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.

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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.

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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)

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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)

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Different measurement use the same numerals (i.e., 1, 2, 3, 4 . . .)But, the numerals 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)

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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

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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 (i.e., •1 = Catholic, 2 = Mormon . . . •1 = Agree, 2 = Disagree •1 = correct, 0 = incorrect

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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 (i.e., •1 = Catholic, 2 = Mormon . . . •1 = Agree, 2 = Disagree •1 = correct, 0 = incorrect

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The Four Main Types of Measurementthey are:

Nominal (1 = Male, 2 = Female)

Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)

Interval (30OF, 40OF, 50O . . .)

Ratio (0 meters, 10 meters, 100 meters . . .)

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•Nominal (1 = Male, 2 = Female)

•Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)

•Interval (30OF, 40OF, 50O . . .)

•Ratio (0 meters, 10 meters, 100 meters . . .)

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Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant )



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Nominal, Ordinal, Interval, Ratio

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Nominal scales use numbers as replacements for names.

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Nominal scales use numbers as replacements for names.1 = American

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2 = Canadian

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2 = Canadian

3 = Mexican

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2 = Canadian

3 = Mexican

Data Set

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2 = Canadian

3 = Mexican

Data Set

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2 = Canadian

3 = Mexican

Data Set

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Nominal


2 = Canadian

3 = Mexican

Data Set

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2 = Canadian

3 = Mexican

Data Set

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

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Nominal scales •assume no quantity of the attribute.

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1 = American

2 = Canadian

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1 is not more than 2 and2 is not less than 1 in this context 1 is not more than 2 and2 is not less than 1 in this context

1 = American

2 = Canadian

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Nominal scales •assume no quantity of the attribute.•has no particular interval

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Nominal scales •assume no quantity of the attribute.•has no particular interval

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.

1 = American2 = Canadian3 = Mexican

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Nominal scales •assume no quantity of the attribute.•has no particular interval.•has no zero or starting point.

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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).


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

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Private1

Corporal2

Sargent3

Lieutenant4

Major5

Colonel6

General7

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Private1

Corporal2

Sargent3

Lieutenant4

Major5

Colonel6

General7

Relative Amount of Authority

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3rd Place15’ 2”

2nd Place16’ 1”

1st Place16’ 3”

Relative in terms of PLACEMENT (1st, 2nd, & 3rd) Slide 40 of 85



3rd Place15’ 2”

2nd Place16’ 1”

1st Place16’ 3”

Relative in terms of PLACEMENT (1st, 2nd, & 3rd) Slide 41 of 85


Ordinal scales •assume quantity of the attribute.

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Lieutenant4

Colonel6

A colonel has more authority than a LieutenantA colonel has more authority than a Lieutenant

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1st place is higher than 3rd place1st place is higher than 3rd place

3rd Place

1st Place

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Ordinal scales •assume quantity of the attribute.•do not have equal intervals.

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3rd Place15’ 2”

2nd Place16’ 1”

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The distance between 3rd and 2nd place (11”) is not the same interval as the distance between 2nd and 1st place (1”)


3rd Place15’ 2”

2nd Place16’ 1”

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3rd Place15’ 2”

2nd Place16’ 1”

1st Place16’ 3”

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3rd Place15’ 2”

2nd Place16’ 1”

1st Place16’ 3”

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3rd Place15’ 2”

3rd Place15’ 2”

2nd Place16’ 1”

2nd Place16’ 1”

1st Place16’ 3”

1st Place16’ 3”

A higher number only represents

more of the attribute than a lower number,

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3rd Place15’ 2”

3rd Place15’ 2”

2nd Place16’ 1”

2nd Place16’ 1”

1st Place16’ 3”

1st Place16’ 3”

. . . but how much more is

undefined.

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3rd Place15’ 2”

3rd Place15’ 2”

2nd Place16’ 1”

2nd Place16’ 1”

1st Place16’ 3”

1st Place16’ 3”

The difference between points

on the scale varies from

point to point

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Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.

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O Completely DisagreeO Mostly Disagree

O Mostly AgreeO Completely Agree

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O Completely DisagreeO Mostly Disagree

O Mostly AgreeO Completely Agree

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O Not at AllO Very Little

O SomewhatO Quite a Bit

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O Not at AllO Very Little

O SomewhatO Quite a Bit

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O Not ImportantO Slightly Important

O Somewhat ImportantO Very Important

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O Not ImportantO Slightly Important

O Somewhat ImportantO Very Important

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Important Point

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Important Point

Numbers on an ordinal scale are limited in the information they carry (i.e., no equal intervals,

no zero point)

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Interesting Note

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Interesting Note

Technically, numbers on an ordinal scale cannot be added or subtracted.

