ADVANCED
PLACEMENT
Statistics
Notes by:
Jeremiah James dela Rosa
Temecula, CA
jeydicos@gmail.com
Thank you, Stats Medic, Luke & Lindsey!
ANALYSIS
CHAPTER 1:DATA
c ategorical
of
The distribution
·
-
-
data
frequency(percent/proportion)
relative
·
Total
1
marginal
j
·
For
a
en
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Total
specific
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variables
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with
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compare
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varies more)
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use
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to
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use
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aboutOUTLIERS:
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mean
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write
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plot
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SHAPE
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low outlier
<
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03 +
high
IQR)
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of
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a
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another
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on
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parameter:a
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CHAPTER 2:MODELING
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CHAPTER 3:EXPLORING
variables
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o r explain
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response
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Unusual Feature:
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CHAPTER 4: COLLECTING DATA
xx
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HOW TO CHOOSE AN
·
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Randomize: Use an RNG to get
n
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to the integers.
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ttempt
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2.
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eshmen
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within each pair.
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in
are
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a productivity
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number
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tex
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a
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ED
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assigned
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20 companies
individuals to
measure their responses.
on
tabled) to assign
effective.
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number
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combine results
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2208)
way
in such a
cannot be distinguished from
each other.
·
placebo: treatment
active
otherwise
no
an
·
to
has
is
like other treatments.
·treatment: a
applied
that
ingredient, but
specific condition
the individuals in
·
subjects: human beings are
experimental units.
variable
Factors: an explanatory
that
is
manipulated
cause
a
change
variable.
and may
in the response
inactive treatment.
·
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).
·
treatment
a
subject
receiving.
can
·
divingassignment: experimental
rare
units
are
assigned to treatments
using a chance process.
sampling variability different
random samples
the people who interact
with them and measure the
response variable don't know
subject is
be distinguished.
way
the response to the treatments.
of
the same
size from the same pop. produce
or
a
each
units that are known before the
experiment to be similar in some
that is expected to affect
single-blind: either the subjects
which treatment
treatment
replication: giving
units so
enough experimental
that any difference in the effects
block: a group of experimental
those
is
for all experimental
·
who interact with
them and measure the
which
response variable know
nor
control: keeping other variables
constant
units.
·double-blind: neither the subj
·
the
·
even an
treatment is
randomly assigned.
control group: used to provide
baseline for comparing the
a
effects of other treatments.
placebo effect: describes the
fact that some subjects in an
experiment will respond
favorably to any treatment,
experiment.
a
a
Factors x levels
·
experimental unit: the object
to which
a
*
response variable
effects on
systematic
to
combination of treatments?
when
associated
that their
are
two variables
values of
Factor-
·confounding: occurs
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.
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.
on
X (n)
random
random
delibaretly impose
treatments
is
is
answers
units so
enough experimental
treatments can be distinguished
effects of the
treatment
For
pattern of inaccurate
process (slips of paper,
units to treatments. This helps create
if a treatment
decide
example:
respons. Experimental
-
RN6,
chosen
sample can't be contacted.
there
treatments.
Group" -> Treatment 1
measures variables
of interest
more
likely
when
response bias: occurs
RANDOMIZED DESIGN
individuals
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and
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TYPES OF STUDIES
observes
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be
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to
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individual.
when
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iF there's a pattern
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first individual,
and choose every kth
be
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that
a chance
each
assignment
-
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can
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WE MIGHT
else can go
but what
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value from
a
identify
in the sample.
design
a
Replication: Impose
individuals ->
·
method
underestimate
treatments are imposed
roughly equivalent groups before
avoid
Control: keep other variables the same for all groups. Control helps
variation in responses, making it
confounding and reduces
or
paper,
select
all the
invitation.
sampling
lead to BIAS,
to an
which leads
of the study.
experimental
and
one
Randomly select
time & money.
