2.
Because of the relative values,
the
data classified can be
ranked or ordered
.
11
IntervalLevel Data
Properties:
1.
Data classifications are ordered according to the amount of the
characteristic they possess.
2.
Equal differences in the characteristic are represented by equal
differences in the measurements.
Example: Women’s dress sizes
listed on the table.
11
RatioLevel Data
z
Practically all quantitative data is recorded on the ratio level
of measurement.
z
Ratio level is the “highest” level of measurement.
Properties:
1.
Data classifications are
ordered
according to the amount of the
characteristics they possess.
2.
Equal differences in the characteristic are represented by equal
differences in the numbers assigned to the classifications.
3.
The zero point is the absence of the characteristic
4.
The
ratio
between two numbers is
meaningful
.
12
IntervalLevel
>
RatioLevel
Data
z
Conversion Possible
z
What Year is it?
z
Year 2010
/
Year 1005
=
?
z
Compare to Baseline
–
Year 2010
vs.
Year 2000
=
10 Years
–
Year 2005
vs.
Year 2000
=
5 Years
Why Know the Level of Measurement of a
Data?
z
The level of measurement of the data dictates the
calculations that can be done to summarize and
present the data.
z
To determine the statistical tests that should be
performed on the data
9
Summary of the Characteristics for
Levels of Measurement
13
z
Nominal

Name
z
Ordinal

Order
z
Interval

Invalid
0
{
Interspaced
Numbers}
z
Ratio

Real
0
{
Ratio
Calculations}
Levels of Measurement
"Quick Tip" to Remember them
NOTE:
This is just an aid to memory; don't
try to overthink it or take it too literally
LYING
with
Statistics
z
Falsifying Data
z
Using Selective Portions
z
Changing Hypothesis after Data
Collection is Completed
–
Different from
Descriptive
or
Investigative
Statistics (Data Mining)
z
Misrepresenting Valid Data
Examples of LYING
1060
1065
1070
1075
1080
1085
1090
1095
1100
1105
Year
1
Year
2
Year
3
Year
4
Year
5
Stock Price
Examples of LYING – Only
UP
1065
1070
1075
1080
1085
1090
1095
Year
2
Year
3
Year
4
Year
5
Stock Price
Examples of LYING
 Only
DOWN
1084
1086
1088
1090
1092
1094
1096
1098
1100
1102
Year 1
Year 5
Stock Price
Examples of LYING  Actual Change
0
200
400
600
800
1000
1200
Year
1
Year
2
Year
3
Year
4
Year
5
Stock Price
GOALS

Chapter 1
1.
Understand why we study statistics.
2.Explain what is meant by descriptive
3.
Differentiate between a
sample
and a
population
4.
Distinguish between a
qualitative
variable
and a
quantitative
variable
.
5.Describe how a discretevariableisdifferent from a continuousvariable.
6.
Distinguish among the
nominal
,
ordinal
,
interval
, and
ratio
levels of measurement.
1
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 Spring '11
 Leany
 Statistics, Inferential Statistics, Level of measurement