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Interesting Note

Technically, numbers on an ordinal scale cannot be added or subtracted.

(but we frequently do it anyway !)

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Ordinal Numbers in a Data Set

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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

Data Set

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1 3 3 32

2 1 5 28

3 3 2 33

4 2 6 27

5 1 1 34

6 2 4 31

Data Set

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1 3 3 32

2 1 5 28

3 3 2 33

4 2 6 27

5 1 1 34

6 2 4 31

Data Set

Nominal

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1 3 3 32

2 1 5 28

3 3 2 33

4 2 6 27

5 1 1 34

6 2 4 31

Data Set

OrdinalNominal

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Interval scales •assume quantity of the attribute.

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Interval scales •assume quantity of the attribute.

Temperature

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Interval scales •assume quantity of the attribute.•have equal intervals.

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40o - 41o

100o - 101o

70o - 71o

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40o - 41o

100o - 101o

70o - 71o

Each set of readings are the same distance apart: 1o

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Interval scales •assume quantity of the attribute.•have equal intervals.•may have an arbitrary zero or starting point.

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Technically, numbers on an interval scale can be added and subtracted

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70o

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100o

70o

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100o

70o

100o is 30o more (+) than 70o

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100o

70o

100o is 30o more (+) than 70o

70o is 30o less (-) than 100o

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Technically, numbers on an interval scale can be added and subtracted but not divided and multiplied.

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100o

50o

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100o

50oAnd 50o is NOT half (/) as hot as 100o

100o is NOT twice (x) as hot as 50o

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100o 100o

50o50oAnd 50o is NOT half (/) as hot as 100o

But 100o is NOT twice (x) as hot as 50o

But many do so anyways

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Interval Numbers in a Data Set

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1 3 3 32

2 1 5 28

3 3 2 33

4 2 6 27

5 1 1 34

6 2 4 31

Data Set

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1 3 3 32

2 1 5 28

3 3 2 33

4 2 6 27

5 1 1 34

6 2 4 31

Data Set

OrdinalNominal Interval

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1 3 3 32

2 1 5 28

3 3 2 33

4 2 6 27

5 1 1 34

6 2 4 31

Data Set


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Ratio scales •assume quantity of the attribute.

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6’5” 5’4”5’3” 6’4” 5’11”5’10”

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Ratio scales •assume quantity of the attribute.•have equal intervals.

6’5” 5’4”5’3” 6’4” 5’11”5’10”

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6’5” 5’4”5’3” 6’4” 5’11”5’10”

Every inch represents a unit of measure that is the same across all inches

Every inch represents a unit of measure that is the same across all inches Slide 98 of 85



6’5” 5’4”5’3” 6’4” 5’11”5’10”

With the interval nature of the data, you can say that player 4 (blue team) is 6 inches taller than Player 19 (yellow team)

With the interval nature of the data, you can say that player 4 (blue team) is 6 inches taller than Player 19 (yellow team)Slide 99 of 85


Ratio scales •assume quantity of the attribute.•have equal intervals.•has a zero or starting point.

6’5” 5’4”5’3” 6’4” 5’11”5’10”

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)

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) Slide 100 of 85

Ratio Numbers in a Data Set

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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”

Data Set


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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”

Data Set

OrdinalNominal Interval Ratio

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Important Point

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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.

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Important Point

Numbers on a ratio scale •carry more information than the same numbers on an interval or ordinal scale.

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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.

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Two more Important Points

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1. More adequate scales can be easily converted to less adequate scales.

2. Most statistical programs will treat interval and ratio data the same.

Ratio - - - > Interval - - - > Ordinal - - - > Nominal

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1. More adequate scales can be easily converted to less adequate scales.

2. Most statistical programs will treat interval and ratio data the same.

Ratio - - - > Interval - - - > Ordinal - - - > Nominal

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ASSESSMENT AND ANALYSIS

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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.

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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

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• Metric measure

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Non-Metric Measure

• Non Metric variables are intrinsic

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• 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.

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Methods of Statistical Analysis

Parametrico Parametric methods deal with the estimation of

population parameters (like the mean).

Non-parametrico non-parametric are distribution free methods.

They rely on ordering (ranking) of observations.

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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.

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“Unfamiliar Words”

• Statistical Analyses• Metric Data• Data Analysis• Variables – The characteristic that is being

studied.• Inferential Techniques

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• Interval Point

• Histogram

• Scattergram

• Probability

• Correlation Matrix

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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.

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Formula:

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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.

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Formula:

Standard Deviation formula

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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.

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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)

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Formula:

chi-square formula

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Thank Youfor

Listening

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Education

p4 statistic no.0001709