Introduction To The Practice Of Statistics, Moore And Mccabe

Front 1

regression line

Back 1

-a straight line that describes how a response variable y changes as an explanatory variable x changes.
-used as a tool to predict the value of y given x

Front 2

fitting a line

Back 2

drawing a line that comes as close as possible to the points

Front 3

equation for a regression line

Back 3

y=a+bx

a=intercept
b=slope

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slope

Back 4

rate of change in y as x changes

Front 5

extrapolation

Back 5

the use of the regression line for prediction far outside the range of values of the explanatory variable

Front 6

least squares regression line
+/-?

Back 6

-error=observed gain -predicted gain
-it always passes through the point xbar, ybar
errors are positive if they lie above the line
negative below

Front 7

equation for least squares regression

Back 7

if a =ybar -bxbar
and b= =r (sy/sx)
then the least squares regression formula is:
yhat=a + bx

Front 8

b=r (sy/sx)

Back 8

a change of one standard deviationin x corresponds to a change of r standard deviations in y

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r squared

Back 9

squares of the correlation-the fraction of the variation in the values of y that is explained by the least squares regression of y on x

Front 10

residuals

Back 10

the difference between an observed value and the value predicted by the regression line
-the mean of the least squares residual is always 0

Front 11

residuals formula

Back 11

observed y-predicted y
y-yhat

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outlier

Back 12

an observation that lies outside the overall pattern of the other observations

Front 13

influential

Back 13

an observation is ____ for a statistical calculation if removing it would markedly change the result of the calculation

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lurking variable

Back 14

a variable that is not among the explanatory or response variable in the study and yet may influence

Front 15

r square in regression

Back 15

the square of the correlation r square, is the fraction of the variation in the values of y that is explained by the least squares regression of y on x

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r=0

Back 16

means that there is no linear function and that it is undefined

Front 17

ybar

Back 17

average
(response variable+rv+rv+rv)/# of subjects)

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x

Back 18

-always on horizontal axis
-explanatory variable

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explanatory variable

Back 19

explains or causes changes in response variables

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y

Back 20

-always on the vertical axis
-response variable

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response variable

Back 21

measures an outcome

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total sum of squares

Back 22

-square the deviation for each subject and sum the squares around the mean ybar
-SST

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formula for SST

Back 23

=∑(y-ybar)squared

Front 24

sum of squares of the errors

Back 24

-SSE
-(y-yhat)squared

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yhat

Back 25

x-1

Front 26

sum of errors

Back 26

always equals zero

Front 27

r

Back 27

correlation coefficient

Front 28

correlation

Back 28

-r is the slope of the least squares regression line when we measure both x and y in standardized units
-makes no distinction between explanatory and response variables
-requires that both variables be quantitative
-always satisfies -1≤r≤1

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regression

Back 29

the square of the correlation r is the fraction of the variance of one variable that is explained by least squares regression on the other variable

Front 30

SRS

Back 30

simple random sample
-each unit has the same chance of being chosen-unbiased
-selection of one unit has no influence on the selction of another

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sample

Back 31

-A sample is any subset of elements selected from the population.
-Subset of the a population. Group of creatures from which one gathers data with the intention of making inferences to all organisms that fit those criteria (i.e., the population).

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stratified sampling

Back 32

the population is divided into homogenous groups

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cluster sampling

Back 33

the population is grouped into small clusters and an srs of clusters is drawn

all objects in the selected cluster are observed

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systemic sampling

Back 34

randomly choose a unit from a population, then select every kth unit thereafter

Front 35

multistage sampling

Back 35

the sampling is chosen in stages. most opinion polls and other national samples use this method

Front 36

experiment

Back 36

-delibrately imposes some treatment on individuals in order to observe their responses
-an act or process that leads to a single result or outcome that cannot be predicted

Front 37

observational study

Back 37

observes individuals and measures variables of interest but does not attempt to influence the responses

