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Definitions--Chapter 1
Introductory Statistics definitions (the nature of statistics)
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Mathematics
Undergraduate 2
02/18/2013

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Term
Descriptive Statistics
Definition
consists of methods for organizing and summarizing information
Term
inferential statistics
Definition
consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the poupulation
Term
population
Definition
the collection of all individuals or items under consideration in a statistical study
Term
sample
Definition
that part of the population from which information is obtained
Term
observational study
Definition
researchers simply observe characteristics and take measurements, as in a sample survey
Term
designed experiment
Definition
researchers impose treatments and controls and then observe characteristics and take measurements
Term
census
Definition
obtaining information for the entire population of interest

may be time consuming, costly, impractical, or even impossible
Term
representative sample
Definition
reflects as closely as possible the relevant characteristics of the population under consideration
Term
probability sampling
Definition
a random device--such as tossing a coin, consulting a table of random numbers, or employing a random-number generator--is used to decide which members of the population will constitute the sample instead of leaving such decisions to human judgement
Term
simple random sampling
Definition
a sampling procedure for which each possible sample of a given size is equally likely to be the one obtained
Term
simple random sample
Definition
a sample obtained by simple random sampling
Term
simple random sampling with replacement
Definition
a member of the population can be selected more than once
Term
simple random sampling without replacement
Definition
a member of the population can be selected at most once
Term
table of random numbers
Definition
a table of randomly chosen digits
Term
systematic random sampling procedure
Definition
1. divide the population size by the sample size and round the result down to the nearest whole number, m

2. Use a random-number table or a similar device to obtain a number, k, between 1 and m

3. Select for the sample those members of the population that are numbered k, k+m, k+2m,...
Term
cluster sampling procedure
Definition
1. divide the population into groups (clusters)

2. obtain a simple random sample of the clusters

3. use all the members of the clusters obtained in step 2 as the sample
Term
stratified sampling
Definition
the population is first divided into strata, and then sampling is done from each stratum. Ideally, the members of each stratum should be homogenous relative to the characteristic under consideration.
Term
strata
Definition
subpopulations
Term
proportional allocation
Definition
the strata are sampled in proportion to their size
Term
stratified random sampling with proportional allocation procedure
Definition
1. Divide the population into subpopulations (strata)

2. From each stratum, obtain a simple random sample of size proportional to the size of the stratum; that is, the sample size for a stratum equals the total sample size times the stratum size divided by the population size

3. Use all the members obtained in Step 2 as the sample
Term
multistage sampling
Definition
used in large-scale surveys

combines one or more of simple random sampling, systematic random sampling, cluster sampling, and stratified sampling
Term
experimental units
Definition
the individuals or items on which the experiment is performed
Term
subject
Definition
term used when the experimental units are humans
Term
treatment
Definition
an experimental condition

for one-factor experiments, the treatments are othe levels of the single factor. for multifactor experiments, each treatment is a combination of levels of the factors.
Term
Principles of Experimental Design:
Control
Definition
two or more treatments should be compared
Term
Principles of Experimental Design:
Randomization
Definition
the experimental units should be randomly divided into groups to avoid unintentional selection bias in constituting the groups
Term
Principles of Experimental Design:
Replication
Definition
A sufficient number of experimental units should be used to ensure that randomization creates groups that resemble each other closely and to increase the chances of detecting any differences among the treatments
Term
treatment group
Definition
the group receiving the specified treatment
Term
control group
Definition
group receiving the placebo
Term
response variable
Definition
the characteristic of the experimental outcome that is to be measured and observed
Term
factor
Definition
a variable whose effect on the response is of interest in the experiment
Term
levels
Definition
the possible values of a factor
Term
completely randomized design
Definition
all the experimental units are assigned randomly among all the treatments
Term
randomized block design
Definition
the experimental units are assigned randomly among all the treatments separately within each block
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