Random Assignment: Use
·
let
Use
Comparison:
·
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letters on identical
hat, shuttle the papers
study b/c of open
BASIC PRINCIPLES OF EXPERIMENTAL DESIGN:
s lips of paper.
bowl
random
individuals choose
both of these
*
individual
selects every 4th
&
based on the population size
desired sample size. Randomly
but similar between
saves
*
-
to be a part of the
-
different
within (HETEROGENEOUS
than SRSs.
·
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systematic
*
c lusters are
precise estimates
of unknown population
paper:
or
x
ter
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reach
to
·voluntary sampling
x
in the chosen clusters
included
are
more
Write corresponding
numbers
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samples tend to give
labels.
selected
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values
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these clusters and
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001
near each other.
to
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these
combine
select: Choose the individuals
who correspond
of
separate
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ichooses individuals
easiest
identical slips of paper
into non-overlapping groups
individuals that are located
response. Then choose a
stratum & then
different integers (ignore
repeats, if necessary).
·
·
population
divide the
-
might affect their
WITHOUT REPLACEMENT
SRS.
when doing
to be chosen
chance
cluster sampling
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N.
1 to
From
stratified random sampling
SAMPLES
remains
SAMPLING
to do
* make sure
the same
given size
a
#
+
SAMPLE
gives every possible sample
of
MPLING WELL
mining
TYPES OF SAMPLING
POPULATION
-
& iFF.
·
estimates.
Statistically significant: the
· bserved
results of a
are
too unusual to be
by
chance alone.
study
explained
SIZE
SAMPLING VARIABILIM & SAMPLE
samples tend to
larger random
closer
are
produce estimates that
the
true population value than
smaller
random samples. In other
to
larger
words, estimates from
samples are
precise.
more
SAANSTALLY SI6 NIFI CANT
% 15%, yes, itis
*
IF
statistically significant
itmay
have
and
happened
by chance alone
% 75%, no, it
*
If
is
mayhave
happened
by coincidence only.
PROCESS
OF
1.)
2.) make a simulation
and
Identifyhow many
3)
the association
between
the explanatory and
the chance
or
3)
study explains
of whatthe
which
cause
Random
mean.
to
the difference
and
rule
mightbe
rull.
and
the
of
sample
estimates
margin
I
of
conducting random
*
Randomize
(oreC
it'svery
here, but
All thesenotes
*
will
essential to
used so
do
you cannot
12 since
chapter 4
is all
your future
and
information
RANDOMLY
Inference aboutpopulation:
Inference about
Inference about
RANDOM
ALWAYS
IS
IMPORTANT 888
ASSIGNED
TO
GROUPS?
NO
YES
cause &eFFect:YES
Inference aboutpopulation:
projects who
First.
& ata
data. There are
INDNIDUALS
studies
collecting your
aboutcollecting
lot
of
know
these
things since
Chapter
in
7 through
a
WERE
be
much
effect.
NO
interval
an
↑
individuals
of
SELECTED?
creates
plausible values.
select
the individuals were
YES
variability
error:
margin of
- All individual data must be kept
confidential. Only statistical summaries
for groups of subjects
YES
RANDOMLY
effect in the
use the
individuals
of
INDIVIDUALS
shows the
assignment:
INFERENCE
OF
SUMMARY:
WERE
continued application
time. The
- All individuals who are subjects in a
study must give their informed consent
before data are collected.
about
groups allows inference
cause
individuals don't.
- All planned studies must be reviewed
in advance by an institutional review
board charged with protecting the
safety and well-being of the subjects.
dotplot.
Assignment
some
Apexam
chosen.
·
associated with
are
possible.
the population
allow inference about
From
group
is believableat
or
Random selection
to
one
The individuals have consistency in the
problem.
of the
·
variable specific
of the explanatory variable
long
link
the association.