Front 38

explanatory variable

Back 38

attempts to explain or is purported to cause differences in a response variable

Front 39

experimental units

Back 39

the individuals on which the experiment is performed

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subjects

Back 40

if human, this is what an experimental unit is called

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treatment

Back 41

a specific experimental condition applied to the units

Front 42

three basic principles of experimental design

Back 42

replication
control
randomization

Front 43

replication

Back 43

the same treatments are assigned to different experimental units

Front 44

control

Back 44

any method that accounts for and reduces natural variability

Front 45

confounding variable

Back 45

one whose effects on the response are indistiguishable from those of the explanatory variable

Front 46

comparison

Back 46

a form of control where 2 or more treatments are compared to prevent confounding the effect of a treatment with other variables

Front 47

blocks

Back 47

a form of control where similarexperimental units are placed into groups

Front 48

randomization

Back 48

the use of chance to divide experimental units into groups

Front 49

double blind

Back 49

those that read the results are also unaware of the treatment

Front 50

calculator key strokes to generate a simple random sample

Back 50

clear lists
highlight list 1
f4:calc
4:probability
a:random seed __
enter
highlight list 1
f4:calc
4:probability
5:randint(1, population size, number of samples needed)

Front 51

the logic of randomization

Back 51

-produces two groups of similar subjects before treatment
-comparative design ensures that outside variables influence equally
-therefore the only reason for the data outcome is the response variable

Front 52

calculator key syrokes for least squares regression

Back 52

-enter data for list1 and list2
-f4:calc
-3:regressions
-1:linreg(a+bx)
-x:list1
-y:list2
-store reqeqn: y1(x)
-enter
-enter

Front 53

statistically significant

Back 53

an observed effect so large that it would rarely occurby chance

Front 54

r values

Back 54

-does not change when we change the units of measure of either x or y or both
- -1≤r≤1
- +r indicates a positive association between the variables
- -r indicates a negative association
- near 0 indicate a weak linear relationship
-strongly affected by outliers

Front 55

sentence for the interpretation of a regression line

Back 55

"in our example, the slope means that the mean reaction time is increasing at a rate of .7 seconds per percent over the sampled range of drug amounts from 1% to 5%

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voluntary response sample

Back 56

people who choose themselves by responding to a general appeal-these are usually biased

Front 57

random

Back 57

we call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large # of repititions
-a kind of order that only occurs in the long run

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probability

Back 58

the proportion of times the outcome of a random phenomenon would occur in a very long series of repititions

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event

Back 59

a specific collection of one or more outcomes

Front 60

sample space

Back 60

the collection of all possible outcomes of an experiment

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equally likely outcomes

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if a random phenomenon has k possible outcomes, all equally likely, then each individual outcome has probability 1/k. the probability of any event A is:
P(A)= outcomes in A/sample space
=outcomes in A/k

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probability rule #1

Back 62

the probability of P(A) of any event A satisfies 0≤P(A)≤1

Front 63

probability rule #2

Back 63

if S is the sample space in a probability model, then P(S)=1

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probability rule #3
the addition rule for disjoint events

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two events A and B are disjoint if they have no outcomes in common and so can never occur together. if A and B are disjoint
P(A or B) = P(A) + P(B)

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probability rule #4
the complement rule

Back 65

the complement of any event A is the event that A does not occur, written as Ac. the complement rule states
P(Ac)=1-P(A)

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probability rule #5
the multiplication rule for independent events

Back 66

two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. if A and B are independent then:
P(A and B)=P(A)P(B)

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probability rule #6
the general addition rule for unions of two events

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for any two events A and B
P(A or B) = P(A) +P(B) - P(A and B)

Front 68

probability rule #7
multiplication rule

Back 68

the probability that both of the two events A and B happen together can be found by P(A and B) = P(A)P(B I A)
here P(B I A) is the conditional probability that B occurs given the information that A occurs

Front 69

venn diagram

Back 69

a picture that shows the sample space S as a rectangular area and events as areas within S

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contingency table

Back 70

cross tabulation tables
present frequency counts for combinations of 2 or more variables

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marginal probabilities

Back 71

probabilities of single events

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joint probabilities

Back 72

P(A and B)

Front 73

conditional probability

Back 73

when P(A)>0, the conditional probability of B given A is
P(B I A) = P(A and B) ÷ P(A)

