p4 statistic no.0001709

Numbers, Measurement and
Numerical Relationships

In quantitative research, dependent,
independent and relevant variables are describe
in numeral form.
Some variables may be easily defined or
measured; other are more abstract and difficult
to define.
Slide 2 of 85

In quantitative research, dependent,
independent and relevant variables are describe
in numeral form.
Some variables may be easily defined or
measured; other are more abstract and difficult
to define.
Slide 3 of 85

Different measurement use the same numerals
(i.e., 1, 2, 3, 4 . . .)
But, the numerals carry different information
and carry different information and symbolize
different phenomena across scales (i.e., 1 =
Catholic, 2 = Mormon . . . or 1 = Agree, 2 =
Disagree, or 1 = correct, 0 = incorrect)
Slide 4 of 85

(i.e., 1, 2, 3, 4 . . .)
and carry different information and symbolize
different phenomena across scales (i.e., 1 =
Catholic, 2 = Mormon . . . or 1 = Agree, 2 =
Disagree, or 1 = correct, 0 = incorrect)
Slide 5 of 85

(i.e., 1, 2, 3, 4 . . .)
and symbolize different phenomena across
scales (i.e., 1 = Catholic, 2 = Mormon . . . or 1 =
Agree, 2 = Disagree, or 1 = correct, 0 = incorrect)
Slide 6 of 85

Different scales of measurement use the same
numerals (i.e., 1, 2, 3, 4 . . .)
But, the numerals carry different information and
symbolize different phenomena across scales
EX:
•1 = Catholic, 2 = Mormon . . .
•1 = Agree, 2 = Disagree
•1 = correct, 0 = incorrect
Slide 7 of 85

numerals (i.e., 1, 2, 3, 4 . . .)
scales (i.e.,
Slide 8 of 85

numerals (i.e., 1, 2, 3, 4 . . .)
scales (i.e.,
Slide 9 of 85

The Four Main Types of Measurement
they are:
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50O . . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 10 of 85

•Nominal (1 = Male, 2 = Female)
•Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
•Interval (30OF, 40OF, 50O . . .)
•Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 11 of 85

Slide 12 of 85

Slide 13 of 85

Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant )
Slide 14 of 85

Nominal, Ordinal, Interval, Ratio
Slide 15 of 85

Nominal scales use numbers as replacements
for names.
Slide 16 of 85

for names.
1 = American
Slide 17 of 85

for names.
1 = American
2 = Canadian
Slide 18 of 85

for names.
1 = American
2 = Canadian
3 = Mexican
Slide 19 of 85

for names.
1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 20 of 85

for names.
1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 21 of 85

for names.
1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 22 of 85

Nominal
for names.
1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 23 of 85

for names.
1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 24 of 85

The root of the term “nominal” is “nom”
meaning “name”.
Slide 25 of 85

Nominal scales
•assume no quantity of the attribute.
Slide 26 of 85

Nominal scales
1 = American
2 = Canadian
Slide 27 of 85

Nominal scales
1 = American
2 = Canadian
1 is not more than 2 and
2 is not less than 1 in this context
1 is not more than 2 and
2 is not less than 1 in this context
Slide 28 of 85

Nominal scales
•has no particular interval
Slide 29 of 85

Nominal scales
•has no particular interval
1 = American
2 = Canadian
3 = Mexican
1 and 2 and 3 are not equal intervals because
there is no quantity involved.
1 and 2 and 3 are not equal intervals because
there is no quantity involved.
Slide 30 of 85

Nominal scales
•has no particular interval.
•has no zero or starting point.
Slide 31 of 85

Nominal scales
1 = American
2 = Canadian
3 = Mexican
Slide 32 of 85

Nominal scales
1 = American
2 = Canadian
3 = Mexican
Because there is no quantity involved there is
no such thing as a zero point (ie., complete
absence of nationality).
Because there is no quantity involved there is
no such thing as a zero point (ie., complete
absence of nationality).
Slide 33 of 85

Slide 34 of 85

Ordinal scales use numbers to represent
relative amounts of an attribute.
Slide 35 of 85

