Stats: Chapters 11, 12, & 13

Front 1

When is an event random?

Back 1

If we know what outcomes could happen, but not which particular values will happen.

Front 2

Random numbers are easy/hard to generate?

Back 2

Hard.

However, random number tables and/or generators easily allow for them to be used to create a random sample, survey, etc.

Front 3

What is a simulation?

Back 3

It models random events by using random numbers to specify event outcomes with relative frequencies that correspond to the true real-world relative frequencies we're trying to model.

Front 4

What is a simulation component?

Back 4

The most basic situation in a simulation in which something happens at random.

Front 5

Outcome

Back 5

An individual result of a component of a simulation is its outcome.

Front 6

Trial

Back 6

The sequence of several components representing events that we are pretending will take place.

Front 7

Response variable =

Back 7

Y; the dependent variable.

Or, ultimately, it's the results of each trial with respect to what we're interested in.

Front 8

Population:

Back 8

The entire group of individuals or instances about whom we hope to learn.

Front 9

Sample:

Back 9

A (representative) subset of a population, examined in hope of learning about the population.

Front 10

Sample survey:

Back 10

A study that asks questions of a sample drawn from some population in the hope of learning something about the entire population.

Polls taken to assess voter preferences are common sample surveys.

Front 11

Bias:

Back 11

Any systematic failure of a sampling method to represent its population.

It is almost impossible to recover from bias, so efforts to avoid it are well spent.

Front 12

What are the main types of bias?

Back 12

(1) Relying on voluntary response

(2) Undercoverage of the population.

(3) Nonresponse bias

(4) Response bias

Front 13

Randomization:

Back 13

The best defense against bias in which each individual is given a fair, random chance of being selected.

Front 14

Matching:

Back 14

Any attempt to force a sample to resemble specified attributes of the population.

Matching may help make better samples, but is no substitute for randomization.

Front 15

Sample size:

Back 15

The number of individuals in a sample.

The sample size determines how well the sample represents the population, NOT the fraction of the population sampled.

Front 16

Census:

Back 16

A sample that consists of the entire population.

Front 17

Population parameter:

Back 17

A numerically valued attribute of a model for a population.

We rarely expect to know the true value of a population parameter. but we do hope to estimate it from sampled data.

Example: the mean income of all employed people in the country.

Front 18

Statistic:

Back 18

Values calculated for sampled data.

Front 19

Representative:

Back 19

A sample is said to be representative if the statistics computed from it accurately reflect the corresponding population parameters.

Front 20

Simple Random Survey (SRS):

Back 20

A simple random sample of sample size (n) is one in which each set of (n) elements in the population has an equal chance of selection.

Front 21

Sampling frame:

Back 21

A list of individuals from whom the sample is drawn.

Individuals who may be in the population of interest but are not in the sampling frame cannot be included in any sample.

Front 22

Sampling variability:

Back 22

The natural tendency of randomly drawn samples to differ, one from another.

Sometimes, unfortunately, called sampling error, sampling variability is no error at all - but just the natural result of random sampling.

Front 23

Stratified Random Sample:

Back 23

A sampling design in which the population is divided into several subpopulations, or strata, and random samples are then drawn from each stratum.

If the strata are homogenous but are different from each other, a stratified sample may yield more consistent results.

Front 24

Cluster Sample:

Back 24

A sampling design in which entire groups, or clusters, are chosen at random.

Cluster sampling is usually selected as a matter of convenience, practicality, or cost.

Each cluster should be heterogenous (and representative of the population), so all the clusters should be similar to each other.

Front 25

Multistage Sample:

Back 25

Sampling schemes that combine several sampling methods.

Example: a national polling service may stratify the country by geographical regions, select a random sample of cities from each region, and then interview a cluster of residents in each city.

Front 26

Systematic Sample:

Back 26

A sample drawn by selecting individuals systematically from a sampling frame.

When there is no relationship between the order of the sampling frame and the variables of interest, a systematic sample can be representative.

Front 27

Voluntary response bias:

Back 27

Bias introduced to a sample when individuals can choose on their own whether to participate in the sample.

Samples based on voluntary response are always invalid and cannot be recovered.

Front 28

Convenience sample:

Back 28

Consists of the individuals who are "conveniently" available.

These samples often fail to be representative seeing as every individual in the population is not equally convenient to the sample.

Front 29

Undercoverage:

Back 29

A sampling scheme that biases the sample in a way that gives a part of the population less representation than it has in the population.

Front 30

Nonresponse bias:

Back 30

Bias introduced to a sample when a large fraction of those sampled fail to respond. Those who actually do respond aren't likely to represent the whole.

Voluntary response bias is a form of nonresponse bias, but nonresponse may occur for other reasons as well.

Front 31

Response bias:

Back 31

Anything in a survey that influences responses including the wording of questions, how you approach them, etc.