Front 74

union probabilities

Back 74

P(A or B)

Front 75

intersection

Back 75

the intersection of events is the event that all of the events occur

Front 76

tree diagram

Back 76

use a table instead

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baye's rule

Back 77

A1, A2, ..., Ak are disjoint events whose probabilities are not 0 and add to 1

P(Ai l C) = [P(C l Ai)P(Ai)] / [P(C l A1)P(A1) + ... + P(Ak)P(C l Ak)

C is another event whose probability is not 0 or 1

Front 78

independent events

Back 78

two events A and B that both have positive probability are independent if
(PB I A)=P(B)

Front 79

random variable

Back 79

a variable that assumes numerical values associated with the random outcomes of an experiment, where one (and only one) numerical value is assigned to each outcome

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discrete random variable

Back 80

-a countable number of possible values

-expressed with a table

-a random variable that may assume either a finite number of values or an infinite sequence of values (number of units sold, customers who enter a bank in one day)

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continuous random variable

Back 81

random variables such as weight and time, which may take on all values in a certain interval or collection of intervals
-uses density curves

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probability distribution

Back 82

of a discrete random variable lists the possible values and their probabilities

Front 83

two requirements for probabilities of discrete random variable

Back 83

-every probability pi is a number between 0 and 1
-p1+p2+p3...+pk = 1
(also no numbers can be negative)

Front 84

≤ vs< in discrete random variable

Back 84

they are not the same

Front 85

to find the mean of a discrete random variable

Back 85

E(X)=µx=∑x p(x)

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to find the variance of a discrete random variable

Back 86

Var(X)=sigma2/x = ∑ (x-µx)squared p(x)

Front 87

to find the standard deviation of a discrete random variable

Back 87

SD(X)=sigmax=square root of the variance

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to find mean, variance and standard deviation of a discrete random variable on the calculator

Back 88

enter values into list1, list2
f4:calc
1:1var stats
list: list1
freq: list2
enter

on the calc
µx=xbar
∑(x-xbar)squared=sigma squared x = variance

Front 89

continuous random variable

Back 89

takes on all values in an interval of numbers

Front 90

probability distribution of a continuous random variable

Back 90

-described by a density curve
-is always on or above the horizontal axis
-has an area exactly 1 underneath it

Front 91

uniform distribution

Back 91

-shape of a box
-find height by multiplying the interval along the x axis by something to equal 0
(interval between 2 and 6 = 4
4 x __ = 1
___=1/4=.25

Front 92

the probability density function

Back 92

f(X) = 1/4, 2≤x≤6
0, elsewhere

Front 93

≤ vs<

Back 93

for continuous random variables these are =

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µx on a uniform distribution

Back 94

lowest x + highest x ÷ 2 = mean

Front 95

percentage from a normal distribution

Back 95

from the question find:
x=what is varying
standard deviation
mean
example:
P(x≥80)=nmcdf(80, ∞, 75, 7.5)

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specific number from a percentage on a normal distribution

Back 96

P(x≤k)=.98
k=invnm=.98, 75, 7.5

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rules for means

Back 97

rule 1: if X is a random variable and a and b are fixed numbers then
µ a+bx=a+bµx

rule 2:if X and Y are random variables then
µx+y = µx + µy
µx-y = µx + µy

Front 98

rules for variances

Back 98

rule 1: if X is a random variable and a and b are fixed numbers then
sigma squared a=bx=bsquared sigmasquaredx
or
sigma a+b=bsigmax

rule 2: if X and Y are independent random variables then
sigmasquared x+y = sigma squaredx +sigmasquaredy

rule 1: if X is a random variable and a and b are fixed numbers then
sigma squared a=bx=bsquared sigmasquaredx
or
sigma a+b=bsigmax

rule 2: if X and Y are independent random variables then
sigmasquared x-y = sigma squaredx +sigmasquaredy

Front 99

the law of large numbers

Back 99

draw independent observations at random from any population with finite mean. as the number of observations are drawn increases, the mean of the observed values eventually approaches the mean of the population as closely as you specified and then stays that close