Private
1
Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Slide 36 of 85

Private
1
Corporal
2
Sargent
3
Lieutenant
4
Major
5
Colonel
6
General
7
Relative Amount of Authority
Slide 37 of 85

Slide 39 of 85

3rd
Place
15’ 2”
2nd Place
16’ 1”
1st
Place
16’ 3”
Relative in terms of PLACEMENT (1st, 2nd, & 3rd) Slide 40 of 85

3rd
Place
15’ 2”
2nd Place
16’ 1”
1st
Place
16’ 3”
Relative in terms of PLACEMENT (1st, 2nd, & 3rd) Slide 41 of 85

Ordinal scales
•assume quantity of the attribute.
Slide 42 of 85

Ordinal scales
Lieutenant
4
Colonel
6
A colonel has more A colonel has more aauutthhoorriittyy tthhaann aa LLiieeuutteennaanntt
Slide 43 of 85

Ordinal scales
3rd
Place
1st
Place
1st place is 1st place is hhiigghheerr tthhaann 33rdrd ppllaaccee
Slide 44 of 85

Ordinal scales
•do not have equal intervals.
Slide 45 of 85

Ordinal scales
3rd
Place
15’ 2”
2nd
Place
16’ 1”
Slide 46 of 85

Ordinal scales
3rd
Place
15’ 2”
2nd
Place
16’ 1”
The distance between 3rd and 2nd place (11”) is not the same
interval as the distance between 2nd and 1st place (1”)
Slide 47 of 85

Ordinal scales
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
Slide 48 of 85

Ordinal scales
3rd
Place
15’ 2”
2nd
Place
16’ 1”
1st
Place
16’ 3”
Slide 49 of 85

Ordinal scales
A higher number
only represents
more of the
attribute than a
lower number,
3rd
Place
15’ 2”
3rd
Place
15’ 2”
2nd
Place
16’ 1”
2nd
Place
16’ 1”
1st
Place
16’ 3”
1st
Place
16’ 3”
Slide 50 of 85

Ordinal scales
3rd
Place
15’ 2”
3rd
Place
15’ 2”
. . . but how
much more is
undefined.
2nd
Place
16’ 1”
2nd
Place
16’ 1”
1st
Place
16’ 3”
1st
Place
16’ 3”
Slide 51 of 85

Ordinal scales
3rd
Place
15’ 2”
3rd
Place
15’ 2”
2nd
Place
16’ 1”
2nd
Place
16’ 1”
1st
Place
16’ 3”
1st
Place
16’ 3”
The difference
between points
on the scale
varies from
point to point
Slide 52 of 85

Ordinal scales
•may have an arbitrary zero or starting point.
Slide 53 of 85

Ordinal scales
O Mostly Disagree
O Completely Disagree
O Completely Agree
O Mostly Agree
Slide 54 of 85

Ordinal scales
O Mostly Disagree
O Completely Disagree
O Completely Agree
O Mostly Agree
Slide 55 of 85

Ordinal scales
Slide 56 of 85

Ordinal scales
O Not at All
O Very Little
O Somewhat
O Quite a Bit
Slide 57 of 85

Ordinal scales
O Not at All
O Very Little
O Somewhat
O Quite a Bit
Slide 58 of 85

Ordinal scales
Slide 59 of 85

Ordinal scales
O Not Important
O Somewhat Important
O Slightly Important
O Very Important
Slide 60 of 85

Ordinal scales
O Not Important
O Somewhat Important
O Slightly Important
O Very Important
Slide 61 of 85

Important Point
Slide 62 of 85

Important Point
Numbers on an ordinal scale are limited in the
information they carry (i.e., no equal intervals,
no zero point)
Slide 63 of 85

Interesting Note
Slide 64 of 85

Interesting Note
Technically, numbers on an ordinal scale cannot
be added or subtracted.
Slide 65 of 85

Interesting Note
Technically, numbers on an ordinal scale cannot
be added or subtracted.
(but we frequently do it anyway !)
Slide 66 of 85

