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TYPES OF DATA
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IS STATISTICS 100% CORRECT?
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SecondaryData Compilation
Observation
Experimentation
Print or Electronic
Survey
PrimaryData Collection
DATA SOURSES
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Data
Categorical Numerical
Discrete Continuous
Examples:
Marital Status
Political Party Eye Color
(Defined categories)Examples:
Number of Children
Defects per hour
(Counted items)
Examples:
Weight
Voltage
(Measured characteristics)
TYPES OF DATA
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Quantitative Data (Numerical) consists ofnumbers representing counts ormeasurements.
Qualitative Data (Categorical) can beseparated into different categories that are
distinguished by some nonnumeric
characteristic.
DEFINITIONS
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Discrete Data result when the number ofpossible values is either a finite number ora countable number.
Continuous Data result from infinitelymany possible values that correspond to
some continuous scale that covers a range
of values without gaps.
DEFINITIONS
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A variable - a characteristic of a populationor a sample, e.g. Examination marks Stock price The waiting time for medical services
Data - Observed values of variables
WHAT IS A VARIABLE?
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Data - Observed values of variables46 49 46 48 45 49 46 45 47 43
45 46 44 47 44 45 49 46 42 4746 44 42 45 46 46 42 45 41 47
48 43 43 49 40 44 46 43 45 44
41 47 43 47 48 42 44 48 48 45
Scores on a Test
EXAMPLE
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TYPES OF VARIABLES
A. Qualitative or Attribute variable - thecharacteristic being studied is nonnumeric.
EXAMPLES: Gender, religious affiliation, type of automobile
owned, state of birth, eye color are examples.
B. Quantitative variable - information isreported numerically.
EXAMPLES: balance in your checking account, minutesremaining in class, or number of children in a family.
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QUANTITAIVE VARIABLES Classifications
Quantitative variables can be classified as eitherdiscrete or continuous.
A. Discrete variables: can only assume certain values
and there are usually gaps between values.EXAMPLE: the number of bedrooms in a house, or the number of hammers sold at the localHome Depot (1,2,3,,etc).
B. Continuous variable can assume any value within a
specified range.
EXAMPLE: The pressure in a tire, the weight of a pork chop, or the height of students in aclass.
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SUMMARY: TYPES OFVARIABLES
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Scales of Measurement
1. Nominal Scale Categorical/qualitative observations Use number to represent the categories. Example: Single=1, Married=2
2. Ordinal Scale Ordered categorical observations Value are in order Example: Poor-1 Fair-2 Good-3
3. Interval Scale Numerical/quantitative observations Numerical bring the meaning of value.
Example: marks, temperature, IQ
4. Ratio Scale Numerical/quantitative observations Have absolute zero value Example: weight, height, income
SCALES OF MEASUREMENT
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SCALES OF MEASUREMENT
Nominal level
data that isclassified into categories andcannot be arranged in anyparticular order.
EXAMPLES: eye color,gender, religious affiliation.
Ordinal level involves dataarranged in some order, but thedifferences between data valuescannot be determined or aremeaningless.
EXAMPLE: During a taste testof 4 soft drinks, MellowYellow was ranked number1, Sprite number 2, Seven-up number 3, and OrangeCrush number 4.
Interval level
similar to the ordinallevel, with the additional property thatmeaningful amounts of differencesbetween data values can bedetermined. There is no natural zeropoint.
EXAMPLE: Temperature on theFahrenheit scale.
Ratio level the interval level with aninherent zero starting point.Differences and ratios aremeaningful for this level ofmeasurement.
EXAMPLES: Monthly income ofsurgeons, or distance traveledby manufacturersrepresentatives per month.
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Nominal Scale is characterized by datathat consists of names, labels, orcategories only.
Ordinal Scale data can be arranged insome order, but differences between data
values either cannot be determined or are
meaningless.
DEFINITIONS
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Interval Scale is like the ordinal scale, withadditional property that the differencebetween any two data values is
meaningful. However, data at this level donot have a natural zerostarting point.
