Week 8 - Lecture
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American Military University *
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Course
300
Subject
Statistics
Date
Jan 9, 2024
Type
docx
Pages
20
Uploaded by papadogiannis
Week
8:
Consumer
of
Scholarly
Research
Overview:
Welcome
to
Week
8.
In
the
previous
lessons,
you
learned
the
importance
of
writing
to
the
audience
(not
addressing
the
audience)
as
you
construct
a
research
proposal.
You
learned
how
to
conduct
a
literature
review.
You
also
learned
the
significance
of
performing
ethical
research.
You
learned
about
the
different
approaches
you
may
use
in
conducting
research
(qualitative,
quantitative,
and
mixed
methods),
the
meaning
and
importance
of
validity
and
reliability
pertaining
to
the
instrument
used
to
obtain
data,
and
the
differences
between
quasi-experimental
and
non-experimental
research.
All
of
this
information
was
intended
to
assist
you
in
becoming
a
better
researcher
and
a
better
consumer
of
research.
The
purpose
of
statistical
analysis
is
to
take
the
numerical
data
obtained
from
the
study
and
interpret
it
in
a
meaningful
way
(Ellis
et
al.,
2010).
This
week's
lesson
focuses
on
interpreting
the
information
before
you.
Course
Objective(s):
CO8:
Produce
an
academic
research
proposal
based
on
a
thorough
analysis
of
a
current
issue
in
the
social
sciences
reflecting
the
need
for
further
study
and
demonstrating
a
well
thought
out
research
design.
MO1:
Understand
basic
statistical
analysis
and
its
interpretation.
MO?2:
Understand
difference
between
descriptive
and
inferential
statistics.
MO3:
Understand
what
is
meant
by
type
|
and
Il
errors.
MO4:
Understand
significance
levels
and
the
importance
of
P-values.
MO5:
Understand
measurements
of
spread,
and
measurements
of
central
tendency.
SSGS300
RESEARCH
METHODS
LESSON
EIGHT
R
e
el
i
N
S
5
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el
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e
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e
A
B
T
Have
you
ever
been
ovenvhelmed
reading
a
research
study?
How
many
times
reading
a
study
have
you
found
yourself
simply
iust
wanting
the
botiom-
line
because
you
are
lost
in
symbols
and
stalistical
jargon?
This
lesson
will
hriefly
describe
what
you
should
look
for
o
find
the
answers
1o
these
guestions
as
well
as
1o
identify
what
you
need
1o
include
in
your
completed
study
when
the
time
comes,
The
purpose
of
statistical
analysis
is
{0
take
the
numerical
data
obtained
from
the
study
and
interpret
it
in
a
meaningful
way.
With
this,
the
data
collected from
the
study
will
turn
into
evidence
that
may
prove
or
disprove
a
phenomenon,
Most
importantly,
T
will
answer
two
of
the
most
important
guestions:
Did
the
introduction
of
a
program
or
a
treatment
make
a
difference
in
the
experimental
group?
And
is
the
difference
statistically
significant?
Topics
10
be
covered
include:
Basic
statistical
analysis
and
#s
interpretation
Descriptive
siatistics
Measurements
of
central
tendency
Measurements
of
spread
inferential
statislics
Common
{esting
methods
Type
|
and
H
errors
Significance
levels
P-values
Descriptive
Statistics
Population
by
Sex
and
Age
Total
Population:
601,723
T
T
1
40,000
20,000
0
20,000
40,000
Male
Female
DESCRIPTIVE
STATISTICS
PROVIDE
SUMMARIES
Descriptive
statistics
provide
summaries
of
the
samples
and
measurements
of
a
study.
They
deal
with
the
graphic
representation,
enumeration,
and
organization
of
data.
Typically,
descriptive
statistics
involve reports
of
the
mean
(average)
and
frequency
(how
often
a
certain
answer/number
occurs).
The
purpose
of
descriptive
statistics
is
to
simply
describe
the
findings
of
a
study,
not
to
draw
conclusions
from
the
statistics.
