stats 210 - general terms, variables, sampling, & bias

test/exam 1

parameter

the characteristic/trait of a population that the researcher wants determine — uses Greek letters as symbols:

1. μ (mew) → mean

2. η (eta) → median

3. σ (sigma) → variance

4. σ² (sigma squared) → standard deviation

5. π (pi) → proportion of successes

6. ρ (rho) → correlation b/w 2 variables

• mnemonic: Mew eta 3 sigmas on pie row

• ex. The parameter of interest is π = proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island

  • must include greek symbol, population, & parameter!

population

the entire subject group that the researcher wants to investigate

• keyword: ALL

• ex. “The population is all visitors to the Bahamas in 2019”

sample

a subset or smaller portion of the target population selected in order to gather the necessary data to make inferences/statements about the pop. & parameter of interest

• representative & randomized!!

statistic

a measure/value determined from data from the sample — uses English letters as symbols

1. x̄ (x-bar) → mean

2. M → median

3. s → variance

4. s² → standard deviation

5. p̂ (p-hat) → sample proportion

6. r → correlation b/w 2 variables

7. n → # of subjects in a sample

• X-men saw 2 snakes wearing hats running nowhere

statistical hypothesis

a testable guess/statement about what the value of the population parameter could be — uses PARAMETER SYMBOLS (greek letters)

• ex. “In this scenario, the hypothesis we want to test is μ =32.4 years.”

parameter vs. statistic

• parameter — value the researcher wants to find, derived from a population, uses Greek letters as symbols

• statistic — value derived from data gathered from a sample, uses Eng letters as symbols

statistical inference

the process of making a broad conclusion/guess/statement about the pop. parameter using data & statistics from the sample — uses tools such as confidence intervals

replication

taking repeated data on the same subject

repetition

taking repeated data on multiple different subjects

constant

characteristic/trait whose measurements don’t change over time or trials

• ex. “days in march”

define variable & its types

• qualitative/categorical

• quantitative

  • discrete

  • continuous

quantitative variables

trait/value that varies from subject to subject that can be ranked or arranged in order of degree/magnitude (greatest to smallest, better or worse) — 2 types:

1. discrete variable

2. continuous variable

• usually involves mean

qualitative/categorical variables

trait/value that varies from subject to subject that can be ranked or arranged in order of degree/magnitude (greatest to smallest, better or worse)

• ex. location, hair color, gender, enjoyed/not enjoyed movie, success/failure

• ex. “how many people enjoyed spiderman: brand new day?”

• usually involves proportion of successes

discrete variable

a quantitative variable whose measurements can be counted & can’t be a decimal

• ex. # of students in a class, votes received by a candidate

continuous variable

a quantitative variable whose measurements has to be calculated or measured & can be a decimal

• measured ex. height, time

• calculated ex. average, rate, %, ratio

• ex. % of dogs to cats at the shelter

list all sampling methods

• simple random sampling

• stratified random sampling

• multistage random sampling

• haphazard sampling

• volunteer response sampling

simple random sampling

method of sampling where you list & assign all of the possible subjects in the target population a # & randomly choose n of the subjects

• ex. 67420 ppl in population → assign each person a 5-digit number: 00001, 00002, 00003… until 67420 → Table of Random Digits (select a line) → break the numbers up in groups of how many digits of population (ex. 5) w/o duplicates & within the range

  • go to next line if needed

• most random & easiest, but doesn’t guarantee representation

stratified random sampling

method of sampling where the population is divided into two or more groups according to a similarity, then through simple random sampling from every group, a sample is taken

• ex. population is split b/w male, female, & nonbinary → simple random sample each group → sample!

• most representative, but loses randomization & is time/cost consuming due to complexity

multistage random sampling

method of sampling where through multiple stages, the population is progressively broken down into smaller groups and then randomly sampled at each stage.

• ex. university population is divided into groups according to major & a random sample is chosen → selected groups are divided into smaller groups & randomly sampled → sample of individuals selected!

• at least 2 randomization stages

• doesn’t select from ALL groups, only a few

• most time/cost efficient & doesn’t need a complete list for a large population, but not very random/representative

haphazard sampling

an informal, non-statistical method of sampling where a person attempts to randomly choose subjects w/o a plan

• data easily acquired, but lacks representation, randomization, or absence of human bias

• ex. surveys @ malls, campuses

what type of sampling is surveys?

haphazard sampling

what type of sampling is polls?

volunteer response sampling

volunteer response sampling

method of sampling where participants voluntarily choose to be part of study

• neither randomized or representative b/c

  • unlikely to be seen by most ppl

  • ppl who feel strongly abt topic will most likely answer → over representative & biased

2 types of experiment

• controlled experiment

• observational experiment

controlled experiment

researcher randomly assigns individuals into groups to selectively assign treatments

• ex. group A is given medicine 1, group B is given medicine 2, group C is given a placebo

• randomized & highly controlled so decreases risk of bias/confounding variables

• can prove cause and effect

observational experiment

researcher observes groups w/o interence & patients themselves choose treatments

• prone to confounding variables & not randomized

• done to find correlations/associations

• ex. ppl are divided into 3 groups according to political party (not randomized) → asked on their stance with abortion law

types of biases

1. selection bias

2. nonresponse bias

3. response/wording-of-question bias

4. experimental bias

selection bias

systematically excluding one or more types of subjects when selecting a sample

• ex. gathering data from athletes on whether gym facilities should be upgraded or not

nonresponse bias

individuals chosen for the sample cannot be contacted, fail, or refuse to respond

• prevalent in surveys or polls

• ex. a company sends a survey on workload to employees → those who are overworked/stressed overlook email, while employees w/ free time reply

response/wording-of-question bias

subjects do give a response, but it is untrustworthy/false

• could be due to social norms, who’s asking, or wording of question

• ex. “would you return someone’s wallet?” vs.

“Would you do the right thing to return someone’s wallet?”

experimental bias

where confounding variables skew the response results — more prevalent w/ observational experiments