Data AnalysisData Analysis

StatisticsStatistics

OVERVIEWOVERVIEW Getting Ready for Data CollectionGetting Ready for Data Collection The Data Collection ProcessThe Data Collection Process Getting Ready for Data AnalysisGetting Ready for Data Analysis Descriptive StatisticsDescriptive Statistics

GETTING READY FOR GETTING READY FOR DATA COLLECTIONDATA COLLECTION

Four stepsFour steps Constructing a data collection formConstructing a data collection form Establishing a coding strategyEstablishing a coding strategy Collecting the dataCollecting the data Entering data onto the collection Entering data onto the collection

formform

THE DATA COLLECTION THE DATA COLLECTION PROCESSPROCESS

Begins with raw dataBegins with raw data– Raw data are unorganized dataRaw data are unorganized data

CONSTRUCTING DATA CONSTRUCTING DATA COLLECTION FORMSCOLLECTION FORMS

ID ID GendGenderer

GradeGrade BuildingBuilding ReadinReading Scoreg Score

Mathematics Mathematics ScoreScore

11

22

33

44

55

22

22

11

22

22

88

22

88

44

1010

11

66

66

66

66

5555

4141

4646

5656

4545

6060

4444

3737

5959

3232

One column for each variable

One row for each subject

CODING DATACODING DATA

Use single digits when possibleUse single digits when possible Use codes that are simple and unambiguousUse codes that are simple and unambiguous Use codes that are explicit and discreteUse codes that are explicit and discrete 

 

VariableVariable Range of Data Range of Data PossiblePossible

ExampleExample

ID NumberID Number 001 through 200001 through 200 138138

GenderGender 1 or 21 or 2 22

GradeGrade 1, 2, 4, 6, 8, or 101, 2, 4, 6, 8, or 10 44

BuildingBuilding 1 through 61 through 6 11

Reading ScoreReading Score 1 through 1001 through 100 7878

Mathematics ScoreMathematics Score 1 through 1001 through 100 6969

Interpretation

• The process of making pertinent inferences and drawing conclusions concerning the meaning and implications of a research investigation

The BasicsThe Basics

Descriptive statisticsDescriptive statistics Inferential statisticsInferential statistics

Sample statisticsSample statistics Population parametersPopulation parameters

Sample--------------Sample--------------populationpopulation

Sample statisticsSample statistics

Variables in a Variables in a sample or sample or measures measures computed from computed from sample datasample data

Population Population parametersparameters

The variables in a The variables in a population or population or measured measured characteristics of characteristics of the populationthe population

Making Data UsableMaking Data Usable

……Or what to do with all those Or what to do with all those numbersnumbers

Descriptive StatisticsDescriptive Statistics

Frequency Frequency DistributionsDistributions

Organizing a set Organizing a set of data by of data by summarizing the summarizing the number of times a number of times a particular value of particular value of a variable occursa variable occurs

Frequency distribution Frequency distribution of ice cream of ice cream consumptionconsumption

AgeAge Frequency Frequency (number in (number in range)range)

00

1-51-5

6-106-10

11-1511-15

TOTALTOTAL

2525

1515

88

22

5050

Percentage DistributionsPercentage Distributions Organizing the frequency Organizing the frequency

distribution into a chart or distribution into a chart or graph that summarizes graph that summarizes percentage values percentage values associated with particular associated with particular values of a variablevalues of a variable

ProportionProportion The percentage of The percentage of

elements that meet some elements that meet some criterion (percentage, criterion (percentage, fraction or decimal)fraction or decimal)

Frequency distribution Frequency distribution of ice cream of ice cream

consumption by ageconsumption by age

AgeAge Percent Percent (of (of people who people who consumed ice consumed ice cream in cream in range)range)

00

1-51-5

6-106-10

11-1511-15

TOTALTOTAL

5050

3030

1616

44

100%100%

Graphic Representations of Data

Pie Chart: Ice cream consumption

WinterSpringSummerFall

Bar Chart: Frequency of Seasonal Ice Cream consumption

0

10

20

30

40

50

60

70

80

90

Winter Spring Summer Fall

Amt

Bar Chart: Frequency of Seasonal Ice Cream consumption Shown By Gender

0

10

20

30

40

50

60

70

80

90

Winter Spring Summer Fall

MaleFemale

Graphical representation of results from cross tab

Cross tabulationCross tabulation

Cross tabulation:Cross tabulation:– a technique for organizing data by a technique for organizing data by

groups, categories or classes, thus groups, categories or classes, thus facilitating comparisons; facilitating comparisons;

– a joint frequency distribution of a joint frequency distribution of observations on two or more sets of observations on two or more sets of variablesvariables

Types of Cross tabsTypes of Cross tabs Contingency table: the results of Contingency table: the results of

a cross tabulation of two a cross tabulation of two variables, such as survey variables, such as survey questionsquestions

Cross tab of question: Do you have children Cross tab of question: Do you have children under the age of six currently living with under the age of six currently living with you? (2 x 2 table)you? (2 x 2 table)YesYes NoNo TotalTotal