EXAMPLES
This
type
of
statistics
takes
large
sets
of
observation
data
and
parses
it
down
into
easily
understandable
and
meaningful
numbers.
An
example
of
descriptive
statistics
is
the
national
population
census
of
the
United
States.
All
the
residents
in
the
United States
were asked
to
provide
information,
such
as
age,
sex,
race,
and
marital
status.
This
data
can
then
be
arranged
into
charts,
graphs,
and
tables
that
describe
the
characteristics
of
the
population
during
a
specific
timeframe.
IMPORTANCE
One
reason
why
it
is
important
to
utilize
descriptive
statistics
in
research
is
because
if
a
researcher
simply
presented
raw
data
it
would
be
difficult
for
the
reader
to
visualize
what
the
data
was
showing,
especially
if
there
was
a
great
amount
of
it.
Descriptive
statistics
therefore
enable
the
researcher
to
present
the
data
in
a
more
meaningful
way,
allowing
for
a
simpler
interpretation
of
the
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data.
Imagine
if
a
police
department
had
a
set
of
data
showing
crimes
committed
in
a
certain region.
The
department
may
be
interested
in
the
overall
rise
or
fall
in
crime
in
that
region,
but
they
would
also
be
interested
in
its
distribution
or
spread;
for
instance,
how
many
crimes
may
be
committed
in
a
certain
neighborhood
as
opposed
to
another.
Descriptive
statistics
allow
for
this.
COMBINATION
OF
FORMATS
When
we
use
descriptive
statistics
it
is
useful
to
summarize
groups
of
data
using
a
combination
of
tabulated
description
(tables),
graphical
description
(graphs
and
charts)
and
statistical
commentary
(textual
explanation).
Generally
speaking,
there
are
two
types
of
descriptive
statistics,
those
that
measure
central
tendency
and
those
that
measure
spread.
Measurements
of
Central
Tendency
mode
50%50%
median
mean
A
graphical
representation
of
the
mode,
median,
and
mean
One
type
of
descriptive
statistics
are
measurements
of
central
tendency.
These
are
numbers
that
describe
the
central
position
of
a
distribution.
Mean:
Most
often
this
central
position
is
the
mean,
or
the
average
of
a
data
set
when
all
numbers
in
the
distribution
are
added
together
and
divided
by
the
number
of
members
in
that
set.
Median:
Other
times
it
can
be the
median,
or
the
number
in
the
center
of
the
data
set
when
the
numbers
are
arranged
from
least
to
greatest.
Mode:
The
mode
is
the
number
that
appears
the
most
frequently
in
the
data
set.
Measures
of
central
tendency
are
sometimes
called
measures
of
central
location
or
summary
statistics.
STRENGTHS
OF
MEAN
The
mean,
while
the
average
of
all
the
numbers
in
a
data
set,
is
not
often
one
of
the
actual
values
that
you
may
observe
in
a
data
set.
One
of
its
important
properties
is
that
it
is
the
one
value
that
is
closest
to
all
the
rest.
An
important
property
of
the
mean
is
that
it
includes
every
value
in
the
set
as
part
of
the
calculation.
In
addition,
the
mean
is
the
only
measure
of
central
tendency
where
the
sum
of
the
deviations
of
each
value
from
the
mean
is
always
zero.
WEAKNESS
OF
MEAN
However,
the
mean
of
a
data
set
is
not
always
the
best
number
to
use
for
a
measurement
of
central
tendency.
It
is
particularly
susceptible
to
the
influence
of
values
that
are
especially
small
or
large
in
numerical
value.
An
example
may
be
a
data
set
containing
the
salaries
of
a
group
of
ten
employees
in
a
local
office.
The
general
manager
at
this
office
makes
a
salary
of
$80,000
a
year,
while
the
assistant
manager’s
salary
is
$60,000.
The
other
eight
employees
each
make
$18,000
a
year.
