AP Statistics Test Review

What are the principles of experimental design?

1. control (the lurking variables in the design) 2. replicate (on many units to reduce variation) 3. randomize (randomly assigning experimental units to treatments and vice versa)

What is Multi-stage sample?

A multi-stage sample is a sample that combine two or more sampling methods.

Define placebo effect

A response to the dummy treatment.

What is sample?

A sample is the part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population.

Define treatment(s)

A specific condition applied to the individuals in an experiment.

What's a table of random digits?

A table of random digits is a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with the properties that each entry in the table is equally likely to be any of the 10 digits 0-9, the entries are independent of each other. That is, knowledge of one part of the table gives no information about any other part.

What is random selection?

A way of ensuring that a sample of people is representative of a population by giving everyone in the population an equal chance of being selected for the sample

What's a simple random sample (SRS)?

An "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.

What is a double-blind experiment?

An experiment where neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.

What does it mean if the results of an experiment are statistically significant?

An observed effect so large that it would rarely occur by chance is called statistically significant.

What are convenience samples?

Choosing individuals who are easiest to reach results is a convenience sample

What does it mean if a study is double-blind? single-blind?

If a study is double-blind, neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received. And if a study is when the subjects are unaware of which treatment they are receiving, but the people interacting with them and measuring the response variable do know.

Explain in experiments why we use random assignment to treatment groups.

If treatments are given to groups that differ greatly, bias will result, so instead random assignment is the solution to this meaning that experimental units are assigned to treatments at random, that is, using some sort of chance process.

How to do experiments, explain if you don't consider lurking variables.

If you design an experiment with a treatment, experimental units, subjects, explanatory variables, and the response variable, but you don't take into consideration the lurking variables; they can make it hard to see the true relationship between the explanatory and response variables making them influence the response variable.

Completely randomized design vs. randomized block design

In a randomized block design, the random assignment of experimental units to treatments is carried out separately within each block. In a completely randomized design, the treatments are assigned to all the experimental units completely by chance.

What is a block?

Is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.

Define treatment group

Is a group that receives a treatment in an experiment.

What is a matched-pairs design?

Is a randomized blocked experiment in which each block consists of a matching pair of similar experimental units. Chance is used to determine which unit in each pair gets each treatment. Sometimes, a "pair" in a matched-pairs design consists of a single unit that receives both treatments. Since the order of the treatments can influence the response, chance is used to determine with treatment is applied first to each unit.

What is a lurking variable?

Is a variable that is not among the explanatory or response variables in a study but that may influence the response variable.

Define response variable

Is something that reacts to changes you make in an experiment.

What is the purpose of a control group? Do all experiments need control groups?

It receives an inactive treatment or an existing baseline treatment. Not all experiments require a control group, because there may not be a need for an inactive treatment.

Explain non-response

Occurs when an individual chosen for the sample can't be contacted or refuses to participate.

What is a confounding variable?

Occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.

What do you use for a SRS?

People often use random numbers generated by a computer or calculator to choose samples. But if no available, you can use a table of random digits.

What the difference between random selection and random assignment?

Random selection uses chance to select a sample. While random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process.

What is sampling error (sampling variability)?

Sampling errors are results that differs from the truth about the population. They come with a margin of error that sets bounds on the size of the likely error.

What are sampling errors?

Sampling errors come from the act of choosing a sample. Random sampling error and undercoverage are common types of error.

When doing experiments explain confounded variables?

The confounding variable in an experiment consists of two variables on a response variable that cannot be separated from each other can affect the experiment. With no association between the lurking variable and the explanatory variable, there can be no confounding.

How is a cluster sample different from a stratified random sample?

The difference between a cluster sample and a stratified random sample is that in a cluster it's the whole cluster that's chosen to represent the population, but in a stratified sample there are an equal amount of individuals chosen in the individual small strata's then combined together to represent the entirety of the population.

What's the difference between stratification and blocking?

The difference between stratification and blocking is that in a strata it is separating a population into groups of similar individuals to represent it as a whole while blocking is selecting a group of somewhat similar experimental units to affect the response to treatments in some way.

