Statistics - Unit 2

control group comparison

this group does not receive the treatment of interest, but a placebo or treatment that is currently used; allows for comparison of treatment results with another group so the effect of the treatment can be measured

randomization

randomizing which participants receive the treatment removes or minimizes the effects of lurking variables

blinding

participants do not know which treatment they are receiving

double blinding

participants and researchers do not know who is receiving what treatment

replication

assigning multiple subjects to each treatment in the experiment

subjects/experimental units (EU)

who or what is receiving the treatment in the study

response

the outcome of interest; what is being measured by the researcher

factors

variables that may affect the response (explanatory variables)

factor levels

the possible categories or levels for each factor

treatments

all combinations of the factor levels considered in the study; exactly what is being randomly assigned to the subjects

single factor design

the effects of only one factor are considered; factor levels and treatments are the same for this design

multifactor design

the effects of two or more factors are considered

block design

only interested in one factor, but know that a second factor may influence the results

block

a second factor that is taken into consideration and is often something that cannot be randomized; “nuisance factor”

probability

the study of a random phenomenon; is a relative frequency measuring the outcomes of random events

empirical probability

probabilities calculated from collected data such as an experiment; “short term” probabilities

sample space

the set of all possible outcomes of a random experiment, typically denoted by S

events

any set of outcomes; a subset of the sample space typically denoted with capital letters from the beginning of the alphabet such as A, B, and C

theoretical probability

probabilities calculated using mathematical reasoning (function/limits), “long term” probability; we did not collect any data/no experiment

the law of large numbers

the more we repeat an experiment (given each repetition is identical and independent), the empirical probabilities of the outcomes will approach their theoretical probabilities

if P(A) = 0

A is impossible, the empty event, denoted ∅

if P(A) = 1

A is certain, the sample space, S

contingency tables

useful tool for examining the association between two categorical variables along with organizing probabilities of different events

rows

represent the categories of one variable in a contingency table

columns

represent the categories of the other variable in a contingency table

cells

where the rows and columns intersect in a contingency table

unions

the event that either A or B or both occur

intersections

the event that both A and B occur

disjoint events/mutually exclusive

if P(A) = 0; events A and B share no common outcomes

complement

the event that A does not happen

conditional probability

the probability that A occurs if we already know that B has occurred or will occur

independent events

event B occurring does not change the probability that event A will occur or vice versa

dependent events

event B occurring changes the probability that event A will occur

discrete variable

a variable that counts (money, pages, students)

continuous random variable

variable that measures (height, age, distance)

expected value (weighted mean/average)

for a discrete probability distribution it can be found as the weighted average of outcomes

what a discrete probability distribution gives 

the possible outcomes of an experiment and the probability (relative frequency) of observing each outcome

1 or 100%

to be a valid distribution, the sum of all of the probabilities must be