chapter 1 vocab

1.1 vocab

statistics

the study of procedures for collecting, describing, and drawing conclusions from information

design in stats

the process of choosing a sample from the population

description in stats

summarization of the data collected

inference in stats

making conclusions about the population using information from the sample

• requires the population to be defined ahead of time

population

the entire group of individuals about which we want information

sample

the part of the population for which we collected data

simple random sample

every set of n individuals has an equal chance to be the sample actually selected

• ex using a random number generator or drawing from a hat

stratified random sample

classifies the population into groups of similar individuals (stratas) and gives each strata a separate simple random sample, combines all SRS at the end to form the full sample

• ex measuring the height of teenagers needs to be broken up by ages into stratas because a 13 year old is not close in height to a 19 year old because they haven’t finished growing

cluster sampling

randomly sampling an entire cluster from a population of clusters (**more efficient use of resources)

• ex wanting to sample high school gpa so you pick 10 very similar schools and sample all the students from 2 of them

systematic sampling

picking every nth element from a sequence

• ex every 5th person in line

1.2 vocab

individuals

objects described by data

variable

any characteristic or measurable quantity pertaining to the individual

qualitative/categorical variable

a variable that places individuals into one of several groups/categories

• ex college, major, color of car

ordinal variable

qualitative variables whose categories have a natural ordering

• ex freshman, sophomore, junior, senior

nominal variable

qualitative variables whose categories have no natural ordering

• ex dog owners or cat owners

quantitative variables

a variable that takes on numerical values on which arithmetic operations can be done

• ex height, age

discrete variables

quantitative variables whose values are countable or can be listed

• ex number of children in a household

• finite numbers or countably infinite

continuous variables

quantitative variables that can take on an uncountable number of values

• ex anything with decimals that keeps going

• uncountably infinite

pi chart

used to describe categorical variables, used for percentages and you need to have 100% of the data

bar graph

used to describe categorical variables, horizontal axis is categories and vertical axis gives the count/percentage in each category

histogram

used to describe quantitative variables, horizontal axis pertains to grouped values (ranges) and vertical axis is the frequency/counts of each variable

stem plot

used to describe quantitative variables, like a histogram but with more information

time plot

used to describe quantitative variables over time, horizontal axis is time and vertical axis is variable value, shows trends over time

1.3 vocab

observational studies

a study in which the assignment to treatment groups is not made by the investigator, the investigator merely observes the date generated by other processes

• the researcher does not impose a treatment

experiment

a study where the researcher does impose a treatment

confounding

when the effects of variables on a response variable cannot be distinguished

confounding variables

an outside factor in a study that affects both the independent variable and the dependent variable

• ex. measuring plant height but can’t tell if growth was due from watering or the sunlight

lurking variables

a hidden factor not included in a study that affects the relationship between the variables you are measuring

• ex. blood pressure of smokers but the lurking variable could be stress levels because that also raises blood pressure

experimental units

the smallest unit of experimental material for which a treatment can be applied independently

• ex. people, plants, animals, things

• ex. a plot of land

sampling unit

the smallest for which a response can be observed independently

• ex 5 plants within a plot of land

treatments

procedures applied to each experimental unit

• always 2 or more treatments in an experiment

how to find the total number of treatments

multiply the product of each option

• ex in a plant study there is

  • sunny/dark

  • watering every day/watering 2x a week/watering every week

  • using organic fertilizer/using chemical fertilizer/using no fertilizer

• 2 × 3 × 3 = 18 possible treatments

experimental design

describes the choice of treatments and how subjects are assigned to treatments

completely randomized design

treatments are completely randomized to experimental units without any other restrictions or constraints

randomized block design

the experimental material or the environment in the lab is not uniform and so changes in some systematic way could impact the value of the response

• used blocked designs to account for the systematic variation

placebo vs nocebo

placebo has no effects and a nocebo has negative effects

single blind experiment

only the subject doesn’t know which treatment they were assigned

double blind experiment

neither the investigators nor the subjects know who has been assigned to which treatments

cohort studies

involves a group of subjects who are monitored over time to determine whether various factors are associated with an outcome

• ex measuring happiness study from teens to old age (harvard study)

case control studies

two samples are drawn, one consisting of subjects with a condition and the other where subjects do not have the condition, researchers look back and compare the differences

1.4 vocab

bias

the degree to which a procedure systematically overestimates or underestimates a population value

undercoverage bias

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

• ex only surveying people with iphones

nonresponse bias

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

• ex a democratic campaign and a republican chooses not to answer

response bias

a systematic pattern of incorrect responses

• ex people exaggerate their incomes for a survey or underexaggerate how many drinks they have had to the police

wording of questions

the most important influence of the answers to a survey

• ex

  • if you found a wallet with $200 would you give it back?

  • if you found a wallet with $200 would you do the right thing and give it back?