If
using
the
mean
to
determine
the
central
tendency
of
this
data
set,
the
result
would
be
$28,400—over
50
percent
more
than
four-fifths
of
the
employees
make,
and
less
than
half
what
the
other
one-fifth
do.
Clearly,
this
is
not
the
best
measurement
to
use
to
describe
the
central
position
of
this
distribution;
median
or
mode
would
work
better
in
this
situation.
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P
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&
Measurements
of
Spread
Measurements
of
spread,
anocther
type
of
descriptive
statistics,
describe
how
the
data
is
spread
out
across
a
distribution,
Usually,
not
all
observed
data
is
near
the
central
position;
rather,
there
often
is
outlving
data.
s
important
(o
understand
the
relationship
between
the
measure
of
the
spread
of
data
values
and
measures
of
central
tendency.
A
measure
of
spread
describes
how
well
the
mean
or
other
number
representing
the
central
position
represents
the
data.
If
the
spread
of
values
in
the
data
set
is
large,
the
mean
does
not
represent
of
the
data
as
well
as
it
would
were
the
spread
smaller.
Alarge
spread
indicates
large
differences
between
numbers
in
a
data
set.
In
researeh,
minimal
variation
within
a
dala
set
is
consideraed
desirable.
Types
of
measurement
of
spread
include
the
range,
the
standard
deviation,
and
the
varance,
Range
The
range,
the
simplest
measure
of
spread,
is
the
difference
between
the
highest
and
lowest
numbers
in
a
data
set
when
the
numbers
are
ordered
from
lowest
1o
highest.
Range
is
calculaled
as
maximum
value
-
minimum
value.
For
example,
assume
that
a
study
is
being
conducted
with
ten
participants
aged
23,
56,
45,
65,
b9,
55,
62,
54,
85,
and
25.
The
mastimum
value
{oldest
participanty
is
85
and
the
minimum
value
(youngest
participant}
is
23.
This
results
in
a
range
of
62,
which
is
85
minus
23,
While
using
therange
as
a
measure
of
spread
is
imited,
it
can
be
useful
it
vou
are
measuring
a
variable
that
has
either
a
critical
ow
or
high
threshold
{or
both)
that
should
not
be
crossed.
The
range
will
instantly
inform
vou
whether
at
least
one
vaiue
broke
these
critical
thresholds,
For
example,
if
the
study
shown
above
was
intended
to
study
only
participants
forty
and
older,
determining
the
rangs
would
immediately
inform
the
researcher
that
they
had
made
an
error
in
choosing
the
study's
sample
size,
Smith
Vargas
9
3
10
7
11
11
12
15
13
19
|
Mean
11
11
I
Range
4
8
J
Measurements
of
Spread:
Variance
and
Standard
Deviation
59
0
0
55
-4
16
62
3
9
54
-5
25
Mean
=
59
Column
Sum
=
86
Sample
variance
is
86
divided
by
the
difference
of
5
and
1,
which
equals
21.5.
Standard
deviation
is
the
square
root
of
the
variance.
The
square
root
of
21.5
is
approximately
4.6.
VARIANCE
Unlike
range,
which
is
only
concerned
with
extremes,
variance
looks
at
all
the
data
points
and
then
determines
their
distribution.
Statistical
variance
gives
a
measure
of
how
the
data
distributes
itself
around
the
central
position.
Determining
variance
is
more
difficult
than
range
and
requires
a
complex
mathematical
formula,
but
to
put
it
plainly,
it
is
simply
the
average
of
the
squared
differences
from
the
mean.
For
the
sake
of
simplicity,
let's
work
with
a
smaller
data
set
when
determining
variance:
65,
59,
55,
62,
and
54.
There
are
five
numbers
in
this
set
and
their
mean
is
59.
CALCULATING
VARIANCE
First,
we
will
take
each
number
in
the
set
and
subtract
the
mean
from
it.
Some
of
the
results
we
will
have
will
be
negative.
In
the
case
of
these
five
numbers,
we
will
end
up
with
6,
0,
—4,
3,
and
—5.
