AP Statistics Unit 3 Vocab

Population

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

Sample

the part of the population from which we actually gather information in order to learn about the population

Randomization

the best defense against bias, in which each individual is given a fair, equal chance of selection

Sample Size

the number of individuals in a sample

Census

a sample that consists of the entire population

Population parameter

a numerically valued attribute of a model for a population; we rarely expect to know the true value, but we estimate it from sampled data

Sample Statistic

actual values calculated for sampled data; used to estimate a parameter

Representative Sample

a sample that accurately reflects the corresponding population

Sampling Frame

a list of individuals from whom the sample is drawn

Sampling Variability

the tendency of randomly drawn samples to differ from one another

Sampling Error

another term used for sampling variability

Increasing Sample Size

tends to reduce sampling variability or sampling error

Random Sampling Methods

*simple random sample

*stratified random sample

*cluster sample

*systematic random sample

Simple Random Sample (SRS)

a sampling method in which every sample of a given size has an equal chance of being selected

Stratified Random Sample

a sampling design in which the population is divided into groups based on shared attributes (homogenous grouping), and a random sample is drawn from each subgroup

Benefits of Stratified Random Sampling

This benefits of this sampling method are that it:

*reduces sampling variability (when the strata are selected appropriately)

*helps to create a representative sample because the same percent of individuals are selected from each strata

When to Use Stratified Random Sampling

*use when the subgroups of a population are of different sizes

*use when there are more than two subgroups of the population that must be represented in the sample

Cluster Sample

a sampling design in which the population is divided into smaller, heterogenous groups that are ideally similar to one another in their composition; a number of groups are chosen at random and all individuals in those groups are part of the sample

Benefit of Cluster Sampling

the benefit of this sampling method is that it can be convenient, practical, and/or low-cost

Systematic Random Sample

a sampling method in which sample members are selected according to a random starting point and a fixed, periodic interval

Benefit of Systematic Random Sampling

the benefit of this sampling method is that it can be more practical or less costly

How to draw an SRS:

1. Label each individual with an integer 1 through N.

2. Use a RNG to generate x unique integers between 1 and N, inclusive.

3. The individuals that correspond to the randomly generated integers will be included in the sample and ...(state what will be done).

How to draw a Stratified Random Sample:

Start with the individuals in the first stratum.

1. Label each individual in the stratum with an integer 1 through N.

2. Use a RNG to generate x% unique integers between 1 and N, inclusive.

3. The individuals that correspond to the randomly generated integers will be included in the sample and ... (state what will be done).

4. Repeat steps 1 through 3 within each stratum, and sample the same percent from each stratum.

How to draw a Cluster Sample:

1. Label each cluster with an integer 1 through N.

2. Use a RNG to generate x unique integers between 1 and N, inclusive.

3. The clusters that correspond to the randomly generated integers will be included in the sample, and all of the individuals within these clusters will ...(state what will be done).

How to draw a Systematic Random Sample:

1. Label each individual with an integer 1 through N.

2. Use a RNG to generate one integer between 1 and N, inclusive.

3. The individual that corresponds to the randomly generated integer will be included in the sample and ...(state what will be done).

**Now decide the frequency at which an individual will be selected (represented by x below).

4. Every "x" individuals in the list after the first individual will be included in the sample and ...(state what will be done).

5. Select every xth individual until the desired sample size is acheived, and start over at the beginning of the list if necessary. Individuals cannot be picked more than once.

Biased Sampling Methods

*voluntary response sample

*convenience sample

Bias

a systematic failure of a sampling method to represent its population; is the result of a poor sampling method

4 Types of Bias

*voluntary response bias

*undercoverage

*nonresponse bias

*response bias

Voluntary Response Bias

occurs when individuals can choose on their own whether to participate in the sample

Undercoverage

occurs when part of the population has less representation in the sample than it has in the population

Nonresponse Bias

occurs when the individuals in the sample cannot or will not respond

Response Bias

occurs when the survey design influences responses

Clusters

heterogenous groups that are ideally representative of the population

Strata

homogenous groups that are a part of the population

Observational Study

a study based on data in which no manipulation of factors has been employed (no treatments)

3 types of Observational Studies

1. Retrosepctive study

2. Prospective study

3. Sample Survey

Retrospective Study

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

Prospective Study

an observational study in which subjects are followed to observe future outcomes

Sample Survey

an observational study in which data is collected from a sample in the hope of learning something about the entire population from which the sample was taken

Experiment

manipulates factor levels to create treatments, randomly assigns subjects to these treatment levels, and then compares the responses of the subject groups across treatment levels

Random Assignment

assigning participants to experimental and control groups by chance, thus minimizing preexisting differences between those assigned to the different groups; necessary for a valid experiment

Factor

an explanatory variable whose levels are manipulated by the experimenter

Levels

the specific values that the experimenter chooses for a factor

Response Variable

an outcome from the experimental units that is measured after the treatments have been administered

Statistically Significant

when an observed difference is too large to believe that it is likely to have occurred naturally or by chance alone

Experimental Units

individuals on whom an experiment is performed

Experimental Units that are People

*Subjects

*Participants

Treatments

the different levels of a single factor or combinations of levels of two or more factors that are applied to the experimental units

Principles of Experimental Design

*Comparison of at least two treatment groups (which could include a control group)

*Random assignment/allocation of treatments to experimental units

*Replication (multiple experimental units in each treatment group)

*Blocking to control potential confounding variables (when appropriate)

Completely Randomized Design

an experimental design in which the experimental units have an equal chance of receiving each treatment

Replication

*Repeating conditions within an experiment to determine the reliability of effects and increase internal validity

*repeating whole experiments to determine the generality of findings of previous experiments to other subjects, settings, and/or behaviors

Purpose of Replication

to isolate and estimate the variability in the response variable among the experimental units

Control

to hold constant the variables that are not being studied for all treatment groups

Control Group

the experimental units that are assigned the control treatment

Purpose of Control

to reduce variability in the response variable, and to provide a baseline to make it easier to detect the differences among treatment groups

Placebo

measures the response of simply administering a treatment to the individuals

Placebo Effect

occurs when experimental units have a response to a placebo

Purpose of Blinding

*to avoid the subconscious (or conscious) altering of data

*to avoid the placebo effect

Single-Blind Experiment

Either:

*the subjects do not know which treatment they are receiving, but members of the research team do

Or:

*the subjects know which treatment they are receiving, but members of the research team do no

Double-Blind Experiment

neither the subjects nor the members of the research team who interact with them know which treatment a subject is receiving

Confounding Variable

a variable that is related to the explanatory variable (or factor) and influences the response variable and may create a false perception of association between the two; the effects of the factor and confounding variable cannot be separated

Blocking

*ensures at the beginning of the experiment that the units within each block are similar to each other with respect to at least one variable that may impact the response variable

*isolates the variability attributable to the differences between the blocks so that the differences caused by the treatments can be more clearly seen

Randomized Complete Block Design

treatments are assigned completely at random within each block

Matched Pairs Design

a randomized blocked experiment in which each block consists of a matching pair of similar experimental units; may be formed naturally or by the experimenter

Causal Relationship

cannot be determined for variables whose data was collected in an observational study; can be determined when there are statistically significant differences among experimental treatment groups

Making Generalizations About a Population

is only appropriate when samples are randomly selected or otherwise representative of that population