Ratio Scale is similar to the interval scalewith additional property that there is an
absolute zero(where zero indicates thatnone of the quantity is present). In thisscale ratios are meaningful.
DEFINITIONS
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SUMMARY: SCALES OFMEASUREMENT
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Ratio/Interval dataAge - income55 75000
42 68000. .
. .eightgain+10+5..
NominalPerson Marital status
Ahmad married
Siva singleAh Keong single. .. .Computer Brand
1 IBM
2 Dell3 IBM. .. .
EXAMPLES
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Ratio/Interval dataAge - income55 75000
42 68000
. .
. .eightgain+10+5..
NominalWith nominal data,
all we can do is,
calculate the proportion
of data that falls intoeach category.
IBM Dell Compaq Other Total25 11 8 6 5050% 22% 16% 12%
EXAMPLES
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Knowing the type of data is necessary to properly select thesuitable technique to be used when analyzing data.
Type of analysis allowed for each type of data
Ratio/Interval data arithmetic calculations/Average
67,74,71,83,93,55,48,82,68,62
Average=70.3
Nominal data counting the number of observation/frequency in each category
Single:1 ,Married:2 Divorced:3, Widowed:4 Data record: 1,2,2,2,4,1,2,2,1,3
Average=2.0; Does this mean average person ismarried????
TYPES of DATA TYPES ofANALYSIS
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Solution of Nominal data Category Code Frequency
Single 1 3
Married 2 5 Divorced 3 2
Widowed 4 4
Ordinal data - computations based on anordering process
TYPES of DATA TYPES ofANALYSIS
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Ratio/Interval* Values are real numbers
All calculations are valid
Data may be treated as ordinal or nominal
Example : Examination Marks
Ordinal
Value must represent the ranked order of the data
Calculation based on an ordering process are valid
Data may be treated as nominal but not as interval
Nominal
Value are the arbitrary numbers that represent
categories. Only calculation based on the frequencies of occurrence
are valid.
Data may not be treated as ordinal or interval
*Higher-level data type may be treated as lower-level ones.
HIERARCHY OF DATA
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This is often a preferred source of data due tolow cost and convenience.
Published data is found as printed material,tapes, disks, and on the Internet.
Data published by the organization that hascollected it is called PRIMARY DATA
For example:Data published by the US
Bureau of Census.
Data published by an organization different than the
organization that has collected it is called
SECONDARY DATA.
For example:The Statistical abstracts of the United States,
compiles data from primary sources
Compustat, sells variety of financial data tapes
compiled from primary sources
PUBLISHED DATA
O S O
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Observational study is one in which measurementsrepresenting a variable of interest are observed andrecorded, without controlling any factor that mightinfluence their values.
Experimental study is one in which measurements
representing a variable of interest are observed andrecorded, while controlling factors that might influencetheir values.
When published data is unavailable, oneneeds to conduct a study to generate thedata.
OBSERVATIONAL orEXPERIMENTAL
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StatisticalStudies
Do youmake observations
only, or do you modify thesubjects?
ExperimentObservational
Whenobservationsare made?
Retrospectivestudy
Prospective
study
Cross-sectionalstudy
Past
At
onepoint
Future Design:1. Control effects of variables2. Use replication
3. Use randomization
STATISTICAL STUDIES
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IS STATISTICS 100% CORRECT?
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Voluntary Response Sample (or self-selected sample) is one in which therespondents themselves decide whether to
be included in the sample. Voluntary response sample might not be
representative of the intended population.
DEFINITIONS
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A good questionnaire must be well designed:
Keep the questionnaire as short as possible.
Ask short,simple, and clearly worded questions.
Start with demographic questions to helprespondents get started comfortably.
Use dichotomous and multiple choice questions.
Use open-ended questions cautiously.
Avoid using leading-questions.
Pretest a questionnaire on a small number of people. Think about the way you intend to use the
collected data when preparing the questionnaire.
QUESTIONNAIRE
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IS STATISTICS 100% CORRECT?