The
next step
will
be
to
square
each
of
these
numbers;
the
results
from
this
step
are
36,
0,
16,
9,
and
25.
Add
together
these
five
numbers
and
divide
the
sum
by
the
number
in
the
set:
86
divided
by
5is
17.2,
which
is
the
variance
for
this
data
set
(the
range
in
this
case
would
be
11).
SAMPLE
VARIANCE
When
are
looking
at
just
a
sample
instead
of
the
whole
population,
you
find
the
sample
variance.
The
sample
variance
will
give
you
an
idea
of
how
spread
out
your
sample
data
is.
In
order
to
use
sample
variance,
simply
subtract
1
from
the
number
of
items
in
the
set:
5
minus
1
is
4.
So
instead
of
dividing
86
by
5,
you
will
divide
86
by
4,
giving
you
a
sample
variance
of
21.5.
STANDARD
DEVIATION
The
last
type
of
measurement
of
spread,
standard
deviation,
is
both
the
most
complex
and
the
most
commonly
used.
Standard
deviation
is
formulating
by
first
determining
the
variance
of
a
data
set,
and
then
by
simply
finding
its
square
root.
In
the
example
above,
the
standard
deviation
would
be
approximately
4.1.
An
important
attribute
of
the
standard
deviation
is
that
if
the
mean
and
standard
deviation
are
known,
it
is
possible
to
compute
the
percentile
rank
of
any
number
in
a
set.
In
a
normal
distribution,
about
68
percent
of
the
numbers
are
within
one
standard
deviation
of
the
mean,
and
about
95
percent
of
the
numbers
are
within
two
standard
deviations
of
the
mean.
For
this
reason,
it
is
often
used
in
situations
where
bell
curves
are
employed,
like
in
testing
and
polling
situations.
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e
e
Ty
g
.
o
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LA
AN
i
i
S
£
4%
o
inferential
Statistics
Draw
Conclusions
inferential
statistics
aliow
researchers
(o
draw
conclusions
from
their
data
sels,
and
n
particular
1o
draw
conclusions
that
extend
beyond
the
observed
data.
In
this
way,
a
researcher
can
make
more
generalized
conclusions
based
an
thelr
study’s
data
sets.
inferential
statistics
are
concerned
with
reaching
conclusions
from
information
that
is
not
complete.
In
other
words,
they
generalize
from
the
population
studied
by
using
information
obiained
from
a
sample
of
the
population
to
say
something
about
the
whole
population,
Opinion
Poll
Example
An
example
of
inferential
statistics
is
an
opinion
poll,
such
as
those
seen
during
a
political
election.
Such
a
poll
attempts
to
make
inferences
about
the
possibie
oulcoms
of
the
election.
You
more
than
likely
have
observed
a
sampling
taken
from
a
televised
poll
consisting
of
a
portion
of
the
population
in
a
specific
county,
state,
or
even
the
entive
country.
The
results
of
the
preferences
selected
are
then
tabulated,
and
inferences
are
drawn
as
o
how
the
entire
population
would
vote
that
day,
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You
may
have
also
noticed
in
your
reading
of
research
that
data
comes
from
o
common
types
of
investigations:
exgeriments
and
surveys.
This
is
not
SUrprising,
as
experiments
and
surveys
are
the
two
fundamental
types
of
research
nvestigations,
Chservational
Survey:
An
observational
survey,
for
example,
involves
data
that
is
ohiained
representing
observations
of
a
phenomenon,
event,
or
group
over
a
period
of
time,
wherein
few
or
no
controls
are
used.
Observational
Example:
An
example
of
an
observational
study
might
involve
the
effects
of
tear
gas
used
by
the
police
on
the
residents
of
Ferguson,
Missourt
during
the
2014
riots,
In
this
example,
the
researcher
obviously
could
not
have
controlled
the
amount
of
tear
gas
that
the
residents
were
exposed
{0
and
s
duration.
