STATS 1000- Weeks 1 and 2

case

an object upon which we collect information that we are interested in studying

respondents

cases that are answering in a survey

subjects/participants

cases who are being studied in an experiment

experimental units

non-human cases being studied in an experiment

variable

a characteristic of a case that differs

identifier variable

provides an identifier for each case, typically a variable that uniquely identifies each case

• it’s possible to have more than one

data

collection of observed values of a variable

observation

collection of observed values from a case

data table

table containing sets of data where observations are contained in rows and each variable gets its own column

what are some sources of data?

• polls

• surveys

• experiments

• observational studies

• census

• brain scans

• genetic measurements

what are the two different kinds of variables?

Categorical and Quantitative

categorical variable

divides cases into groups, placing each case into exactly one or more categories. It consists of groups or category names.

• ex) eye color, marital status, political party

what are the two types of categorical variables?

nominal and ordinal

nominal categorical variables

the order of the categories does not matter

ordinal categorical variables

the ordering of the categories does matter

• ex) clothing sizes, final grade

nominal or ordinal: year in college

ordinal

nominal or ordinal: which award would you rather win- nobel prize, gold olympic medal, academy award

nominal

quantitative variable

measures a numerical quantity for each case. It consists of numerical measures or counts

• ex) height, temperature, number of children in a family

discrete quantitative variables

can only take on a set number of values

• usually a whole number (unless like all of the available options are decimals- what matters is that it can’t just be ANY number)

• ex) classes missed in a week (you can’t miss more than 2 because there only ARE two and you can’t miss 1.283 days or something)

continuous quantitative variables

can take on any value within some interval

• ex) height, weight, speed

how can we provide context when analyzing the source of data?

we can try to find the:

• who

• what

• where

• why

• when

• how

of the experiment

population

any complete collection of people or objects that a statistician is interested in studying

parameter

value that describes a characteristic of a population

• what we actually want to study about the population. what do we want to know?

sample

set of units selected from a population that a statistician analyzes to better understand the population

statistic

value calculated from a sample that serves as an estimate of a parameter

inference/inferential statistics

the process of using data from a sample to gain information about the population

sampling frame

list of cases from which a population is drawn; usually a large subset of the population

• like the contact info of all the cases

in order to be valid, samples must be:

• representative: characteristics of the sample closely resemble the characteristics of the population

• selected randomly: observations are chosen by chance rather than by deliberately and intentionally selecting specific cases

• large enough: need enough information to understand the population

sampling error

difference between the sample and population, can be large or small.

• larger samples tend to have a smaller sampling error

simple random sample

method of sampling in which every member of the sampling frame has the same chance of being chosen

systematic sample

method of sampling where members are sampled according to some predetermined rule by skipping a certain number of people and then sampling the nth person

systematic sample

method of sampling in which the population is first divided into groups according to some characteristic (called strata) and then a random sample is taken from within each stratum

cluster sample

sampling method where the population is divided into similar groups (called clusters), a simple random sample of the clusters is taken, and then every member in each selected cluster becomes part of the sample

multistage sample

sampling scheme that combines several methods

census

an attempt to collect data on the entire population of interest

convenience sample

a sample obtained from the people who were the easiest to access

voluntary sample

a sample obtained when a large group of individuals is invited to participate, and all responses are recorded; statistician does little to no work other than offer the opportunity to participate

sampling bias

any systematic failure of a sampling method to represent its population

what are the two types of non-sampling bias?

nonresponse bias and response bias

nonresponse bias

introduced to a sample when a large fraction of those sample fails to respond

response bias

anything in the survey that influences responses

survey

method of data collection where respondents are asked questions and self-report responses on various topics

what are some sources of bias in designing survey questions?

• complicated questions (more than one part)

• vague questions

• leading questions

• central tendency bias (neutral responses)

• error prone response options (answers out of a typical order)

• voluntary response bias (some people don’t respond)

response/dependent variable

the variable of interest, what researchers are measuring

explanatory/independent variable

any variable that may influence or explain the response variable

observational study

a method of data collection where researchers allow subjects to live their lives naturally without interfering and record their behavior

• looks for associations between the variables that allows researchers to make informed decisions

• cannot prove the explanatory variable causes the response to occur

what are the two types of observational studies?

retrospective and prospective

retrospective observational studies

studies that analyze an outcome in the present by delving into historical records

• require accurate records/subjects to recall history

• more prone to bias

prospective observational studies

studies that identify a set of subjects in advance and collect data in the future as events unfold

• researcher is involved in the collection of data

• less prone to bias

lurking variable

a third variable that is associated with both the explanatory variable and the response variable

experiment

a type of study where the experimenter manipulates some aspect of one (or more) explanatory variables, assigns them to a subject/experimental unit, and observes a response in the future

factor

another name for an explanatory variable in an experiment

level

one of several possible attributes that can be assigned to a subject/experimental unit

treatment

combination of all factor levels assigned to a subject/experimental unit

control

making conditions as similar as possible for all treatment groups

randomize

each subject/experimental unit is assigned a treatment randomly in an attempt to spread out sources of variability evenly amongst all treatments; this is the most important step in controlling for confounding variables

replicate

taking more than one observation at each factor level to estimate the variability of measurements. when an experiment is repeated in entirety, it is said to be replicated

blocking

grouping subjects/experimental units together based on a factor that cannot be randomized, but may have an effect on the response variable; this can reduce within-treatment variability

completely randomized design

an experimental design where every possible treatment is assigned to at least one subject/ experimental unit

randomized block design

an experimental design where subjects/ experimental units are first divided into their respective blocks and are then assigned treatments within each block

factorial design

an experiment with more than one manipulated factor

• a full factorial design that contains treatments for all possible combinations of factors at all levels