Statistics: Concepts & Controversies Exam #1

Individuals

objects described by a set of data; may be people, but they may also be animals or things

Variable

any characteristic of an individual; it can take different values for different individuals

Response

a variable that measures an outcome or result of a study

Observational Study

observes individuals and measures variables of interest but does not intervene in order to influence the responses; the purpose of an observational study is to describe some group or situation

Sample Surveys

an important kind of observational study; they survey some group of individuals by studying only some of its members, selected not because they are of special interest but because they represent the larger group

Population

is the entire group of individuals in a statistical study, which we want information on

Sample

the part of the population from which we actually collect information and is used to draw conclusions about the whole

Census

a sample survey that attempts to include the entire population in the sample

Experiment

deliberately imposes some treatment on individuals in order to observe their responses; the purpose of an experiment is to study whether the treatment causes a change in the response

Biased

the design of a statistical study systematically favors certain outcomes

Convenience Sampling

selection of whichever individuals are easiest to reach; often biased

Voluntary Response Sample

chooses itself by responding to a general appeal, write-in or call-in opinion polls are examples; often biased

Simple Random Sample (SRS)

of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected

Table of Random Digits

lists a long string of randomized digits, entries are independent of each other and helps in the selection of an SRS

Parameter

a number that describes the population; it is a fixed number, but in practice we don't know the actual value of this number

Statistic

a number that describes the sample; the value of a statistic is known when we have taken a sample, but it can change from sample to sample; often used to estimate an unknown parameter

Bias

a consistent, repeated deviation of the sample statistic from the population parameter in the same direction when we take many samples

Variability

describes how spread out the values of the sample statistic are when we take many samples; large variability means that the result of good sampling is not repeatable

Good Sampling Method

has both small bias and small variability

To reduce bias

use random sampling; when we start with a list of the entire population, an SRS produces unbiased estimates: the values of a statistic computed from an SRS neither consistently overestimate nor consistently underestimate the value of the population parameter

To reduce the variability

of an SRS, use a larger sample; you can make the variability as small as you want by taking a large enough sample

Confidence Statement

has two parts: a margin of error and level of confidence

Margin of Error

says how close the sample statistic lies to the population parameter

Level of Confidence

says what percentage of all possible samples satisfy the margin of error

Sampling Errors

are errors caused by the act of taking a sample; they cause sample results to be different from the results of the census

Random Sampling Error

the deviation between the sample statistic and the population parameter caused by chance in selecting a random sample; the margin of error in a confidence statement includes only random sampling error

Nonsampling errors

are errors not related to the act of selecting a sample from the population, they can be present even in a census

Undercoverage

occurs when some groups in the population are left out of the process of choosing the sample

Processing Errors

mistakes in mechanical tasks such as doing arithmetic or entering responses into a computer

Response Error

another type of nonsampling error, which occurs when a subject gives an incorrect response

Nonresponse

is the failure to obtain data from an individual selected for a sample; most nonresponse happens because some subjects can't be contacted or because some subjects who are contacted to cooperate

Probability sample

a sample chosen by chance

Stratified Samples

Simple Random Samples

Response Variable

A variable that measures an outcome or result of a study

Explanatory Variable

A variable that we think explains or causes changes in the response variable

Subjects

Individuals studied in an experiment

Treatment

Any specific experimental condition applied to the subjects; if an experiment has several explanatory variables, a treatment is a combination of specific values of these variables

Lurking Variable

A variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variables studied

Confounded

Two variables are confounded when their effects on a response variable cannot be distinguished from each other; the confounded variable may either be explanatory variables or lurking variables

Clinical Trials

Experiments that study the effectiveness of medical treatments on actual patients

Placebo Effect

A placebo is a dummy treatment with no active ingredients

Double-blind

An experiment in which neither subjects nor physicians recording the symptoms know which treatment was received

Randomized Comparative Experiment

Compare two or more treatments, use chance to decide which subjects get each treatment, and use enough subjects so that the effects of chance are small

Control Group

Comparing the treatment and control groups allows us to control the effects of lurking variables

Statistically Significant

An observed effect of a size that would rarely occur by chance

Nonadherers

Subjects who participate but don't follow the experimental treatment, can also cause bias

Dropouts

Subjects who begin the experiment but do not complete it

Completely Randomized

All the experimental subjects are allocated at random among all the treatments

Matched Pairs Design

Compares just two treatments; common design that combines matching with randomization by choosing pairs of subjects that are as closely matched as possible

Block

A group of experimental subjects that are known before the experiment to be similar in some way that is expected to affect the response to the treatments

Block Design

The random assignment of subjects to treatments is carried our separately within each block

Institutional Review Board

Organization that carries out the study must be reviewed by this board; they review all planned studies in advance in order to protect the subjects from possible harm

Informed Consent

All individuals who are subjects in a study must give their informed consent before data are collected

Confidential

All individual data must be kept confidential; only statistical summaries for groups of subjects may be made public

Anonymity

Subjects are anonymous, their names are not known even to the director of the study; confidentiality is not the same as anonymity

Measure

A property of a person or thing when we assign a number to represent a property

Instrument

An item used to make a measurement; we may have a choice of the units we use to record the measurements

Variable

The results of measurement is a numerical variable that takes different values for people or things that differ in whatever we are measuring

Valid

A variable is valid measure of a property if it is relevant or appropriate as a representation of that property

Rate

A fraction, proportion, or percentage at which something occurs is a more valid measure than a simple count of occurences

Predictive Validity

A measurement of a property has predictive validity if it can be used to predict success on tasks that are related to the property measured

Bias

A measurement process has bias if it systematically tends to overstate or understate the true value of the property it measures

Random Error

A measurement process has random error if repeated measurements on the same individual give different results.

Reliable

If the random error is small, we say the measurement is reliable

Variance

To determine if the random error is small, we can use a quantity called variance

Average

The average of several repeated measurements of the same individual is more reliable (less variable) than a single measurement