What's the difference between the conclusions you can make in an observational study vs. an experiment?

The difference between the conclusions you can make in an observational study vs. an experiment is that the goal of an observational study can be to describe some group or situation, to compare groups, or to examine relationships between variables by not attempting to influence the responses but the conclusions can be affected by lurking variables or confounding between the explanatory variable. While the purpose of an experiment is to determine whether the treatment causes a change in response by deliberately imposing some treatment on individuals to measure their responses with limiting the amount of extra variables.

What is the distinction between sample and population?

The distinction between population and sample is that the population is the entirety of the group of individuals while the sample is only a part of the population. You must know what population the sample represents.

What are random assignments?

The experimental units are assigned to treatments at random, that is, using some sort of chance process

What are non-sampling errors?

The most serious errors are nonsampling errors. Common types of sampling error include nonresponse, response bias, and wording of questions.

What is population?

The population in a statistical study is the entire group of individuals about which we want information.

What is strata?

The population of groups of similar individuals.

What's the problem with convenience samples?

The problem with convenience samples are that they often produce unrepresentative data. Typically the sample doesn't represent the population as a whole.

What is a randomized block design?

The random assignment of experimental units to treatments is carried out separately within each block

Explain question wording

The wording of questions is the most important influence on the answers given to a sample survey. Confusing or leading questions can introduce strong bias, and changes in wording can greatly change a survey's outcome, even the order in which questions are asked matter.

Define experimental units/subjects

They are the smallest collection of individuals to which treatments are applied, when the units are human beings they are called subjects.

What is the purpose of random assignment? a. to balance the effects of...

To balance the effects of bias.

What is the purpose of replication? a. To make it easier to...

To make it easier to distinguish the differences in the effects of the treatments from chance differences between groups.

What are 2 reasons for controlling as much of the experiment as possible? a. to prevent lurking variables from... b. to reduce variability in the...

To prevent lurking variables from affecting the explanatory and response variables to ultimately reduce the variability in the results.

What is stratified sample?

To select a stratified sample, first classify the population into groups of similar individuals. Then choose a separate SRS in each stratum and combine these simple random samples to form the full sample.

What is Cluster sample?

To take a cluster sample, first divide the population into smaller groups. Ideally, these clusters should mirror the characteristics of the population. Then choose an SRS of the clusters. All individuals in the chosen clusters are included in the sample.

Explain undercoverage sample

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

Explain response

When an individual chosen for the sample is contacted and actively participates.

How should you choose which variables to block for?

You should choose the experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments. Form blocks based on the most important unavoidable sources of variability (lurking variables) among the experimental units.

What is a treatment?

a specific condition applied to the individuals in an experiment

What does statistically significant mean?

an observed effect so large that it would rarely occur by chance

Define level(s)

combination of specific values

What's a voluntary response sample?

consists of people who choose themselves by responding to a general appeal. They show bias because people with strong opinions (often in the same direction) are most likely to respond.

What is an experiment?

deliberately imposes some treatment on individuals to measure their responses.

What is bias?

design of a statistical study that systematically favors certain outcomes.

Define placebo

is a "dummy pill" or inactive treatment that is indistinguishable from the real treatment.

What is a matched pairs design?

is a randomized blocked experiment in which each block consists of a matching pair of similar experimental units. Chance is used to determine which unit in each pair gets each treatment. Sometimes, a "pair" in a matched-pairs design consists of a single unit that receives both treatments. Since the order of the treatments can influence the response, chance is used to determine with treatment is applied first for each unit.

What is an observational study?

observes individuals and measures variables of interest but does not attempt to influence the responses

What is a simple random sample? a. hat, random number generator

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.

What is a control group?

receives an inactive treatment or an existing baseline treatment

Define factor(s)

the explanatory variables in an experiment are called factor(s)

What is inference?

the process of drawing conclusions from related pieces of evidence and previous experience with the evidence. The process of drawing conclusions about a population on the basis of sample data.

What are the experimental units?

the smallest collection of individuals to which treatments are applied

What is a completely randomized design?

the treatments are assigned to all the experimental units completely by chance

What are subjects?

when experimental units are humans