AP Stats Unit 1 Vocab

statistics

study of variation (how data varies allowing us to draw reliable to draw reliable conclusions with that data)

individual

an object described in a set of data (people, animals, things)

variable

characteristic that can take different values for different individuals

categorical variable

takes values that re labels, which place each individual into a group called a category

quantitive variable

number values that are quantities (counts or measurements)

discrete variables

numeric/quantitive variables that have a countable number of values between any two values (whole numbers)

continuous variables

numeric/quantitive variables that have an infinite number of values between any two values

distribution

tells us what values the variable takes and how often it takes each variable

frequency table

shows number of individuals having each value

relative frequency table

shows the proportion or percentage of individuals having each value

population (of interest)

entire group of individuals we want information about

census

collects data from every individual in the population

sample

a subset of individuals in the population from which we collect data

sample survey

a study that collects data from a sample to learn about the population from which the sample was selected

random sampling

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

statistic

a number that describes some characteristic of a sample

parameter

a number that describes some characteristic of the population

mean

average

parameter: mu=…

statistic: x (bar over)=…

standard deviation

measure of spread

parameter: lowercase sigma=

statistic: sx (x sub exponent)=…

proportion

percent

parameter: p=…

statistic: p (w/ hat ^ over)=…

statistical inference

using information from a sample to infer, or draw conclusions

sampling frame

list of the items or people that have a chance to be chosen for the sample (should match the population of interest, or else problems can happen) can generalize results to the population sampled from

observational study

observes individuals and measures variables of interest, but does not attempt to influence the responses (cannot prove causation from this study)

experiment

deliberately imposes treatments on experimental units to measure their responses (can prove causation)

simple random sample (SRS)

a sample chosen in such a way that every group of n individuals in the population has an equal chance to be selected as the sample (every combination is possible in the end)-selected by grouping all names together and using random process to pick n names, you can never group them prior

sampling without replacement

an individual from a pop can only be selected once

sampling with replacement

an individual from a pop can be selected more than once

(3) Ways to take and SRS

1. random number table

2. calculator/random number integer

3. slips in a hat

*review processes in notes

sampling variability (or sampling error)

the fact that statistical measures taken from good random samples will yield different statistics from sample to sample

bias

procedure generates samples (often from bad sampling techniques) that yield statistical measures that consistently underestimate or consistently overestimate the parameter of interest

unbiased estimator

if the mean or average of a statistic (when repeated with many samples) is equal to the true population parameter

strata

groups of individuals in a n population that share characteristics thought to be associated with the variables being measured in a study (singular form is stratum)

stratified random sample

sample selected by choosing an SRS from each stratum and combining the SRSs into one overall sample-when done right, will produce statistics with less sampling variability (closer to the true parameter)

cluster

a group of individuals in the population that are located near each other (heterogenous mix of people)

cluster sample

a sample selected by randomly choosing clusters and including each member of the selected clusters in the sample

systematic random sample

sample selected from an ordered arrangement of the population by randomly selecting one of the first k individual and choosing every kth individual thereafter (no statistical advantage, just easier to obtain)

convenience sample

consists of individuals from the population who are easy to reach-can lead to bias

voluntary response sample

consists of people who choose to be in the sample by responding to a general invitation, sometimes called self-selected sample (can result in voluntary response bias)

under coverage

occurs when some members of the population are less likely to be chosen or cannot be chosen in a sample (can result in under coverage bias)

nonresponse

occurs when an individual chosen for the sample can’t be contacted or refuses to participate (can result in nonresponse bias)

response bias

occurs when there is a constant pattern of inaccurate responses to a survey (influenced by social pressures, wording of a question, etc.)

response variable

measures an outcome of a study

explanatory variable

help explain or predict changes in a response variable

confounding

occurs when two variable are associated in such a way that their effect on a response variable cannot be distinguished from each other (3 variables at play)

treatment

specific condition applied to the individuals in an experiment (if multiple explanatory variables, a treatment is combo of specific values of these variables)

experimental units

object/subjects to which a treatment is randomly assigned

placebo

a treatment that has no active ingredient but is otherwise like other treatments

factor

explanatory variable that is manipulated and may cause a change in the response variable (different values are called levels)

comparison/control group

used to provide a baseline for comparing the effects of other treatments, depending on the purpose of the experiment, control group may be given an inactive treatment(placebo), active treatment, or no treatment at all

-helps determine if it was in fact the explanatory variable that influenced the response variable

control

keeping other variables constant for all experimental units

-helps reduce variability in the response variable as much as possible and therefore will allow you to better determine if the explanatory variable is causing a difference in the response variable

placebo effect

describes the fact that some subjects in an experiment will respond favorably to any treatment, even an inactive treatment

double-blind

neither the subjects nor those who interact with them and measure the response variable know which treatment a subject is receiving

single-blind

either the subject or the people who interact with them and measure the response variable don’t know which treatment a subject is receiving

random assignment (randomization)

treatments are assigned to experimental units (or vice versa) using a chance process

-create groups that are as equal as possible across the many variables that you have no control over+any observed differences in responses after treatment can be attributed to explanatory variable

replication

giving each treatment to enough experimental units so that a difference in the effects of the treatments can be distinguished from chance variation due to the random assignment

-ensure random assignment does balance out the groups

4 principles of a well-designed experiment

1. comparison

2. randomization

3. replication

4. control

completely randomized design (of experiment)

the experimental units are assigned to the treatments completely at random

block

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

randomized block design

the random assignment of experimental units to treatments is carried out separately within each block (separation of treatments happens in “mini experiment” within each block

matched pairs design

comparing two treatments that uses block of size 2, with 2 very similar experimental units being paired and the two treatments are randomly assigned within each pair (in others each experimental unit receives both treatments in a random order)

scope of inference

-random selection of individuals justifies inference about the population from which the individual were chosen

-random assignment of individuals to groups in an experiment with statistically significant results justifies inference bat cause and effect

statistically significant

observed difference in responses between the groups in an experiment is so large that it is unlikely to be explained by chance variation in the random assignment, the results are called statistically significant (ex:less than 5%)