ADVANCED
PLACEMENT
Statistics
CHAPTER 1: DATA ANALYSIS
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SECTION 1.1:
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CHAPTER
MODELING
2:
DISTRIBUTIONS
QUANTTATIVE
SECTION 2.1:Describing Location
in
Distribution
a
Percentiles
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to it,
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CHAPTER
EXPLORING TWO-VARIABLE
QUANTIATIVE DATA
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simple random sample (SRS)
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CHAPTER
4: COLLECTING DATA
SRS?
·
Technology:
individual
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the sample.
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paper:
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based
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paper they got.
on the slip of
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observes
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but
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to
ttempt
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20
treatments
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size
2.
In
units
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assigned
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unit receives
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number
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->
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the same
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(h)
I
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combine
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(n)
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random
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compare
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f
t
->
treatments
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example:
random
eshmen
#
a
randomly
grade
levels
-
->
number
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generator -
(100)
- &ophomores
->
(400)
within each pair.
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in
->
&
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MPD,
and the
are
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7
2->Treatment 2
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very similar experimental
two
(n)
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some
to assign
effective.
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compare
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sources
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combine results
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compare
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a
2208)
A track coach wants to know whether his long-distance
runners are faster running the track clockwise or
counterclockwise. Design an experiment that uses a
matched-pairs design to investigate this question. Explain
your method of pairing.
in such
effects
way
a
cannot be
distinguished from
each other.
·
that
placebo: treatment
active
otherwise
no
ingredient,
an
·
has
is
like other treatments.
·treatment:
applied
but
a
specific
condition
the individuals in
to
to which
a
subjects:
human
are
experimental units.
variable
Factors: an explanatory
that
cause
is
manipulated
a
change
variable.
survey
question.
Description:
- Form blocks based on grade level
(Individuals + Blocks) because scores
on the geometry final exam are
likely to vary by grade level since
Freshmen who takes geometry tend
to be more advanced in their math
coursework.
- Assign each individual student
from 1 to 100 for Freshmen. Use a
random number generator to obtain
50 random integers (random
assignment), select these students
and assign them to online (Block 1 +
Treatment 1). The remaining
students are assigned to teacher
taught (Block 1 + Treatment 2).
- Assigned each individual student
from 1 to 400 for Sophomores. Use
a random number generator again to
obtain 200 random integers (random
assignment), select these students
and assign them to online (Block 2 +
Treatment 1). The remaining
students are assigned to teacher
taught (Block 2 + Treatment 2).
- At the end of the course, let them
take the same geometry final exam
and compare the scores (compare).
- Once all students have taken the
test, and the scores have been
compared for each treatment for
each block, then combine the results
and compare (combine and compare).
and may
in the response
levels
inactive treatment.
·double-blind:
neither the
·
·
can
subject is receiving.
either the subjects
the people who interact
or
with them and measure the
response variable don't know
which treatment
a
units
using
are
a
subject
is
experimental
assigned to treatments
chance process.
experimental
each
a
treatment
group of experimental
units that
are
experiment
before
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the
to be similar in some
to affect
way that is expected
the response to the treatments.
·
single-blind:
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rare
all
distinguished.
be
block:
subj
a
for
replication: giving
units so
enough experimental
that any difference in the effects
·
those
treatment
control: keeping other variables
constant
units.
who interact with
them and measure the
which
response variable know
nor
·
beings
x
control group: used to provide
baseline for comparing the
a
even an
treatment is
the
·
a
effects of other treatments.
placebo effect: describes the
fact that some subjects in an
experiment will respond
favorably to any treatment,
unit: the object
randomly assigned.
·
Factors
·
experiment.
experimental
a
*
response variable
on
systematic
to
combination of treatments?
when
associated
that their
are
two variables
values of
Factor-
occurs
·confounding:
levels: different
·
VOCABS988
random order.
Description:
Have each long distance runner race 1 mile in each
direction. Some runners are faster than others, so using
each runner as his or her own “pair” accounts for variation
in 1-mile race times among the runners. For each runner,
randomly assign the order in which the treatments
(clockwise a nd counterclockwise) are assigned — by
flipping a coin. Heads indicates the runner will race
clockwise first and counterclockwise second; tails indicates
the runner will race counterclockwise first and clockwise
second. Allow adequate recovery time between the races.
For each runner, record the 1-mile race times for each
direction.
1503
online
(200)
random
experimental
both treatments
example:
online
a
Description:
- Number the companies from 1 to 20
(20 individuals)
- Use a random number generator to
produce 10 different random integers
from 1 to 20 (random assignment)
- Select the first 10 different
integers (Group 1) and assign them to
additional lighting (Treatment 1)
- Select the remaining companies
(Group 2) and assign them to the
same lighting (Treatment 2).
- Compare the increase in worker
productivity between the two groups.
treatments.
groups.
For
pattern of inaccurate
(n)
BLOCK
DESIGN
design for comparing two
that
X
Group"
is
there
on
between
differences
chance
random
experimental
common
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is
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a
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chosen
sample can't be contacted.
answers
tabled)
likely
when
response bias: occurs
Treatments
ED
moman
PAIRS
more
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less
are
individual
the
not
(slips of paper, RN6,
units to treatments. This helps create
Block
individuals to
measure their responses.
on
an
is
population
units so
enough experimental
treatments can be distinguished
effects of the
assignment
companies
BOMIZED
delibaretly impose
treatments
or
members
population
monomn andreassignmenttorepeaterintothebroch
(conditions)
->
scompare
tex
random
↑
respons. Experimental
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if
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some
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example:
measures variables
and
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WRONG ???
occurs when
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population.
compares two
that
design
->
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pattern
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of the study.
be
be chosen or cannot
to
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individual.
when
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ordered,
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RANDOMIZED DESIGN
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EXPERIMENTAL DESIGN:
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and
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open invitation.
sampling
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sampling
and choose every kth
be
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individuals choose
be a part of the
both
*
treatments are imposed
roughly equivalent groups before
avoid
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variation in responses, making it
confounding and reduces
·
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random
value
a
identify
time & money.
Random Assignment: Use
identical
on
s lips of paper.
select
all the
experimental
Write corresponding
numbers
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Comparison:
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·
OF
to
individual
selects every 4th
&
based on the population size
desired sample size. Randomly
but similar between
BASIC PRINCIPLES
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select
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ichooses individuals
to reach
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than SRSs.
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and
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ter
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WITHOUT REPLACEMENT
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individuals that are located
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TYPES OF SAMPLING
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sampling variability different
random samples
size from the
& iFF.
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the same
same
pop. produce
estimates.
Statistically significant: the
·
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are
by
results of
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SAMPLING VARIABILIN & SAMPLE
random samples tend to
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STAMSTICALLY SIGNIFICANT
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OF
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plausible.
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used
be
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of
values.
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RANDOMLY
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ASSIGNED
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YES
YES
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projects
collecting your
information
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YES
your future
collecting
of
know
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studies
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things since
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12 since
through
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so
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the
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chapters
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these notes
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individuals
SUMMARY:
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The cause is believable, not
f
about
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cause
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before data are collected.
study is statistically
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ME SCOPE
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mean
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individuals don't.
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in advance by an institutional review
board charged with protecting the
safety and well-being of the subjects.
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the chance
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EXPERIMENT:
WAH WE CAN'T DO AN
The association between
strong.
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random samples. In other
smaller
ESTABLISHING CAUSATION
No
YES
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cause
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cause
YES
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5: PROBABILITY
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variables
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