MalesMales 55 1515 2020

FemaleFemaless

1010 2020 3030

TotalTotal 1515 3535 5050

Types of Cross tabsTypes of Cross tabs Percentage cross-tab. Using percentages Percentage cross-tab. Using percentages

helps us make relative comparisons. The helps us make relative comparisons. The total number of respondents/observations total number of respondents/observations may be used as a base for computing the may be used as a base for computing the percentage in each cellpercentage in each cell

Percentage Cross tab : Do you have children Percentage Cross tab : Do you have children under the age of six currently living with under the age of six currently living with you? you? YesYes NoNo TotalTotal

MalesMales 20%20% 80%80% 100% 100% (20)(20)

FemalesFemales 33.33%33.33% 66.66%66.66% 100% 100% (30)(30)

TotalTotal 30%30% 70%70% 100% 100% (50)(50)

Elaboration Analysis of Elaboration Analysis of

Cross tabsCross tabs Analysis of the basic cross-tab for each level Analysis of the basic cross-tab for each level of another variable, such as subgroups of the of another variable, such as subgroups of the same samplesame sample

Percentage Cross tab : Do you have children Percentage Cross tab : Do you have children under the age of six currently living with under the age of six currently living with you? you?

Aged 17-25Aged 17-25 Aged 25 and up Aged 25 and upMaleMale FemalFemal

ee

YesYes 00 22

NoNo 1010 2020

MaleMale FemalFemalee

55 88

00 00

Calculating Rank DataCalculating Rank Data

Please place in rank order the Please place in rank order the following varieties of cookies (1= following varieties of cookies (1= most preferred to 4=least most preferred to 4=least preferred) preferred)

__ Chocolate chip__ Chocolate chip __ Marshmallow__ Marshmallow __ Oatmeal__ Oatmeal __ Oreo__ Oreo

Choco Choco chipchip

MarshMarshmm

OatmealOatmeal OreoOreo

11 11 22 44 33

22 11 33 44 22

33 22 11 33 44

44 22 44 33 11

55 22 11 33 44

66 33 44 11 22

77 22 33 11 44

88 11 44 22 33

99 44 33 22 11

1010 22 11 33 44

Chocolate chip: (3X1) +(4X2) + (2X3) +(1X4) = 21

Marshmallow: (3X1) +(1X2) + (3X3) +(3X4) = 26

Oatmeal: (2X1) +(2X2) + (4X3) +(3X4) = 26

Oreo: (2X1) +(2X2) + (2X3) +(4X4) = 28

Measures of central Measures of central tendencytendency Mode: the value that occurs most oftenMode: the value that occurs most often

Median: the midpoint; the value below Median: the midpoint; the value below which half the values in a distribution fallwhich half the values in a distribution fall

Mean: the arithmetic averageMean: the arithmetic average

Remember: what type of scale you use Remember: what type of scale you use determines the type of statistic you may determines the type of statistic you may calculatecalculate

WHEN TO USE WHICH WHEN TO USE WHICH MEASUREMEASUREMeasure of Measure of

Central Central TendencyTendency

Level of Level of MeasurementMeasurement

Use When Use When ExamplesExamples

ModeMode NominalNominal Data are categoricalData are categorical Eye color, party Eye color, party affiliationaffiliation

MedianMedian OrdinalOrdinal Data include extreme Data include extreme scoresscores

Rank in class, Rank in class, birth orderbirth order

MeanMean Interval and Interval and ratioratio

You can, and the data You can, and the data fitfit

Speed of Speed of response, age in response, age in yearsyears

Measures of dispersionMeasures of dispersion

What is the tendency for measures to What is the tendency for measures to depart from the central tendency?depart from the central tendency?

Range:Range: simplest measure of dispersion simplest measure of dispersion Deviation scoresDeviation scores- quantitative index of - quantitative index of

dispersiondispersion– VarianceVariance: the sum of squared deviation : the sum of squared deviation

scores divided by sample size minus 1- often scores divided by sample size minus 1- often used. (variance is in squared units, eg used. (variance is in squared units, eg squared dollars)squared dollars)

– Standard Deviation:Standard Deviation: square root of variance square root of variance

MEASURES OF MEASURES OF VARIABILITYVARIABILITY

Variability is the degree of spread or Variability is the degree of spread or dispersion in a set of scoresdispersion in a set of scores

Range—difference between highest and Range—difference between highest and lowest scorelowest score

Standard deviation—average difference Standard deviation—average difference of each score from meanof each score from mean

THE MEAN AND THE THE MEAN AND THE STANDARD DEVIATIONSTANDARD DEVIATION

STANDARD DEVIATIONS STANDARD DEVIATIONS AND % OF CASESAND % OF CASES

The normal curve is symmetricalThe normal curve is symmetrical One standard deviation to either side of the mean contains 34% of One standard deviation to either side of the mean contains 34% of

area under curvearea under curve 68% of scores lie within 68% of scores lie within ± 1 standard deviation of mean± 1 standard deviation of mean