Front 32

Basics of Stratified Sampling:

Back 32

(1) Homogeneous; population broken into different groups.

(2) "Some of all"

Front 33

Basics of Cluster Sampling:

Back 33

(1) Heterogeneous; taking all student responses from some of the classrooms.

(2) "All of some"

Front 34

Basics of Systematic Sampling:

Back 34

(1) Often the least expensive method of sampling.

(2) Randomly pick the first person but after them choose every 10th person.

ONLY works if the first person is chosen randomly.

Front 35

Basics of Multistage Sampling:

Back 35

Incorporates various methods of sampling.

Front 36

Basics of Nonresponse Bias:

Back 36

Can arise when sampled individuals will not or cannot respond.

Front 37

Basics of Response Bias:

Back 37

When the answers of those responding may be influenced by external factors such as the wording of the questions, how they're approached, or interviewer behavior.

Front 38

What samples are most likely to be biased?

Back 38

Voluntary response samples.

Front 39

Basics of Undercoverage Bias:

Back 39

Not including people in the population such as those who do not have cell phones, internet connection, are homeless, are unlisted, etc.

Front 40

Basics of Overcoverage Bias:

Back 40

Voluntary responses; those who use InstaPolls or online polls/samples/surveys.

Only those who are interested in responding will respond and that doesn't represent a larger realm of people that is needed to be sampled.

Front 41

How is the population of interest usually determined?

Back 41

By "why"

Front 42

What are the subjects called?

What are humans called?

Back 42

Experimental units; if humans use the term participants or subjects.

Front 43

Observational Study:

Back 43

A study based on data in which no manipulation of factors has been employed.

Front 44

Confounding:

Back 44

Essentially something that you didn't control that affected your experiment and its results (i.e. lurking variables).

Something else that could explain your results.

Front 45

What are the two types of observational studies; briefly describe.

Back 45

Retrospective: looking back and studying previous behaviors or conditions.

Prospective: subjects are followed to observe future outcomes.

Front 46

Retrospective study:

Back 46

An observational study in which subjects are selected and then their previous behaviors or conditions are determined.

Because retrospective studies are not based on random samples, they usually focus on estimating differences between groups or associations between variables.

Front 47

Prospective study:

Back 47

An observational study in which subjects are followed to observe future outcomes.

Because no treatments are deliberately applied, a prospective study is not an experiment.

They're typically focused on estimating differences among groups that might appear as the groups are followed during the course of the study.

Front 48

Experiment:

Back 48

An experiment MANIPULATES factor levels to creat treatments, RANDOMLY assigns subjects to these treatment levels, and then compares the responses of the subject groups across treatment levels.

Front 49

Random assignment:

Back 49

To be valid, an experiment must assign experimental units to treatment groups at random.

Front 50

Factor:

Back 50

A variable whose levels are controlled by the experimenter.

Experiments attempt to discover the effects that differences in factor levels may have on the responses of the experimental units.

Front 51

Response:

Back 51

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.

Front 52

Experimental units:

Back 52

Individuals on whom an experiment is performed.

Usually called subjects and/or participants when they're human.

Front 53

Level:

Back 53

The specific values that the experimenter chooses for a factor are called the levels.

Front 54

Treatment:

Back 54

The process, intervention, or other controlled circumstance 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.

Front 55

Principles of Experimental Design:

Back 55

(1) Control: aspects of the experiment that we know may have an effect on the response.

(2) Randomize: subjects to treatments to even out effects that we cannot control.

(3) Replicate: as many subjects as possible. If the subjects are not representative of the population of interest, replicate the entire study with a different group of subjects - preferably from a different part of the population

(4) Block: to reduce efects of identifiable attributes of the subjects that cannot be controlled.

Front 56

Statistically significant:

Back 56

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.

Front 57

Control group:

Back 57

The experimental units assigned to a baseline treatment level, typically either the default treatment, which is well understood, or a null, placebo treatment.

Their responses provide a basis for comparison.

Front 58

Blinding:

Back 58

Any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups is said to be "blind."

Front 59

Single-blind/Double-blind:

Back 59

There are two main classes of individuals who can affect the outcome of an experiment:

(1) Those who could influence the results (the subjects, treatment administrators, or technicians).

(2) Those who evaluate the results (judges, treating physicians, etc.)

When every individual in either of these cases is blinded = single-blind.

When everyone in both cases is blinded = double-blind case.

Front 60

Placebo:

Back 60

A treatment known to have no 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.

Front 61

Placebo Effect:

Back 61

The tendency of many human subjects (often 20% or more of experiment subjects) to show a response even when administered a placebo.

Front 62

Block:

Back 62

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.

Examples: blocking full-term babies from premature, ethnicity, gender, etc.

Front 63

Matching:

Back 63

In a 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 variation.

Front 64

Matched Pairs:

Back 64

Putting the same type of person (very similar statistics) in different testing environments to make more accurate statements of your data.