Ordinal Numbers in a Data Set
Slide 67 of 85

Data Set
Student Nationality Place Test
Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Slide 68 of 85

Data Set
Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Slide 69 of 85

Data Set
Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Nominal
Slide 70 of 85

Data Set
Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Nominal Ordinal
Slide 71 of 85

Slide 72 of 85

Interval scales
Slide 73 of 85

Interval scales
Temperature
Slide 74 of 85

Interval scales
•have equal intervals.
Slide 75 of 85

Interval scales
Slide 76 of 85

Interval scales
100o - 101o
70o - 71o
40o - 41o
Slide 77 of 85

Interval scales
100o - 101o
70o - 71o
40o - 41o
Each set of readings are the same
distance apart: 1o
Slide 78 of 85

Interval scales
Slide 79 of 85

Technically, numbers on an interval scale can be
added and subtracted
Slide 80 of 85

70o
Slide 81 of 85

100o
70o
Slide 82 of 85

100o
70o
100o is 30o more (+) than 70o
Slide 83 of 85

100o
70o
100o is 30o more (+) than 70o
70o is 30o less (-) than 100o
Slide 84 of 85

added and subtracted but not divided and
multiplied.
Slide 85 of 85

multiplied.
100o
50o
Slide 86 of 85

multiplied.
100o
100o is NOT twice (x) as hot as 50o
And 50o is NOT half (/) as hot as 100o 50o
Slide 87 of 85

multiplied.
But many do so
anyways 
110000o o
But 100o is NOT twice (x) as hot as 50o
And 50o is NOT half (/) as hot as 100o 5500oo
Slide 88 of 85

Interval Numbers in a Data Set
Slide 89 of 85

Data Set
Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Slide 90 of 85

Data Set
Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Nominal Ordinal Interval
Slide 91 of 85

Data Set
Scores
1 3 3 32
2 1 5 28
3 3 2 33
4 2 6 27
5 1 1 34
6 2 4 31
Slide 92 of 85

Slide 93 of 85

Ratio scales
Slide 94 of 85

Ratio scales
Slide 95 of 85

Ratio scales
5’3” 5’10” 6’4” 6’5” 5’11” 5’4”
Slide 96 of 85

Ratio scales
5’3” 5’10” 6’4” 6’5” 5’11” 5’4”
Slide 97 of 85

Ratio scales
5’3” 5’10” 6’4” 6’5” 5’11” 5’4”
Every inch represents a unit of measure that is the
Every inch represents a unit of measure that is the
same across all inches Slide 98 of 85
same across all inches

Ratio scales
5’3” 5’10” 6’4” 6’5” 5’11” 5’4”
With the interval nature of the data, you can say that player 4
(blue team) is 6 inches taller than Player 19 (yellow teaSmlide) 99 of 85
With the interval nature of the data, you can say that player 4
(blue team) is 6 inches taller than Player 19 (yellow team)

Ratio scales
•has a zero or starting point.
5’3” 5’10” 6’4” 6’5” 5’11” 5’4”
With a zero starting point (0’0”) you can say that
player 6 (blue team) is 4/5 the size of player 4 (blue
With a zero starting point (0’0”) you can say that
player 6 (blue team) is 4/5 the size of player 4 (blue
team)
team)
Slide 100 of 85

Ratio Numbers in a Data Set
Slide 101 of 85

Data Set
Scores
Height
1 3 3 32 5’2”
2 1 5 28 6’3”
3 3 2 33 6’0”
4 2 6 27 5’8”
5 1 1 34 6’1”
6 2 4 31 5’5”
Slide 102 of 85

Data Set
Scores
Height
1 3 3 32 5’2”
2 1 5 28 6’3”
3 3 2 33 6’0”
4 2 6 27 5’8”
5 1 1 34 6’1”
6 2 4 31 5’5”
Nominal Ordinal Interval Ratio
Slide 103 of 85

Important Point
Slide 104 of 85

Important Point
Numbers on a ratio scale
•carry more information than the same numbers
on an interval or ordinal scale.
•can be
– added,
– subtracted,
– multiplied, or
– divided.
Slide 105 of 85

