MATH 160 INTRO TO APPLIED TO STATISTICS MIDTERM

Based off Introduction to Modern Statistics (2e) Chapte5rs 1-

data

observations collected from field, surveys, experiments

statistics

study of how best to collect analyze, draw conclusions from data

treatment group

group that gets the treatment

control group

group that does not receive the treatment

summary statistics

a single number summarizing data from a sample.

(unit of) observation / case

a row

variable 

a characteristic of a case/observation represented in a column

data frame

a convenient and common way to organize data, especially if collecting data in a spreadsheet

tidy data

where each row is a unique case (observational unit), each column is a variable, and each cell is a single value

numerical variable

can take a wide range of numerical values, and it is sensible to add, subtract, or take averages with those value

Discrete

can only take numerical values with jump. compare to continuous.

Categorial

possible values are called a variables level

ordinal

a categorical variable, but the levels have a natural ordering

nominal

a regular categorical variable without this type of special ordering

sample statistic

n a number is being calculated on a sample of data

Population Parameter

considered for calculation on the entire population

bias

overrepresent that person’s interests, which may be entirely unintentional

Stratified sampling

The population is divided into groups called strata. The strata are chosen so that similar cases are grouped together, then a second sampling method, usually simple random sampling, is employed within each stratum.

Simple random sampling 

each case in the population has an equal chance of being included in the final sample and knowing that a case is included in a sample does not provide useful information about which other cases are included.

cluster sample

break up the population into many groups, called clusters. Then we sample a fixed number of clusters and include all observations from each of those clusters in the sample.

multistage sample

like a cluster sample, but rather than keeping all observations in each cluster, we would collect a random sample within each selected cluster

Randomized Ezperiment

Studies where the researchers assign treatments to cases are called experiments. When this assign ment includes randomization, e.g., using a coin flip to decide which treatment a patient receives, it is called a randomized experiment

confounding variable

a variable that is associated with both the explanatory and response variables. Randomizing patients into the treatment or control group helps even out such differences

replication

The more cases researchers observe, the more accurately they can estimate the effect of the explanatory variable on the response. In a single study, we replicate by collecting a sufficiently large sample.

replication crisis

refers to the ongoing methodological crisis in which past findings from scientific studies in several disciplines have failed to be replicated.

Pseudoreplication

occurs when individual observations under different treatments are heavily dependent on each other.

blocking

Researchers sometimes know or suspect that variables, other than the treatment, influence the response. Under these circumstances, they may first group individuals based on this variable into blocks and then randomize cases within each block to the treatment groups. This strategy is often referred to as blocking.

treatment group

receives treatment

control group

does not get the treatment

blind

When researchers keep the patients uninformed about their treatment, the study is said to be blind

double-blind

where doctors or researchers who interact with patients are, just like the patients, unaware of who is or is not receiving the treatment.

placebo

give a fake treatment to patients in the control group

placebo effect

Oftentimes, a placebo results in a slight but real improvement in patients. This effect has been dubbed the placebo effect.

observational studies

Studies where no treatment has been explicitly applied (or explicitly withheld)

Making causal conclusions based on experiments is often reasonable, since we can randomly assign the explanatory variable(s), i.e., the treatments. However, making the same causal conclusions based on observational data can be treacherous and is not recommended.

prospective study

identifies individuals and collects information as events unfold.

retrospective

collect data after events have taken place