Data Analysis

Statistics

OVERVIEW

Getting Ready for Data CollectionThe Data Collection ProcessGetting Ready for Data AnalysisDescriptive Statistics

GETTING READY FOR DATA COLLECTION

Four stepsConstructing a data collection formEstablishing a coding strategyCollecting the dataEntering data onto the collection form

THE DATA COLLECTION PROCESS

Begins with raw dataRaw data are unorganized data

CONSTRUCTING DATA COLLECTION FORMS

ID Gender

Grade Building Reading Score

Mathematics Score

12345

22122

8284

10

16666

5541465645

6044375932

One column for each variable

One row for each subject

CODING DATA

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

 

Variable Range of Data Possible

Example

ID Number 001 through 200 138

Gender 1 or 2 2

Grade 1, 2, 4, 6, 8, or 10 4

Building 1 through 6 1

Reading Score 1 through 100 78

Mathematics Score 1 through 100 69

Interpretation

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

The Basics

Descriptive statisticsInferential statistics

Sample statisticsPopulation parameters

Sample--------------population

Sample statistics

Variables in a sample or measures computed from sample data

Population parameters

The variables in a population or measured characteristics of the population

Making Data Usable

…Or what to do with all those numbers

Descriptive Statistics

Frequency Distributions

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

Frequency distribution of ice cream consumptionAge Frequency

(number in range)

01-56-1011-15TOTAL

25158250

Percentage DistributionsOrganizing the frequency distribution into a chart or graph that summarizes percentage values associated with particular values of a variable

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

Frequency distribution of ice cream

consumption by age

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

01-56-1011-15TOTAL

5030164

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

Cross tabulation

Cross tabulation: a technique for organizing data by groups, categories or classes, thus facilitating comparisons; a joint frequency distribution of observations on two or more sets of variables

Types of Cross tabsContingency table: the results of a cross tabulation of two variables, such as survey questionsCross tab of question: Do you have children under the age of six currently living with you? This is a 2X2 table, why

Yes No Total

Males 5 15 20

Females

10 20 30

Total 15 35 50

Types of Cross tabsPercentage cross-tab. Using percentages helps us make relative comparisons. The total number of respondents/observations may be used as a base for computing the percentage in each cellPercentage Cross tab : Do you have children under the age of six currently living with you? Yes No Total

Males 20% 80% 100% (20)

Females 33.33% 66.66% 100% (30)

Total 30% 70% 100% (50)

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

Elaboration Analysis of Cross tabs

Analysis of the basic cross-tab for each level of another variable, such as subgroups of the same samplePercentage Cross tab : Do you have children under the age of six currently living with you? Moderator Variable; Spurious relationship

Aged 17-25 Aged 25 and up

Male Female

Yes 0 2

No 10 20

Male Female

5 8

0 0

Calculating Rank Data

Please place in rank order the following varieties of cookies (1= most preferred to 4=least preferred) __ Chocolate chip__ Marshmallow__ Oatmeal__ Oreo

Choco chip

Marshm

Oatmeal Oreo

1 1 2 4 3

2 1 3 4 2

3 2 1 3 4

4 2 4 3 1

5 2 1 3 4

6 3 4 1 2

7 2 3 1 4

8 1 4 2 3

9 4 3 2 1

10 2 1 3 4Chocolate 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 tendency

Mode: the value that occurs most often

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

Mean: the arithmetic average

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

WHEN TO USE WHICH MEASURE

Measure of Central

Tendency

Level of Measurement

Use When Examples

Mode Nominal Data are categorical Eye color, party affiliation

Median Ordinal Data include extreme scores

Rank in class, birth order

Mean Interval and ratio

You can, and the data fit

Speed of response, age in years

Measures of dispersion

What is the tendency for measures to depart from the central tendency?Range: simplest measure of dispersionDeviation scores- quantitative index of dispersion Average deviation: never used Variance: the sum of squared deviation scores

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

Standard Deviation: square root of variance

MEASURES OF VARIABILITY

Variability is the degree of spread or dispersion in a set of scoresRange—difference between highest and lowest scoreStandard deviation—average difference of each score from mean

THE MEAN AND THE STANDARD DEVIATION

STANDARD DEVIATIONS AND % OF CASES

The normal curve is symmetricalOne standard deviation to either side of the mean contains 34% of area under curve68% of scores lie within ± 1 standard deviation of mean