experiments when some other variable associated with a factor has an effect on the response variable- can't be thought of as causing
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Verified questions
PROBABILITY
A manager selects a random sample of 12 employees from the company’s total workforce and gives them a test that measures job related tension on a scale from 0 to 100. The scores from the 12 employees have a sample mean of 63.32 and a sample standard deviation of 18.40. The manager makes a report and states that based on these data, the average job related tension score for the whole workforce can be estimated as 63.32. This estimate has a standard error of about: A. 2.3 B. 3.3 C. 4.3 D. 5.3
STATISTICS
One-hour carbon monoxide concentrations in air samples from a large city have an approximately exponential distribution with mean 3.6 ppm (parts per million). Find the probability that the carbon monoxide concentration exceeds 9 ppm during a randomly selected one-hour period.
QUESTION
Suppose that in a random sample of 300 employed Americans, there are 57 individuals who say that they would fire their boss if they could. Calculate a 95% confidence interval for the population proportion. Write a sentence or two that interprets this interval.
PROBABILITY
For the model of Exercise 12.7 on page 451, test the hypothesis that \beta_{2}=0 at the 0.05 level of significance against the alternative that \beta_{2} \neq 0
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