ap stats unit 1 pt 2

experiment

a study in which researchers deliberately impose treatments on experimental units to measure their responses

response variable

variable that measures an outcome of a statistical study

explanatory variable

variable that may help predict or explain changes in a response variable

factors

explanatory variable in an experiment that is manipulated and may cause a change in the response variable

treatments

specific condition applied to the items or individuals in an experiment. if an experiment has several factors, a treatment is a combination of specific levels of these factors.

experimental units

item or individual to which a treatment is assigned

subjects

experimental units that are human beings

observational study

statistical study that observes items or individuals and measures the variables of interest, but does not impose treatments

retrospective

observational study in which observational units are selected at a point in time and data about them are gathered from the past

prospective

observational study that selects observational units at a point in time and gathers data about them both at that time and into the future

extraneous variables

variable other than the explanatory variable that may have an effect on the response variable

confounding variable

extraneous variable

→ associated with both the explanatory variable and the response variable in a statistical study

→ makes it difficult to determine whether changes in the explanatory variable cause changes in the response variable

random sampling

a chance process to determine which members of a population are chosen for the sample

simple random sample (SRS)

sample chosen in such a way that every group of n items or individuals in the population has an equal chance to be selected as the sample

sample without replacement

an item or individual from a population can be selected only once when choosing a sample

sample with replacement

an item or individual from a population can be selected more than once when choosing a sample

stratified random sample

sample selected by dividing the population into non-overlapping groups (strata) of items or individuals that share characteristics thought to be associated with the variables being measured in a study, selecting an SRS from each stratum, and combining the SRSs into one overall sample

strata (stratum)

groups of items or individuals in a population that share characteristics thought to be associated with the variables being measured in a study

homogenous

the items or individuals in a group are quite similar with respect to the variable of interest.

→ ideally, the items or individuals in a stratum are homogeneous

cluster random sample

sample selected by choosing an SRS of clusters and including each member of the selected clusters in the sample

clusters

group of items or individuals in the population that are located near each other

heterogenouse

the items or individuals in a group differ considerably with respect to the variable of interest.

→ ideally, the items or individuals in a cluster are heterogeneous, and each cluster mirrors the variability in the population

systematic random sample

sample selected by choosing individuals from an ordered arrangement of the population by randomly selecting one of the first k items or individuals in the population and choosing every kth item or individual thereafter

convenience sample

sample that consists of members of the population that are easy to reach.

→ leads to bias when the members of the sample differ from the population in ways that affect their responses

bias in statistical studies

shows bias if the resulting sample statistic is very likely to underestimate or very likely to overestimate the population parameter because of a flaw in the data collection process

voluntary response samples

sample that consists of people who choose to be in the sample by responding to a general invitation.

→ sometimes called self-selected samples.

→ leads to voluntary response bias when the members of the sample differ from the population in ways that affect their responses

undercoverage

when some members of the population are less likely to be chosen or cannot be chosen for a sample.

→ undercoverage bias occurs when the underrepresented items or individuals differ from the population in ways that affect their responses

sampling frame

list of all items or individuals in a population

nonresponse

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

→ nonresponse bias occurs when the individuals who can’t be contacted or who refuse to participate differ from the population in ways that affect their responses

questioning word bias

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 matters

response bias

when responses to a survey question consistently differ from the truth in the same way. includes bias due to question wording

random assignment

chance process to assign experimental units to treatments (or treatments to experimental units)

→ helps create roughly equivalent groups of experimental units by balancing the effects of extraneous variables among the treatment groups, allowing for cause-and-effect conclusions.

completely randomized design

the experimental units are assigned to the treatments completely at random

replication

give each treatment to multiple experimental units. using many experimental units in each treatment group helps researchers determine whether one treatment is more effective than another

direct control

keeping the values of some extraneous variables the same for all experimental units.

→ helps avoid confounding and reduces variability in the response variable

comparison

a design that compares two or more treatments.

→ some experiments include a control group to establish a baseline for measuring the effects of other treatments

blocks

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

blocking variable

variable used to form blocks in a randomized block design

randomized block design

forms groups (blocks) consisting of items or individuals that are similar in some way that is expected to affect the response to the treatments and then randomly assigns experimental units to treatments separately within each block so that all treatments occur within each block

matched pairs design

comparing two treatments that uses blocks of size 2. In some matched pairs designs, each experimental unit receives both treatments in a random order.

statistically significant

1) when the difference in responses between the groups is so large that it is unlikely to be explained by the chance variation in the random assignment

2) if the P-value is less than or equal to α, in that case, we reject the null hypothesis H(0) and conclude that there is convincing evidence for the alternative hypothesis H(a).

randomized distribution

distribution of a statistic generated by repeatedly reassigning the response values in an experiment to treatment groups, assuming that the specific treatment received doesn’t affect the response values

inference abt the population

conclusion about the larger population based on sample data. requires that the observational units are randomly selected from the population of interest

inference abt cause+effect

conclusion from the results of an experiment that the treatments caused the difference in responses. requires a well-designed experiment in which the treatments are randomly assigned to the experimental units and results that are statistically significant

informed consent

participants must be informed in advance about the nature of a study and any risk of harm it may bring

confidential

basic principle of data ethics that requires that a participant’s data be kept private

institutional review board (IRB)

board charged with protecting the safety and well-being of the participants in advance of a planned study and with monitoring the study itself

anonymity

names of individuals participating in a study are not known even to the director of the study