Alleged cause precedes effectin
the study is statistically
state if
not in the context
significant
THE SCOPE
a
response variable. This reduces
other
some
4)
dots are
5%
that
stronger responses.
explanatory variable, and
equal to the mean difference.
the
one
Larger values
than
are greater
many dots
to
strong.
is
consistent. Many studies ordifferent kinds shows
The association is
the percentage of
calculate
5)compare
EXPERIMENT:
explanatory variable
2)
4)
or
the
between
strong. The association
and the response variable
greater or equal to
in mean from
step 1.
how
is
WHEN WE CAN'T
DO AN
*
(P-VALUES
PERCENAGE
in
ESTABLISHING CAUSATON
In sampling
IDENTFYING TE
the difference
Identify
1)
FOR
placemeans
are
statistically significant
not
and it
I
CRITRIA
No
cause &eFFect:YES
Inference aboutpopulation:
Inference about
YES
cause &CFFest: NO
Inference aboutpopulation:
No
Inference about
cause &eFFert:NO
CHAPTER 5:PROBABILITY
Minim
Definitions;
Formulas:
·
·
P(A)
A
outcomes in event
number of
=
+
Addition
Rule:
P(A) P(B)
P(AUB)
·
-
+
=
·
mutually
exclusive
·
simulation
P(AnB)
·
P(A)
imitates
a
event can
random
happen at
process
in
such
time.
the same
simulated
way
that
a
consistent
with
real-world
outcomes.
simulation process:
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③ Use
Y*
=
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no
-
outcomes are
P(given event occurs)
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("given that"):
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approaches the true
probability.
=
General
proportion
process, the
trials ofany
more and more
we observe
if
-
random
P(AUB) P(A) P(B)
·
determined purely
to 1.
law of
large numbers
·
for mutually exclusive events:
Rule
are
0 and 1.
between
outcome
-
-must add
P(A)
-
=
Addition
probability
·
rule:
P(AY) 1
that
outcomes
process-generates
by chance.
total number of outcomes in sample space
Complement
·
random
·
·
sample space
·
conditional
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how
the result
·
answer
to
possible
reptition)
trial (one
the
question.
outcomes.
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probability
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if
knowing
occurred
other
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=
does
event
known to have
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event
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trials (repetitions)
many
all
list of
simulate
you will
whether or
not
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change
not one
the
that
happened.
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event
probability
that
the
happen.
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or
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·
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·
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=
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least
probability
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TO
FOR
IS
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US
know
to
ifthere is
the
From
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the
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the
the
total
SAY
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convincing evidence
or
proportion
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simulation.
number
number
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of
out
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simulation.
of
IF:
proportion of dots
*
From
#3
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it is statistically
significant
based
on
the
question.
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proportion of dots
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#3
(1)
intersection
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5%,
itis not statistically
significant
based
A
A
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1
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AR-pcanc
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ACPIBIAY:
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P(A1B)
P(A'nB)
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P(Are)
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CHAPTER 6:Random Variables & ProbabilityDistributions
DEFINITONS:
FORMULAS:
variables
Random
Discrete
·
missing
P(X k), where i s
Fk)
1
P(X
P(X k)
*
=
+
+
+
+
.
variables
discrete random
=
·
Mx E(X) (X,)(P.) (x2)(P2) +
=
+
=
54 (x,
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=
Mx)
-
(P.) (xz
-
+
Mx)YP2)
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+
.
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mean
process.
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standard deviation of a discrete
variable
x_x*neige
#
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of the
*
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density curve
t
E
the
Normal density curve-used in
deviations
transformation
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same
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mean:
y: b.*: b
same
on
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independent
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a
bMx
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standard deviation.
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VARIABILIM.
CHAPTER 7:SAMPLING DISTRIBUTION
Parameter (p, M,0)
·
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Statistic (I, X,sx)
char. OFSAMPLE.
some
Distribution
sampling
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17
CHAPTER 8:
ESTIMATING
The
point estimator:a
chosen statistic
(B, x, sx)
will provide
reasonable
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a
aboutthe
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Congratulations!
You have finished the AP Statistics Course!
—Mr. Jeremiah James dela Rosa
Thank you to Stats Medic, Luke Wilcox, and Lindsey Gallas!