Class notes
STATS 250: ALL Lecture Notes
- Course
- STATS 250
- Institution
- University Of Michigan - Ann Arbor
CUMULATIVE lecture notes for STATS250 at the University of Michigan. Class was taken FA2023 under Prof. Alicia Romero
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Lecture1
-
8/28
●
Observational
Unit:
individual
cases
in
a
data
set
●
Variables:
information/characteristics
in
each
observational
unit
○
Can
you
compute
the
average?
■
Yes
→
Quantitative
Variable
●
Quantitative
Discrete:
values
can
only
be
mapped
to
integers
○
Ex:
vote
count,
number
of
ppl
(can’t
have
.27
ppl)
●
Quantitative
Continuous:
any
number
of
infinite
values
in
an
interval
○
Ex:
movie
runtime
(can
have
90.74
minutes)
■
No
→
Categorical
Variable
●
Categorical
Ordinal:
natural
ranking
within
○
Ex:
Movie
ratings
(PG-13,
R,
etc)
●
Categorical
Nominal:
no
natural
ranking
○
Ex:
Movie
genre
○
Ex:
movie
runtime
(Q),
movie
genre
(C)
●
EXAMPLES
○
How
long
did
you
sleep
last
night?
■
Quantitative
Continuous
○
More
than
7
hours
of
sleep
last
night?
■
Categorical
Nominal
○
Number
of
credits?
■
Quantitative
Discrete
○
What
proportion
of
students
are
left
handed?
■
N/A
○
Dominant
hand?
■
Categorical
Ordinal
(if
ambidextrous
is
considered)
Lecture
2
-
8/30
●
Prework:
○
1:
b
○
2:
b
○
3:
c
○
4:
b
○
5:
d
●
Variables
play
diff
roles
in
research
○
Explanatory
variable:
independent
variable
■
Manipulated
by
researchers
■
Thought
to
cause
a
difference
in
the
outcome
○
Response
variable:
dependent
variable
■
Observed
by
researchers ■
Gets
changed
because
of
the
explanatory
variable
●
Common
data
collection
methods:
○
Experiments
○
Observational
studies
○
Sampling
●
Salk
Polio
Vaccine
Field
Trials:
investigated
effectiveness
of
polio
vaccine
○
Explanatory:
given
vaccine
or
not/given
placebo
○
Response:
rate
of
infection
○
Design
#1:
■
■
Issues:
diff
ages
for
treatment/control,
no
informed
consent,
no
placebo/blindness
■
Need
treatment
+
control
groups
to
be
the
same
except
for
treatment
condition
○
Design
#2:
■
■
Fixes:
avoids
bias
(internal
or
otherwise)
in
choice
of
treatment/control
subjects,
acknowledges
all
age
groups
and
consent,
gives
placebo,
double
blind
study
○
Random
Assignment:
decreases
influence
of
confounding
factors
(underlying
factors
such
as
consent),
which
affect
both
explanatory
and
response
variables
●
Placebo
control
study
provided
stronger
evidence
for
vaccine
effectiveness
●
Well-designed
experiments
that
use
random
assignment
allow
us
to
make
causal
inferences
about
relationships
between
explanatory
and
response
variables
●
May
not
be
possible
to
construct
ethical
experiments,
placebos,
etc
●
Observational
studies:
researchers
simply
observe
subjects
without
interfering
in
their
behavior
○
Case
study:
are
infants
raised
w/o
exposure
to
darkness
more
likely
to
have
myopia?
■
Explanatory:
exposure
to
darkness
■
Response:
myopia ○
Observed
(rather
than
assigned)
which
child
chose
to
sleep
with
or
without
a
night
light
■
Found
that
those
that
had
night
lights
more
likely
to
develop
myopia
○
HOWEVER,
observational
studies
can
only
show
associations
,
not
make
causal
conclusions!
○
Conclusion:
there
is
an
association
between
these
two
variables,
not
necessarily
a
causal
relationship
■
Can
we
explain
this
association
otherwise?
●
→
many
of
the
infants
studied
were
children
of
myopic
parents,
who
were
more
likely
to
leave
the
light
on
at
night
to
attend
to
infants
than
parents
who
could
see
well
○
Parent’s
vision
(genetics)
was
a
confounding
variable
■
Random
Sampling
●
Population
of
Interest:
target
of
the
research,
collection
of
all
the
people/items/observational
units
we
want
to
learn
about
●
Sampling:
instead
of
measuring
an
entire
population
of
interest,
researchers
will
gather
data
from
a
subset
of
the
population,
called
the
sample
○
How
not
to
take
a
sample:
“I
met
2
UM
students
who
took
more
than
7
years
to
graduate,
so
it
must
take
longer
to
graduate
at
UM!”
■
Anecdotal
data!
●
Usually
remembered
because
they
are
recalled
based
on
striking/unusual
characteristics
○
Choosing
a
sample
at
random
makes
it
more
likely
that
it
will
be
representative
of
the
population
■
More
accurate
inferences,
can
generalize
results
to
the
whole
population
●
2
sample
questions:
○
How
is
global
warming
influencing
coral
reef
health
in
the
Pacific
Ocean? ■
Population
of
interest:
coral
reefs
in
the
Pacific
Ocean
○
Over
the
last
5
years,
what
is
the
average
time
to
complete
a
degree
for
UM
undergrads?
■
Population
of
interest:
UM
alumni
who
have
received
an
undergrad
degree
in
the
last
5
years
→
inferences
to
the
population
can
be
drawn
↓
Causal
inference
can
be
drawn
Group
work:
melanoma/sunscreen
●
Explanatory:
sunscreen
sales
●
Response:
melanoma
numbers
●
Confounding
variable:
climate,
melanoma
development
before
2015/during
time
frame,
ethnicity,
access
to
healthcare/having
medical
records
●
Research
question:
do
sunscreen
sales
affect
melanoma
levels?
●
Physical
activity:
sweating/swimming
so
sunscreen
comes
off
regardless
of
application,
might
be
outside
a
lot
more
●
Not
generalizable:
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