AP STAT MIDTERM

definitions found on the ap stat midterm list

Categorical data

Categorical data

Words

Ex- male/female, eye color, breed of dogs

Quantitative data

Numerical

Ex- weight of hamsters, amounts of chemicals in beverages

Bar graphs

Bars do not touch- for graphing one variable

Pie charts

Percentages must sum up to 100%, for graphing one variable

Dot plots

Can resemble probability curves, for graphing more than one variable

Stem and leaf plots

Remember to put key, split the stems if there is too much data

Histogram

Looks like a bar graph but allows bars to touch, groups data into classes, shape is easily visible

Box plot

Shows 5-number summary and outliers, side-by-sides are good for comparing quartile, median, and spread

Scatterplots

Look for relations between variables

Describe using form, strength, and direction

Linear correlation coefficient (r)

Measures the strength of the linear relationship -1>r>1

Least squares regression line (LSRL)

used for prediction

Minimizes the vertical distances from each data point to the line drawn

y-hat

Predicted y value

Extrapolation

Predicting a y value when the x is far from the other x values and not represented on the visual graph

Coefficient of Determination (r^2)

gives the proportion (%) of variation in the values of y that can be explained by the linear relationship with x seen in the regression line

Residual (y-y hat)

Vertical distance from actual data point to the regression line

Residual plot

Scatterplot of observed x values and predicted y values or (x, y hat)

Lurking variables

Variables not identified or considered

Confounding variables

A third party variable affects the response variable only

Common response

A third party variable affects both the explanatory and response variables

Census

Contacts every individual in the population to obtain data

Mean and SD are parameters and are only used with population data

Sample survey

Collects data from a part of a population in order to learn about the entire population

Voluntary response sample

Participants choose themselves, usually only those with strong opinions choose to respond

Ex- online surveys, call-in opinion questions

Convenience sample

Investigators choose to sample those people who are easy to reach

Ex- marketing surveys done in a mall

Bias

The design systematically favors certain responses or outcomes

Ex- surveying pacifist church members on their opinions about war

Simple random sample

A group of n individuals chosen from a population in such a way that every set of n individuals has an equal chance of being the chosen sample

A statistically significant result and follows all of the rules of experimentation

What can claim causation?

Stratified random sample

divide the population into groups (strata) of similar individuals (by some chosen category) then choose a simple random sample of each of the groups

systematic random sampling

choosing every nth individual after choosing the first randomly

cluster random sample

divide the population into groups (most likely by location), randomly select one or multiple of these groups, and survey each member from each of the selected groups

undercoverage, nonresponse, response bias, wording of questions

Cautions (things that could ruin the sample):

Undercoverage

when some groups of the population are left out, often because a complete list of the population from which the sample was chosen was not available

nonresponse

when an individual appropriately chosen for the sample cannot or does not respond

response bias

when an individual does not answer a question truthfully due to shame, embarrassment, or pride

question wording

questions are worded to illicit a particular response (self-fulfilling prophecy)

after sample is obtained

When does experimental design take place?

observational study

observes individuals in a population or sample, measures variables of interest, but does not in any way assign treatments or influence responses

experiment

deliberately imposes some treatment on individuals (experimental units or subjects) in order to observe a response- can only give evidence for causation is designed well and statistically significant

control

controls lurking variables by assigning the units to groups that do NOT get the treatment (normal person)

randomize

use simple random sampling to assign units to treatment groups or control groups

replicate

use the same treatment on many units to reduce the variation due to chance

double blind

“best experiments,” neither the researchers nor the subject know which treatments are being used on which subjects (placebos are commonly used)

block designs

subjects are grouped before the experiment based on a certain characteristic or set of characteristics, then simple random samples are taken within each block to assign treatments

matched pairs

a type of block design where two treatments are assigned, sometimes to the same subject or sometimes to another subject matched with them (very common for twins)

long term, short term

probability refers to “…..” not “……”

independent

one event does not change or have an effect on another event

1

all probabilities for one event must sum to…