Probability and Statistics Midterm Vocab

Anecdotal evidence

one or a few specific cases/stories

Non-response bias

only a small fraction of the randomly sampled people choose to respond, the survey may no longer be representative of the population

Voluntary response

sample consists of people who volunteer to respond because they have strong opinions on the subject

Convenience sample

individuals who are easily accessible are more likely to be included in the sample

Perspective study

identifies individuals and collects information as events unfold

Retrospective studies

collect data after events have taken place

Simple sampling

randomly select cases from population, no implied connection between points selected

Stratified sample

strata are made up of similar observations. we take a simple random sample from each strata

Cluster sample

clusters are not made up of homogeneous observations, we take a simple random sample of clusters and then sample all observations in that cluster

Multistage sample

clusters are usually not made up of homogeneous observations. we take a random sample of clusters and then take a random sample of observations from sampled clusters

Principles of experimental design

control, randomize, replicate, block

Block

if there are variables that are known or suspected to affect the response variable. first group subjects into blocks based on these variables, and then randomize cases within each block to treatment groups

Double-blind

both subject and researchers don’t know what group subjects are in

P-value

probability value. The probability that we would get results this extreme assuming the null hypothesis is true

One-sided hypothesis

focuses on one specific value

p (hat)

sample proportion

Null hypothesis

“There is nothing going on.” The variables are independent, observed differences are due to chance

Alternative hypothesis

“There is something going on.” Variables are dependent, not due to chance.

Either reject or ____ the null hypothesis

fail to reject

Convincing evidence

allows us to reject the null hypothesis

Type 1 error

rejecting the null hypothesis when its true

Type 2 error

don’t reject the null hypothesis when the alternative hypothesis is true

two-sided

looking for extreme results on either side of the distribution

Confirmation bias

we only look for data that supports our own idea

Random process

is a situation in which we know what outcomes could happen, but we don’t know what particular outcome we will get

Frequentist interpretation

the probability of an outcome is the proportion of times the outcome would occur if we observed the random process an infinite number of times

Bayesian interpretation

interprets probability as a subjective degree of belief. for the same events, two separate people could have different viewpoints

Law of large numbers

states that as more observations are collected, the proportion of occurrences with a particular outcome, p(hat)n, converges to the probability of that outcome, p (population proportion)

Gambler’s fallacy

random processes are supposed to compensate for whatever happened in the past (ex. 10 heads, next one should be tails)

Disjoint (mutually exclusive) outcomes

cannot happen at the same time (can’t get heads and tails on a single coin toss)

Non-disjoint outcomes

can happen at the same time (can’t get heads and tails on a single coin toss)

General addition rule

P(A or B) = P(A) + P(B) - P(A and B) for disjoint events: P(A or B) = P(A) + P(B)

Probability distribution

lists all possible events and the probabilities with which they occur

Rules for probability distributions:

1. the events listed must be disjoint

2. each probability must be between 0 and 1

3. the probabilities must total 1

Sample space

all the possible outcomes of a trial

Complementary events

two mutually exclusive events whose probabilities add up to 1

Independent

knowing the outcome of one provides no useful info about the outcome of the other

Associated or dependent

The outcome of one affects the outcome of another

Product rule for independent events

if A and B are independent events, then P(A and B) = P(A) x P(B)

Complementary events

are opposite, but always add up to 1 (like heads and tails)

Conditional probability

P(A|B) = P(A and B)/P(B) (A given B is true)

General multiplication rule

If A and B represent two outcomes or events, then P(A and B) = P(A|B) x P(B)

Rule of thumb

if we are sampling without replacement, then the rule of thumb is if we sample less than 10% of the population, the effect on conditional probability is small, so we assume independence

The probability of 1 specific value amongst infinite values is ______

effectively zero

Normal distribution

Unimodal and symmetric, bell shaped curve

Measures of spread

variance, standard deviation, and range

z score

how many SD we are from the mean (only for normal!)

percentile

percentage of observations that fall below a given data point

Unusual

observations that are more than 2 SDs away from the mean

Statistic

any number that’s used to represent something

One version of scientific methodology:

observe data, form hypothesis, gather more data, test/evaluate/adjust hypothesis, gather more data, etc.

explanatory variable

variable that is manipulated or changed

Response variable

outcome (yes or no)

Population

all those who could be tested

Sample

subgroup or subset of the population

Numerical variable

continuous (number line) or discrete (gaps between numbers)

Categorical variable

ex. (T-shirt size) nominal or ordinal (natural order)

68-95-99.7 Rule

for nearly normally distributed data:

• about 68% falls within 1 SD of mean

• about 95% falls within 2 SD of the mean

• about 99.7% falls within 3 SD of the mean

Population proportion

percentage of a population that meets some specific criterion

Sample proportion

how many in the sample meet that criterion divided by the total amount in the sample (p hat)

Plurality

not the majority, but the highest number

Population parameter of interest

the # we want to know

Sample statistic

usually a point estimate, the # we get from a sample

Central Limit Theorem (proportion version)

sample proportions will be nearly normally distributed with mean equal to the population proportion, p, and standard error equal to ______

CLT conditions

• Independence - n<10% of population

• Sample size - there should be at least 10 expected successes and 10 expected failures

Confidence interval

a plausible range of values for the population parameter

significance level (alpha)

probability of a Type 1 error, usually 0.05