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report 4th year
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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
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 5 of 85
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)
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
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
Slide 8 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 (i.e., •1 = Catholic, 2 = Mormon . . . •1 = Agree, 2 = Disagree •1 = correct, 0 = incorrect
Slide 9 of 85
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 . . .)
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
Nominal (1 = Male, 2 = Female)
Ordinal (1 = Private, 2 = Sergeant, 3 = Lieutenant . . .)
Interval (30OF, 40OF, 50O . . .)
Ratio (0 meters, 10 meters, 100 meters . . .)
Slide 12 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 13 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 14 of 85
Nominal, Ordinal, Interval, Ratio
Slide 15 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.
Slide 16 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.1 = American
Slide 17 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.1 = American
2 = Canadian
Slide 18 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.1 = American
2 = Canadian
3 = Mexican
Slide 19 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 20 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 21 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 22 of 85
Nominal
Nominal scales use numbers as replacements for names.1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 23 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales use numbers as replacements for names.1 = American
2 = Canadian
3 = Mexican
Data Set
Slide 24 of 85
Nominal, Ordinal, Interval, Ratio
The root of the term “nominal” is “nom” meaning “name”.
Slide 25 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales •assume no quantity of the attribute.
Slide 26 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales •assume no quantity of the attribute.
1 = American
2 = Canadian
Slide 27 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales •assume no quantity of the attribute.
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
Slide 28 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales •assume no quantity of the attribute.•has no particular interval
Slide 29 of 85
Nominal, Ordinal, Interval, Ratio
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
Slide 30 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales •assume no quantity of the attribute.•has no particular interval.•has no zero or starting point.
Slide 31 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales •assume no quantity of the attribute.•has no particular interval.•has no zero or starting point.
1 = American2 = Canadian3 = Mexican
Slide 32 of 85
Nominal, Ordinal, Interval, Ratio
Nominal scales •assume no quantity of the attribute.•has no particular interval.•has no zero or starting point.
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).
1 = American2 = Canadian3 = Mexican
Slide 33 of 85
Nominal, Ordinal, Interval, Ratio
Slide 34 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Slide 35 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Private1
Corporal2
Sargent3
Lieutenant4
Major5
Colonel6
General7
Slide 36 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Private1
Corporal2
Sargent3
Lieutenant4
Major5
Colonel6
General7
Relative Amount of Authority
Slide 37 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
Slide 39 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
3rd Place15’ 2”
2nd Place16’ 1”
1st Place16’ 3”
Relative in terms of PLACEMENT (1st, 2nd, & 3rd) Slide 40 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales use numbers to represent relative amounts of an attribute.
3rd Place15’ 2”
2nd Place16’ 1”
1st Place16’ 3”
Relative in terms of PLACEMENT (1st, 2nd, & 3rd) Slide 41 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.
Slide 42 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.
Lieutenant4
Colonel6
A colonel has more authority than a LieutenantA colonel has more authority than a Lieutenant
Slide 43 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.
1st place is higher than 3rd place1st place is higher than 3rd place
3rd Place
1st Place
Slide 44 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.
Slide 45 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.
3rd Place15’ 2”
2nd Place16’ 1”
Slide 46 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the same interval as the distance between 2nd and 1st place (1”)
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”
Slide 47 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.
3rd Place15’ 2”
2nd Place16’ 1”
1st Place16’ 3”
Slide 48 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the same interval as the distance between 2nd and 1st place (1”)
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”
1st Place16’ 3”
Slide 49 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the same interval as the distance between 2nd and 1st place (1”)
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”
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,
Slide 50 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the same interval as the distance between 2nd and 1st place (1”)
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”
3rd Place15’ 2”
2nd Place16’ 1”
2nd Place16’ 1”
1st Place16’ 3”
1st Place16’ 3”
. . . but how much more is
undefined.
Slide 51 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.
The distance between 3rd and 2nd place (11”) is not the same interval as the distance between 2nd and 1st place (1”)
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”
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
Slide 52 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
Slide 53 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
O Completely DisagreeO Mostly Disagree
O Mostly AgreeO Completely Agree
Slide 54 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
O Completely DisagreeO Mostly Disagree
O Mostly AgreeO Completely Agree
Slide 55 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
Slide 56 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
O Not at AllO Very Little
O SomewhatO Quite a Bit
Slide 57 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
O Not at AllO Very Little
O SomewhatO Quite a Bit
Slide 58 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
Slide 59 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
O Not ImportantO Slightly Important
O Somewhat ImportantO Very Important
Slide 60 of 85
Nominal, Ordinal, Interval, Ratio
Ordinal scales •assume quantity of the attribute.•do not have equal intervals.•may have an arbitrary zero or starting point.
