AP Statistics Unit 2 KNIGHT

population

the whole group that we want info about

bias

results of a study consistently over or underestimate the value of a parameter we want to know

convenience sampling

taking a sample consisting of individuals that are easy for the experimenter to reach

Why is convenience sampling biased?

The individuals that are easiest to reach will likely differ from the population at large in some systemic fashion

Voluntary response sample

consists of individuals who choose to respond to a survey

Why is a voluntary response sample biased?

The people who choose to respond most likely have stronger opinions than the average individual, which cannot be generalized to the population at large

Random sampling

requires a chance process

Simple random sample

a sample of size n that is chosen so that every possible group of n individuals in the population have an equal chance of being selected for the sample

sampling frame

a list of individuals from whom the sample is drawn

downsides of simple random sampling (srs)

1. sampling frames are difficult to construct accurately (especially for large populations) 2. selection of subjects takes a long time

stratified random sampling

population is divided into groups of similar individuals (strata) and a simple random sample will then be taken in each stratum and the combined results will be the actual sample (SIMILAR WITHIN, DIFFERENT BETWEEN)

Cluster sample

population is divided into groups of individuals located near each other (clusters) (DIFFERENT WITHIN, SIMILAR BETWEEN) each cluster should be a small-scale population

larger samples....

are more precise and decrease variation

selection bias (undercoverage)

some members of the population cannot be chosen in a sample (ex: survey mailed to homes dont cover homeless ppl)

nonresponse bias

individual who is chosen for the saample cannot be contacted or refuses to participate

wording of question bias

questions that are leading, loaded, or poorly written can lead to markedly different result

response bias

gender, age, race, ethnicity, or the behavior of the interviewer affects the responses in some systematic way

response variable

a measured outcome of a study

explanatory variable

something that can explain the response variable

observational study

individuals are observed and variables of interest are measured; no treatment is imposed (NO CAUSE AND EFFECT CAN BE DETERMINED)

experiment

deliberately imposes treatment on the subject (CAN BE USED TO DETERMINE CAUSE AND EFFECT)

controlled experiment

some subjects are given a treatment and others given a placebo (used a comparison group)

confounding

2 or more variable are associated in such a way that their effects on the response cannot be distinguished from each other

experimental units

smallest collection of individuals to which treatments are applied

4 principles of good experimental design

comparison, random assignment, control, replication

principle of comparison

a good experimental design will be used to compare 2 or more treatments

principle of random assignment

units are to be assigned to treatments by some chance process (purpose of random assignment is to CREATE APPROX EQUAL GROUPS FOR COMPARISON)

principle of control

keeping outside variables that might affect the response constant (as much as possible). This REDUCES VARIABILITY in the response variable

principle of replication

to use enough experimental units in each group to distinguish the results (from the treatment) from chance differences between the groups

statistically significant

the effect is large enough to rarely occur by chance alone

practical importance

Something can be statistically significant but not practically important (Ex: avg test score goes from 90 to 92% due to a test prep site can be statistically significant but not practically important)

block

a group of experimental units that are known before the experiment begins to be similar in some way that is thought to affect the response (purpose: TO REDUCE VARIABILITY THAT MIGHT ARISE FROM RANDOM ASSIGNMENT)

matched pairs design

pairs of similar experimental units are matced up and one of the units in the pair is randomly assigned the treatment (and other the control) Alternatively, both treatment and control can be assigned to the same unit with the order of reception randomized

random selection

if so, you can make an inference about the population

random assignment to groups

if so, you can assume cause and effect

Types of bias

response bias, nonresponse bias, wording of question bias, selection bias (undercoverage)

factor

explanatory variables in an experiment

level

each possible value a factor can take on