ap stats final

population

the entire group of individuals about which we want information

sample

a subset of the population from which we collect information from

census

collects data from the entire population

convenience sample

choosing individuals who are easiest to reach, not randomized

voluntary response sampling

allows people to choose to be in the sample by responding to a general invitation (biased)

simple random sample (SRS)

every group of n individuals in the population has an equal chance to be selected as the sample

stratified random sample

selects a sample by choosing an SRS from each stratum and combining SRS's into one overall sample

cluster sample

obtained by selecting all individuals within a randomly selected collection or group of individuals

strata

groups within a population that are homogeneous (similar) based on a characteristic that is relevant to the study.

cluster

groups within diverse populations and ideally represent the population on a smaller scale (location)

systematic random sample

selects a sample from an ordered arrangement of the population by randomly selecting one of the first k individuals and choosing every kth individual thereafter

bias

the systematic favoring of certain outcomes due to the method of collecting data, usually due to the design of the statistical study and its over/underestimation of the value we want to know

sampling frame

a list of all individuals in the population

nonresponse bias

occurs when an individual chosen for the sample can't be contacted or refuses to respond

undercoverage

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

observational study

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

response bias

when participants in a study or survey provide answers that are inaccurate, false, or misleading, often due to the way the questions are asked or other outside influences

association

a relationship between two or more variables, but does NOT imply causation

confounding variable

an outside factor that influences both the independent and dependent variable, potentially distorting the true relationship between them

experiment

imposes treatment on individuals to measure their responses

treatment

a specific condition applied to the individuals

factors

the explanatory variables that are being manipulated and may cause a change in the response variable (smoking & drinking)

levels

different values of the factors (0, 1, or 2 packs of cigarettes/beers)

placebo

a treatment with no active ingredient, but is "similar" to the other treatments

single-blind study

either the subjects or the researchers are unaware of who receives active treatment or placebo

double-blind study

neither the participant nor the researcher knows whether the participant has received the treatment or the placebo

placebo effect

experimental results caused by expectations alone

control group

the group that does not receive the experimental treatment; used to provide a basis for comparison

random assignment

creates groups that are roughly equivalent at the beginning of an experiment (cause and effect)

statistical significance

a statistical statement of how likely an obtained result occurred by chance (p < 0.05)

replication

giving each treatment to a sufficient number of experimental units so that any observed differences in treatment effects can be distinguished from random variation caused by the process of random assignment

completely randomized design

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

randomized block design

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

matched pairs design

A method of assigning subjects to groups in which pairs of subjects are first matched on some characteristic and then individually assigned randomly to groups.

inference

using information from a sample to draw conclusions about the population

sampling variability

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

scope of inference

the extent to which we can make conclusions

frequency table

summarizes one categorical variable using counts

relative frequency table

summarizes one categorical variable using percentages/proportions

two-way table

A table containing counts for two categorical variables, displaying totals for different categories

marginal relative frequency

the percent or proportion of individuals that have a specific value for one categorical variable (two-way table)

joint relative frequency

the percent or proportion of individuals that have a specific value for one categorical variable and a specific value for another categorical variable (two-way table)

conditional relative frequency

the percent or proportion of individuals that have a specific value for one categorical variable among individuals who share the same value of another categorical variable (the condition)

mosaic plot

a modified segmented bar graph in which the width of each rectangle is proportional to the number of individuals in the corresponding category

SUCS

For describing distribution - Shape, Unusual Values, Center, Spread

stemplot

a graphical representation of a dataset that organizes and displays data in a way that preserves the original values. Includes a stem and single-digit leaves. MUST HAVE A KEY

5 number summary

min, Q1, median, Q3, max

density curve

A mathematical model used to describe the overall pattern of the distribution of a random variable. Always above x-axis and has an area of exactly 1 underneath.

DUFS

For describing correlation - direction, unusual values, form, strength

high leverage points

points with much larger/smaller x-values than the other points in the data set

outliers (regression)

points that do not follow the pattern of the data and have large residuals

influential point

An extreme value whose removal would drastically change the slope, y-intercept, correlation, r², or SD of the LSRL.

regression line (LSRL)

predicted y = a + bx

power model

when logging both variables linearizes the data (y=ax^p)

exponential model

when logging only the y variable linearizes the data (y = abˣ)

large counts condition

using normal approximation when np>=10 and n(1-p)>=10

central limit theorem

when the number of samples is ≥3, the sampling distribution of the sample mean is approximately normal