O Not ImportantO Slightly Important
O Somewhat ImportantO 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
Ordinal Numbers in a 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
Data Set
Slide 68 of 85
Ordinal Numbers in a 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
Data Set
Slide 69 of 85
Ordinal Numbers in a 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
Data Set
Nominal
Slide 70 of 85
Ordinal Numbers in a 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
Data Set
OrdinalNominal
Slide 71 of 85
Nominal, Ordinal, Interval, Ratio
Slide 72 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales •assume quantity of the attribute.
Slide 73 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales •assume quantity of the attribute.
Temperature
Slide 74 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales •assume quantity of the attribute.•have equal intervals.
Slide 75 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales •assume quantity of the attribute.•have equal intervals.
Slide 76 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales •assume quantity of the attribute.•have equal intervals.
40o - 41o
100o - 101o
70o - 71o
Slide 77 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales •assume quantity of the attribute.•have equal intervals.
40o - 41o
100o - 101o
70o - 71o
Each set of readings are the same distance apart: 1o
Slide 78 of 85
Nominal, Ordinal, Interval, Ratio
Interval scales •assume quantity of the attribute.•have equal intervals.•may have an arbitrary zero or starting point.
Slide 79 of 85
Technically, numbers on an interval scale can be added and subtracted
Slide 80 of 85
Technically, numbers on an interval scale can be added and subtracted
70o
Slide 81 of 85
Technically, numbers on an interval scale can be added and subtracted
100o
70o
Slide 82 of 85
Technically, numbers on an interval scale can be added and subtracted
100o
70o
100o is 30o more (+) than 70o
Slide 83 of 85
Technically, numbers on an interval scale can be added and subtracted
100o
70o
100o is 30o more (+) than 70o
70o is 30o less (-) than 100o
Slide 84 of 85
Technically, numbers on an interval scale can be added and subtracted but not divided and multiplied.
Slide 85 of 85
Technically, numbers on an interval scale can be added and subtracted but not divided and multiplied.
100o
50o
Slide 86 of 85
Technically, numbers on an interval scale can be added and subtracted but not divided and multiplied.
100o
50oAnd 50o is NOT half (/) as hot as 100o
100o is NOT twice (x) as hot as 50o
Slide 87 of 85
Technically, numbers on an interval scale can be added and subtracted but not divided and multiplied.
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
Slide 88 of 85
Interval Numbers in a Data Set
Slide 89 of 85
Interval Numbers in a 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
Data Set
Slide 90 of 85
Interval Numbers in a 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
Data Set
OrdinalNominal Interval
Slide 91 of 85
Interval Numbers in a 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
Data Set
OrdinalNominal Interval
Slide 92 of 85
Nominal, Ordinal, Interval, Ratio
Slide 93 of 85
Nominal, Ordinal, Interval, Ratio
Ratio scales •assume quantity of the attribute.
Slide 94 of 85
Nominal, Ordinal, Interval, Ratio
Ratio scales •assume quantity of the attribute.
Slide 95 of 85
Nominal, Ordinal, Interval, Ratio
Ratio scales •assume quantity of the attribute.
6’5” 5’4”5’3” 6’4” 5’11”5’10”
Slide 96 of 85
Nominal, Ordinal, Interval, Ratio
Ratio scales •assume quantity of the attribute.•have equal intervals.
6’5” 5’4”5’3” 6’4” 5’11”5’10”
Slide 97 of 85
Nominal, Ordinal, Interval, Ratio
Ratio scales •assume quantity of the attribute.•have equal intervals.
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
Nominal, Ordinal, Interval, Ratio
Ratio scales •assume quantity of the attribute.•have equal intervals.
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
Nominal, Ordinal, Interval, Ratio
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
Slide 101 of 85
Ratio Numbers in a Data Set
Student Nationality Place Test 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”
Data Set
OrdinalNominal Interval
Slide 102 of 85
Ratio Numbers in a Data Set
Student Nationality Place Test 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”
Data Set
OrdinalNominal 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
Numbers on a ratio scale •carry more information than the same numbers on an interval or ordinal scale.
Slide 106 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 107 of 85
Two more Important Points
Slide 108 of 85
Two more Important Points
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
Slide 109 of 85
Two more Important Points
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
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
Slide 116 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
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.
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 Youfor
Listening
Slide 129 of 85
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