Experiment:
in
contrast,
an
experiment
would
purposely
involve
the
use
of
controls
over
the
amount
and
duration
of
tear
gas
exposure
given
a
study
popuiation
over
a
specified
period,
Testing
the
Hypothesis
Researchers
typically
use
inferential
statistics
to
determine
whether
or
not
the
data
obtained
from
a
study
supports
a
particular
hypothesis.
In
social
research,
the
investigator
usually
attempts
to
determine
if
the
null
hypothesis
IS
supported
or
not.
CORRELATION
For
a
correlation,
the
null
hypothesis
states
that
the
correlation
is
not
reliably
different
from
zero
but
simply due
to
chance.
COMPARISON
For
a
comparison
of
two
data
sets,
the
null
hypothesis
states
that
any
observed
group
difference
is
not
reliable,
but
due
to
chance.
TESTING
THE
HYPOTHESIS
Inferential
statistical
tests
tell
what
the
chances
are
that
the
null
hypothesis
is
“true.”
If
the
chances
are
low,
less
than
5
percent,
then
people
(usually)
reject
the
null
hypothesis.
This
leaves
the
alternate
hypothesis,
which
states
that
the
difference
or
correlation
is
real
or
reliable.
If
the
null
hypothesis
is
“true”
less
than
5
percent
of
the
time,
people
say
the
correlation
or
difference
is
statistically
significant.
STATISTICAL
SIGNIFICANCE
“Statistically
significant”
does
not
mean
“important”;
it
means
“reliable,”
and
“reliable”
means
that
the
observed
difference
is
likely
to
show
up
if
the
same
kind
of
data
is
collected
again.
Common
Testing
Methods
VARIATION
BETWEEN
GROUPS
<l
[
_—
FREQUENCY
VARIATION
WITHIN
GROUPS
<zl
-
<
e
|
I
I
I
I
I
SCORE
There
are
many
methods
of
testing
a
hypothesis.
The
researcher
must
choose
the
method
most
appropriate
based
on
the
type
of
data
obtained
from
their
research.
T-TEST
The
t-test
is
a
statistical
analysis
of
the
means
of
two
populations.
It
determines
whether
there
is
a
real
variation
of
the
two
distributions,
and
assesses
whether
the
means
of
two
groups
are
statistically
different
from
each
other.
This
analysis
is
appropriate
whenever
you
want
to
compare
the
means
of
two
groups.
There
are
three
basic
types
of
t-tests:
the
one-sample
t-test,
the
independent-samples
t-test,
and
the
dependent-samples
(or
paired-
samples)
t-test.
All
three
types
of
t-tests
look
at
the
difference
between
the
means
and
divide
that
difference
by
some
measure
of
variation.
ANALYSIS
OF
VARIANCE
An
ANOVA
is
a
statistical
test
that
is
also
used
to
compare
means.
This
test
is
used
to
determine
if
there
are
significant
differences
between
more
than
two
independent
groups.
The
difference
between
a
t-test
and
an
ANOVA
is
that
a
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t-test
can
only
compare
two
means
at
a
time,
whereas
an
ANOVA
can
compare
multiple
means
at
the
same
time.
ANOVAS
can
also
compare
the
effects
of
different
factors
on
the
same
measure.
They
can
become
very
complicated,
and
only
trained
statisticians
should
conduct
their
analyses.
There
are
several
types
of
ANOVAS,
including
the
one-way
ANOVA,
within-
groups
(or
repeated-measures)
ANOVA,
and
factorial
ANOVA.
EVE
The
chi-square
is
an
inferential
statistical
technique
designed
to
test
for
significant
relationships
between
two
variables
organized
in
a
table
showing
two
variants.
This
test
measures
how
well
the
anticipated
or
expected
results
of
the
study
fit
with
the
observed
values.
The
chi-square
requires
no
assumptions
about
the
shape
of
the
population
distribution
from
which
a
sample
is
drawn.
However,
like
all
inferential
techniques
it
assumes
random
sampling.
