Statistics

Statistics - Basic
Statistics
for
Emg
Lab
 
...

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Unformatted text preview: Basic
Statistics
for
Emg
Lab
 
 Introduction

 Statistics
is
a
mathematical
science
pertaining
to
the
collection,
analysis,
 interpretation
or
explanation,
and
presentation
of
data.


There
are
two
types
of
 statistical
methods
we
will
be
using
in
the
emg
lab:
descriptive
statistics
and
 inferential
statistics.


 
 Descriptive
statistics
such
as
the
mean,
standard
deviation
and
standard
error
can
 be
used
to
summarize
or
describe
a
collection
of
data.
In
addition,
patterns
in
the
 data
may
be
modeled
in
a
way
that
accounts
for
randomness
and
uncertainty
in
the
 observations,
and
then
used
to
draw
inferences
about
the
process
or
population
 being
studied;
this
is
called
inferential
statistics.

A
t‐test
and
an
Analysis
of
Variance
 (ANOVA)
are
both
types
of
inferential
statistics.
 
 Mean
 Definition
–
the
mean
is
the
arithmetic
average
of
a
set
of
values
or
a
statistical
 distribution.

For
a
data
set,
the
mean
is
the
sum
of
the
observations
divided
by
the
 number
of
observations.
 Ex:

Suppose
you
are
a
swimmer
training
for
the
Olympic
Games
in
2012
and
you
 want
to
know
what
the
mean
time
was
for
the
men
in
the
100
meter
butterfly.

The
 times
in
the
finals
are
listed
below.
 Swimmer
Name
 Michael
Phelps
 Milorad
Cavic
 Andrew
Lauterstein
 Ian
Crocker
 Jason
Dunford
 Takuro
Fujii
 Andrii
Serdinov
 Ryan
Pini
 
 Time
(seconds)
 50.58
 50.59
 51.12
 51.13
 51.47
 51.50
 51.59
 51.86
 To
calculate
the
mean
you
would
sum
the
times
and
divide
the
sum
by
the
number
 of
swimmers
(below).
 sec
 Standard
Deviation
(σ )
 Definition
–
a
measure
of
the
variability
of
a
collection
of
values.
 Calculating
SD
 1) 2) 3) 4) 5) Find
the
mean
of
the
values
in
your
data
set:
xm
=
(x1+
x2+...+
xn)
÷n.
 For
each
value
(xi)
calculate
its
deviation
from
the
mean
(xi‐xm).
 Calculate
the
squares
of
these
deviations
(xi‐xm)2.
 Find
the
mean
of
the
squared
deviations.

This
quantity
is
the
variance.
 Take
the
square
root
of
the
variance.

This
quantity
is
the
standard
deviation.
 Ex:

Find
the
standard
deviation
for
the
men’s
100meter
butterfly
times.
 1) Mean
=51.23
 2) Deviation
from
the
mean
 a. Michael
Phelps
=
(50.58‐51.23)
=
‐0.65
 b. Milorad
Cavic
=
(50.59‐51.23)
=
‐0.64
 c. Andrew
Lauterstein
=
(51.12‐51.23)
=
‐0.11
 d. Ian
Crocker
=
(51.13‐51.23)
=
‐0.1
 e. Jason
Dunford
=
(51.47‐51.23)
=
0.24
 f. Takuro
Fujii
=
(51.50‐51.23)
=
0.27
 g. Andrii
Serdinov
=
(51.59‐51.23)
=
0.36
 h. Ryan
Pini
=
(51.86‐51.23)
=
0.63
 3) Calculate
the
square
of
the
deviations
 a. Michael
Phelps
=

‐0.652
=
0.4225
 b. Milorad
Cavic
=
‐0.642
=
0.4096
 c. Andrew
Lauterstein
=
‐0.112
=
0.0121
 d. Ian
Crocker
=
‐0.12
=
0.01
 e. Jason
Dunford
=
0.242
=
0.0576
 f. Takuro
Fujii
=
0.272
=
0.0729
 g. Andrii
Serdinov
=
0.362
=
0.1296
 h. Ryan
Pini
=
0.632
=
0.3969
 4) Find
the
mean
of
the
squared
deviations
(the
variance
σ2).
 
 5) Take
the
square
root
of
the
variance
which
is
the
standard
deviation
(σ).
 sec
 
 Standard
Error
of
the
Mean
(SEM)
 Purpose
–
The
mean
of
a
sample
of
data
is
an
estimate:
it
estimates
the
“true”
mean
 of
the
whole
population,
or
the
“true”
mean
of
the
statistical
distribution.

For
 example,
the
mean
height
of
students
in
this
lab
is
an
estimate
of
the
mean
height
of
 the
whole
population
of
Harvard
students.

We
want
to
quantify
the
likely
error
 between
the
sample
mean
and
the
“true”
mean.
 Definition
–
SEM
is
an
unbiased
estimate
of
expected
error
in
the
sample
estimate
 of
the
population
mean.

SEM
is
calculated
by
dividing
the
standard
deviation
of
a
 sample
by
the
square
root
of
the
sample
size.
 
 Ex:

Suppose
you
want
to
know
the
amount
of
standard
error
for
the
average
time
 for
the
men’s
100
meter
butterfly.
 
sec
 The
average
and
standard
error
for
this
data
set
would
be
presented
as
 51.23±0.15sec.
 
 T­test
 Purpose:

If
you
want
to
compare
two
data
sets
to
determine
whether
there
is
a
 significant
difference
between
the
means
of
the
two
data
sets,
you
would
use
a
t‐test
 to
determine
a
P‐value.
 Types
of
t­tests
 Unpaired
t­tests:

This
type
of
t‐test
is
used
when
you
have
independent
samples
–
 in
other
words,
samples
that
are
not
directly
related
to
each
other.

For
example:
 Test
scores
between
males
and
females.
 Paired
t­tests:

This
type
of
t‐test
is
used
when
you
have
dependent
samples,
for
 example
when
you
collect
data
both
before
and
after
some
manipulation
of
your
 subjects.

Ex:

Stress
hormone
levels
before
and
after
an
exam.

 
 Analysis
of
Variance
(ANOVA)
 Purpose:
If
you
want
to
compare
three
or
more
data
sets
to
each
other
to
determine
 if
there
is
a
significant
difference
between
the
means
of
the
data
sets
you
would
use
 an
ANOVA
to
determine
a
P‐value.
 
 Interpreting
Your
Results
 Both
t‐tests
and
ANOVA
tests,
when
run
on
either
Excel
or
SPSS,
will
generate
a
 number
called
a
p‐value.

A
p‐value
is
the
smallest
significance
level
at
which
a
null
 hypothesis
may
be
rejected:
the
smaller
the
p‐value,
the
stronger
the
evidence
 against
the
null
hypothesis.

A
p‐value
of
0.05
or
smaller
is
usually
considered
 statistically
significant
in
the
biological
sciences.

Therefore
if
you
run
your
tests
and
 the
resultant
p‐value
is
less
than
or
equal
to
0.05,
you
have
a
statistically
significant
 difference
in
the
mean
values
you
measured.
 
 ...
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This note was uploaded on 03/29/2012 for the course LS 2 taught by Professor Andrewa.biewener,petert.ellison,anddaniele.lieberman during the Fall '10 term at Harvard.

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