Important Point
Slide 106 of 85

Important Point
•can be
– added,
– subtracted,
– multiplied, or
– divided.
Slide 107 of 85

Two more Important Points
Slide 108 of 85

1. More adequate scales can be easily
converted to less adequate scales.
Ratio - - - > Interval - - - > Ordinal - - - > Nominal
2. Most statistical programs will treat interval
and ratio data the same.
Slide 109 of 85

1. More adequate scales can be easily
converted to less adequate scales.
Ratio - - - > Interval - - - > Ordinal - - - > Nominal
2. Most statistical programs will treat interval
and ratio data the same.
Slide 110 of 85

ASSESSMENT AND ANALYSIS
Slide 111 of 85

Assessment and Analysis…
The type of assessment measures determinants
both the extent to which the data can be
compared and the type of statistical analyses
that can ba applied to these comparisons.
Slide 112 of 85

Metric measures
• Allow the full range of mathematical procedures to
be applied.
• These categories are measured by the percent that
complete the task, how long it takes to complete the
tasks, ratios of success to failure to complete the
task, time spent on errors, the number of errors,
rating scale of satisfactions, number of times user
seems frustrated, etc
Slide 113 of 85

• Metric measure
Slide 114 of 85

Non-Metric Measure
• Non Metric variables are intrinsic
Slide 115 of 85

• Metric variables have numbers associated
with them. For example: Team Members in a
Call Center can be evaluated by how many
calls they take per day. How many minutes
they spend on average on those calls. The
difficulty level of the calls they took, etc. Non
Metric variables are intrinsic. The weather can
affect an outdoor wedding, that is a non
metric variable. In the record business, the
non metric variable of illegal downloads
affects the bottom line for the record
producer. In this case the number of
downloads is an unknown. Slide 117 of 85

Methods of Statistical Analysis
Parametric
o Parametric methods deal with the estimation of
population parameters (like the mean).
Non-parametric
o non-parametric are distribution free methods.
They rely on ordering (ranking) of observations.
Slide 118 of 85

If data is normally distributed then you can
apply parametric tests that compare the
means among the groups and if data is not
normally distributed then you can apply non
parametric test that compare the median
among the groups.
Slide 119 of 85

“Unfamiliar Words”
• Statistical Analyses
• Metric Data
• Data Analysis
• Variables – The characteristic that is being
studied.
• Inferential Techniques
Slide 120 of 85

• Interval Point
• Histogram
• Scattergram
• Probability
• Correlation Matrix
Slide 121 of 85

What is (M)
• “M” is means “means of data, scores”
• expresses the mean difference between two
groups in standard deviation units.
• Is a qualitative measure describing the
characteristic of a population and therefore, it
is a parameter.
Slide 122 of 85

Formula:
Slide 123 of 85
Means formula

What is (SD)
• means Standard Deviation
• is a widely used measurement of variability or
diversity used instatistics and probability
theory. It shows how much variation or
"dispersion" there is from the "average"
(mean, or expected/budgeted value).
• standard deviation of a statistical population,
data set, orprobability distribution is
the square root of its variance.
Slide 124 of 85

Formula:
Standard Deviation formula
Slide 125 of 85

Correlation and Regression
Analysis
• Correlation and regression analysis are
related in the sense that both deal with
relationships among variables.
The correlation coefficient is a measure of
linear association between two variables.
Values of thecorrelation coefficient are
always between -1 and +1.
Slide 126 of 85

Chi-square Statistic
• A measurement of how expectations compare
to results. The data used in calculating a chi
square statistic must be random, raw,
mutually exclusive, drawn from independent
variables and be drawn from a large enough
sample.
• A statistical test used to compare expected
data with what we collected.(collected vs.
expected no.s)
Slide 127 of 85

Formula:
chi-square formula
Slide 128 of 85

Thank You
for
Listening

Slide 129 of 85

p4 statistic no.0001709

More Related Content

Viewers also liked

Similar to p4 statistic no.0001709

Recently uploaded

p4 statistic no.0001709

Editor's Notes