Type
|
and
Il
Errors
NEED
TO
PREVENT
ERRORS
In
order
to
determine
if
the
results
of
a
study
are
significant,
the
researcher
must
set
initial
parameters
to
compare
their
results
against.
This
must
be
done
to
help
prevent
a
type
|
error,
in
which
a
null
hypothesis
is
falsely
rejected,
or
a
type
Il
error,
in
which
it
is
falsely
accepted.
SIGNIFICANCE
LEVEL
The
process
of
hypothesis
testing
can
seem
to
be
quite
varied,
but
regardless
of
the
topic
or
discipline
the
general
process
is
the
same.
Hypothesis
testing
involves
the
statement
of
a
null
hypothesis,
and
the
selection
of
a
significance
level.
The
null
hypothesis
is
either
true
or
false,
and
represents
a
default
claim.
After
formulating
the
null
hypothesis
and
choosing
a
level
of
significance,
we
acquire
data
through
observation.
Statistical
calculations
tell
us
whether
or
not
we
should
reject
the
null
hypothesis.
TYPE
|
ERROR
In
an
ideal
world
we
would
always
reject
the
null
hypothesis
when
it
is
false,
and
we
would
not
reject
the
null
hypothesis
when
it
is
indeed
true.
There
are
two
other
scenarios
that
are
possible,
each
of
which
will
result
in
an
error.
The
first
kind
of
error
that
is
possible
involves
the
rejection
of
a
null
hypothesis
that
is
actually
true,
a
type
|
error
or
error
of
the
first
kind.
Type
|
errors
are
equivalent
to
false
positives.
TYPE
Il
ERROR
The
other
kind
of
error
that
is
possible
occurs
when
we
do
not
reject
a
null
hypothesis
that
is
false,
a
type
Il
error,
also
referred
to
as
an
error
of
the
second
kind.
Type
Il
errors
are
equivalent
to
false
negatives.
The
probability
of
a
type
Il
error
is
given
by
the
Greek
letter
beta.
ERROR
CANNOT
BE
ELIMINATED
COMPLETELY
Type
|
and
Type
Il
errors
are
part
of
the
process
of
hypothesis
testing
and
cannot
be
completely
eliminated,
but
one
type
of
error
can
be
minimized.
When
researchers
try
to
decrease
the
probability
one
type
of
error,
the
probability
for
the
other
type
increases.
Many
times
the
real
world
application
of
a
hypothesis
test
will
determine
if
the
public
is
more
accepting
of
type
|
or
type
Il
errors,
and
the
researcher
can
think
accordingly
when
he
or
she
develops
a
statistical
design.
Hypothesi
True
False
'
B
Type
|
error
Correct
Reject
(False
interpretation
of
Experimental
positive)
data
Result
S,
Correct
align="center"Type
Rzljecc:)t
interpretation
|
Erro_r(FaIse
B
B
of
data
Negative)
Significance
Levels
Set
Significance
Level
BEFORE
Conduct
Test
The
researcher
must
initially
set
a
significance
level
before
conducting
an
inferential
test.
The
significance
level,
also
called
the
alpha
value,
is
a
value
chosen
before
testing.
This
may
seem
confusing
to
a
person
who
is
not
well-
versed
in
statistical
analysis,
but
this
is
the
only
value
you
need
to
be
familiar
with
along
with
its
meaning.
This
coupled
with
an
explanation
of
a
very
few
basic
statistical
terms
and
symbols
will
make
you
a
better
consumer
of
research.
The
symbol
for
significance
level
is
a
for
“alpha.”
The
significance
level
is
a
measure
as
to
how
significant
a
result
is.
Higher
Alpha
Means
Greater
Confidence
The
concept
of
statistical
significance
is
fundamental
to
hypothesis
testing.
In
a
study
that
involves
drawing
a
random
sample
from
a
larger
population
in
an
effort
to
prove
some
result
that
can
be
applied
to
the
population
as
a
whole,
there
is
the
constant
potential
for
the
study
data
to
be
a
result
of
sampling
error
or
simple
coincidence
or
chance.
