# Stats Exam 2

## 95 terms · Ch. 11-17

### randomness

draws conclusions from data, best defense against bias

### simulation

an imitation of the real process that we can manipulate and control

### trial

each time a simulated answer is obtained

### component

basic building block of a simulation (outcome isn't the desired result)

### simulation process step 1

identify component to be repeated

### simulation process step 2

explain how you will model the component's outcome

### simulation process step 3

state clearly what the response variable is

### simulation process step 4

explain how you will combine the compoents into a trial to model the response variable

### simulation process step 5

run several trials

### simulation process step 6

collect and summarize the results of all the trials

### random numbers on calculator

MATH to PRB to RandInt(low,high,#)

### simple random sample

sample size n is one in which each set of n elements in the population has an equal chance of selection

### stratified sample

population divided into serveral subpopulations (strata) and random samples are then drawn from each strata (less sampling variability)

### cluster sample

entire groups (clusters) chosen at random (selected b/c of convenience, practicality, or cost)

### systematic sample

selecting individuals systematically from a sampling frame (give everyone a number, then pick every 3rd number)

### multi-stage samples

combine several random sampling methods (ex. stratify state, select random cities, interview clusters of residents)

### bias

systematic failure of a sampling method to represent it's population (voluntary response, undercoverage, nonresponse bias, response bias)

### nonresponse bias

individuals can't or won't respond

### response bias

external influences

### voluntary response samples

individuals can choose to participate in a sample, always biased

### convienience sample

individuals are conveniently available, always biased

### population

entire group of individuals

### sample

a subset of a population

### sample survey

study that asks questions of a sample drawn from some population

### sample size

# of individuals in a sample (size determines how well sample represents the population)

### population parameter

number value of a model for a population (estimate it from sampled data)

### statistics

values calculated for sampled data

### sampling frame

a list of individuals from whom the sample is drawn

### sampling variability

natural tendency of randomly drawn samples to differ, one from another

### undercoverage

sampling scheme that biases the sample s.t. it gives a part of the population < representation than it has in ithe population

### observational study

data in which no manipulation of factors has been employed

### retrospective study

subjects are selected and their previous conditions or behaviors are determined (focus on estimating differences between groups or associations between variables)

### prospective study

subjects are followed to observe future outcomes (no treatment applied: not an experiment) (focuses on estimating differences among groups)

### experiment

manipulates factor levels to create treatments (randomly assigns subjects to levels and compares responses)

### random assignment

a vaild experiment must asasign experimental units to treatment groups at random

### factor variable

a variable whose levels are controlled by the experimentor

### response varibale

a varibale whose values are compared across different treatments

### experimental units

individuals on whom experiment is preformed (subjects or participants)

### principles of experimental design

control, randomize, replicate, block

### control group

experimental units assigned to baseline treatment level (null/placebo treatment) (their result is a basis for comparison)

### block (what it does)

reduces effects of identifiables attributes of the subjects that cannot be controlled

### statistically significant

when an observed difference is too large for us to believe that it is likely to have occurred naturally

### blinding

any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups

### classes of individuals who effect outcome of experiment

1. those who could influence the results (subjects, ect.) 2. those who evaulate the results (judges, treating physicians, ect.)

### single blind study

when every individual in either of the classes is blinded

### double blind study

when everyone in both classes is blinded

### placebo

a treatment known to have no effect

### placebo effect

when subject respond to placebo treatment

### block (what it is)

gathers groups of experimental units that are similar (isolates variability)

### matching

retrospective and prospective studies: subjects who are similar in ways not under study compared with each other on the variables of interest

### randomized block design

randomization occurs within blocks

### completely randomized design

all experiemental units have an equal chance of recieving any treatment

### confounding

when one cannot seperate out the effects of one factor from the effects of the other factor

### probability

a number btween 0 and 1: reports liklihood of an event's occurance, biased on long-run relative frequencies

### random phenomenon

if we know what outcomes could happen, but not which particular values will happen

### trial

single attempt or realization of a random phenomenon

### outcome

the value measured, observed, or reported for an individual instance of a trail

### event

a collection of outcomes (identify to attach probablities to)

### sample space

collection of all possible outcome values (has a probability of 1)

### law of large numbers

the long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency = as the number of trials increases

### independence

the outcome of one event does not influence the probability of the other event, A and B are independent when P(A I B) = P(A)

### theoretical probability

comes from a model (ex. equally likely outcomes)

### emperical probability

comes from long-run relative frequency of the events occurance

### personal probability

probability is subjective and represents your personal degree of belief

### probability assignment rule

the probability of the entire sample space must be 1: P(S)=1

### complement rule

P(A)=1-P(A^c) (A^c: complement of A)

If A and B are disjoint events: P(A or B)=P(A) + P(B)

### disjoint (mutually exclusive)

two events that are not independent, share no outcomes in common, and knowing that one occured means the other did not

### disjoint example

if A and B are disjoint, then knowing that A occurs tells us that B cannot occur

### legitimate probability assignment

an assignment of probabilities to outcomes is legitimate if: each probability is between 0 and 1, and if the sum of the probabilites is 1

### multiplication rule

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

for any two events, P(A or B)=P(A) + P(B) - P(A and B) (subtract so you dont count it twice)

### conditional probability

the probability of B given A, P(B I A) = P(A and B) / P(A)

### general multiplication rule

for any two events, P(A and B)= P(A) x P(B I A)

### conditional probability uses

determine whether two events are independent, to work with events that are not independent

### tree diagram

a display of conditional events or probabilities that is helpful in thinking through conditioning

### drawing without replacement

sampling without replacement means that once one object is drawn it doesn't go back into the pool: changes the probability constant

### random variable

a variable that assumes any of several different numeric values as a result of some random event (denoted by capital letters)

### discrete random variable

a variable that can take one of a finite number of distinct outcomes

### continuous random variable

a variable that can take any numeric value within a range of values (range could be infinite, or bounded at either or both ends)

### probability model

function that associates a probability P with each values of a discrete random variable (X), denoted P(X=x) or with any interval of values of a continuous random variable

### expected value

long-run average value of a random variable, center of it's model, denoted u of E(X)

### standard deviation

describes the spread in the model

### variance

the expected value of the squared deviation from the mean of a random variable

look up **

look up**

### bernoulli trials condition 1

2 possible outcomes (success and failure), yes/no

### bernoulli trials condition 2

probability of success (p) is constant (probability doesn't change after 1 trial occurs)

### bernoulli trials condition 3

the trials are independent (one trial doesn't rely on another)

### geometric probability model

counts the # of B. trials until the first success

### 10% condition

sample must be smaller than 10% of the population

### binomial probability model

counts the # of successes in a fixed number of B. trials

### success/failure condition

binomial model is approximately Normal if we expect at least 10 successes and 10 failures