The
significance
level,
in
the
simplest
of
terms,
is
the
threshold
probability
of
incorrectly
rejecting
the
null
hypothesis
when
it
is
in
fact
true
(a
type
|
error).
The
significance
level
or
alpha
is
therefore
associated
with
the
overall
confidence
level
of
the
test.
This
essentially
means
that
the
higher
the
alpha
value,
the
greater
the
confidence
in
the
test.
P-Values
The
researcher
must
also
determine
the
p-value
of
their
statistical
test
to
compare
against
the
significance
level.
A
p-value
is
the
probability
of
finding
extreme
results
when
the
null
hypothesis
is
true.
If
the
level
of
significance
a
=
p,
this
demonstrates
the
probability
of
rejecting
the
null
hypothesis.
If
the
p-
value
is
less
than
or
equal
to
alpha
(p
<
.05),
the
null
hypothesis
is
rejected
and
is
said
to
be
statistically
significant.
In
other
words,
more
than
likely
something
besides
chance
alone
from
the
data
evaluated
lead
to
the
finding.
|
>
A
If
the
p-value
is
greater
than
alpha
(p
>
.05),
the
data
evaluated
failed
to
indicate
the
need
to
reject
the
null
hypothesis
and
the
result
is
not
statistically
significant.
In
other
words,
the
results
from
the
data
evaluated
more
than
likely
can
be
explained
by
chance
alone.
SIGNIFICANT
OR
NOT
In
quantitative
research,
the
findings
often
indicate
the
results
were
either
statistically
significant
(p
<
.05)
or
not
statistically
significant
(p
>
.05).
This
simply
means
that
the
data
from
the
sample
population
and
either
did
or
did
not
support
the
null
hypothesis;
therefore,
the
null
hypothesis
in
the
studies
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you
read
will
be
either
supported
or
rejected
based
on
the
p-value.
The
statistical
probability
or
confidence
level
for
a
=
0.05
is
95
percent.
ASTERISKS
You
may
have
also
observed
in
tables
in
studies
or
journals
the
use
of
asterisks
in
the
interpretation
of
the
p-values.
No
asterisk
(as
in
p
>
0.05)
means
that
the
result
was
not
significant;
one
asterisk,
such
as
“*
if
p
<
0.05”,
means
the
result
was
significant;
and
two
asterisks,
“**
if
p
<
0.01”,
means
the
result
was
highly
significant.
Inconclusive
Results
However,
just
because
a
result
is
found
not
to
be
significant
does
not
mean
the
null
hypothesis
is
fully
supported
and
the
alternate
hypothesis
should
be
rejected.
You
may,
in
your
reading
of
a
study,
notice
from
time
to
time
that
while
the
researcher
opted
not
to
reject
the
null,
the
alternate
was
not
fully
rejected.
This
may
be
for
various
reasons.
One
reason
may
be
simply
that
the
researcher
made
the
determination
that
the
population
sample
was
too
small
to
provide
a
sufficient
indication
to
support
or
reject
the
null
and
therefore
guestions
the
accuracy
of
the
findings.
Another
reason
could
be
that
knowledge
regarding
the
survey
or
the
participants
(or
both)
indicated
there
was
a
problem
with
the
data
after
the
collecting
was
closed.
Therefore,
this
needed
to
be
taken
into
account
when
reporting
the
findings
as
well
as
providing
an
explanation
as
to
what
happened
so
future
researchers
as
well
as
research
consumers
could
understand
what
the
problem
was.
Conclusion
In
conclusion,
in
the
midst
of
all
the
numerical
jargon
and
presentation
in
the
study
or
in
tables
and
graphs,
the
focus
is
solely
on
the
p
(significance)
or
a
(alpha
—
also
significance)
value.
The
statistical
process
as
to
how
the
significance
level
is
reached
or
determined
is
not
important
at
this
time.
You
do
not
need
to
worry
about
the
equations
or
any
other
part
of
the
statistics.
What
is
important
is
for
you
to
be
a
better
consumer
of
research
by
understanding
the
meaning
and
importance
of
the
significance
level
as
you
read
research.
You
will
learn
about
the
how
and
when
if
you
take
a
course
in
statistics.
KEY
TERMS
Descriptive
statistics:
Brief
descriptive
coefficients
that
summarize
a
given
data
set,
which
can
be
either
a
representation
of
the
entire
population
or
a
sample
of
it.
Inferential
statistics:
A
model
that
makes
inferences
about
populations
using
data
drawn
by
collecting
a
sample
or
samples
from
the
millions
of
residents
and
using
it
to
make
inferences
about
the
entire
population.
Mean:
The
average
of
a
group
of
numbers.
Measurement
of
central
tendency:
A
single
value
that
describes
the
way
in
which
a
group
of
data
clusters
around
a
central
value.
Measurement
of
spread:
A
single
value
that
describes
how
similar
or
varied
the
set
of
observed
values
are
for
a
particular
variable.
Median:
The
number
in
the
center
of
a
set
when
the
set
is
arranged
in
order.
Mode:
The
number
that
appears
most
often
in
a
set.
P-value:
The
probability
of
finding
the
observed,
or
more
extreme,
results
when
the
null
hypothesis
of
a
study
question
is
true.
Range:
The
area
of
variation
between
upper
and
lower
limits
on
a
particular
scale.
Significance
level:
The
probability
of
rejecting
the
null
hypothesis
in
a
statistical
test
when
it
is
true.
Standard
deviation:
A
quantity
calculated
to
indicate
the
extent
of
deviation
for
a
group
as
a
whole.
Statistics:
The
practice
or
science
of
collecting
and
analyzing
numerical
data
in
large
quantities,
especially
for
the
purpose
of
inferring
proportions
in
a
whole
from
those
in
a
representative
sample.
Type
|
error:
The
incorrect
rejection
of
a
true
null
hypothesis
(a
“false
positive”).
Type
Il
error:
Incorrectly
retaining
a
false
null
hypothesis
(a
“false
negative”).
Variance:
The
expectation
of
the
squared
deviation
of
a
random
variable
from
its
mean,
which
informally
measures
how
far
a
set
of
numbers
are
spread
out
from
their
mean.
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Sources
Creswell,
J.
W.
(2003).
Research
design:
Qualitative,
quantitative,
and
mixed
methods
approach.
Thousand
Oaks,
CA:
Sage.
Ellis,
L.,
Hartley,
R.
D.,
&
Walsh,
A.
(2010).
Research
methods
in
criminal
justice
and
criminology:
An
interdisciplinary
approach.
(2nd
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Blue
Ridge
Summit,
PA:
Rowman
&
Littlefield.
Frommer,
G.P.
(1999).
Inferential
Statistics.
Retrieved
from
http.//www.indiana.edu/~p1013447/dictionary/inf
stat.htm.
Mason,
M.
(2010).
Sample
size
and
saturation
in
PhD
studies
using
qualitative
interviews.
Forum:
Qualitative
Social
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11(3),
article
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from
http.//www.qualitative-research.net/index.php/fqs/article/view/1428/3027
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Taylor,
C.
(2016).
What
Is
the
difference
between
type
|
and
type
Il
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from
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W.M.K.
(2006).
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t.php.
Images
Stock
images
provided
by
123rf.com
Graph
of
U.S.
population
grouped
by
age
and
gender
http://www.census.gov/2010census/img/state
profile
dc
2010home.qif
Visualisation
mode
median
mean
By
Cmglee
(Own
work)
[CC
BY-SA
3.0
or
GFDL],
via
Wikimedia
Commons
President
Truman
holding
the
infamous
issue
of
the
Chicago
Daily
Tribune
https.//en.wikipedia.org/wiki/Dewey
Defeats
Truman#/media/File:Dew
evtrumanlZ2.jpg
Ferguson
Day
6,
Picture
44
By
Loavesofbread
(Own
work)
[CC
BY-SA
4.0],
via
Wikimedia
Commons
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