Data Analysis

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Data Analysis

• Statistics

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OVERVIEW

• Getting Ready for Data Collection
• The Data Collection Process
• Getting Ready for Data Analysis
• Descriptive Statistics

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GETTING READY FOR DATA COLLECTION Four steps

• Constructing a data collection form
• Establishing a coding strategy
• Collecting the data
• Entering data onto the collection form

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THE DATA COLLECTION PROCESS

• Begins with raw data
• Raw data are unorganized data

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CONSTRUCTING DATA COLLECTION FORMS
One column for each variable
ID Gender Grade Building Reading Score Mathematics Score
1 2 3 4 5 2 2 1 2 2 8 2 8 4 10 1 6 6 6 6 55 41 46 56 45 60 44 37 59 32
One row for each subject
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CODING DATA
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

• Use single digits when possible
• Use codes that are simple and unambiguous
• Use codes that are explicit and discrete

   
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Interpretation

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

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The Basics

• Descriptive statistics
• Inferential statistics
• Sample statistics
• Population parameters

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Sample--------------population
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• 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

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Making Data Usable
1 2 3 4 5 6 7 8 9

• Or what to do with all those numbers

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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 consumption

Age Frequency (number in range)
0 1-5 6-10 11-15 TOTAL 25 15 8 2 50
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• Frequency distribution of ice cream consumption
  by age

• Percentage Distributions
• Organizing the frequency distribution into a
  chart or graph that summarizes percentage values
  associated with particular values of a variable
• Proportion
• The percentage of elements that meet some
  criterion (percentage, fraction or decimal)

Age Percent (of people who consumed ice cream in range)
0 1-5 6-10 11-15 TOTAL 50 30 16 4 100
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Graphic Representations of Data
Pie Chart Ice cream consumption
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Bar Chart Frequency of Seasonal Ice Cream
consumption
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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

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Types of Cross tabs

• Contingency table the results of a cross
  tabulation of two variables, such as survey
  questions
• Cross 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
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Types of Cross tabs

• Percentage 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 cell
• Percentage 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)
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Graphical representation of results from cross tab
Bar Chart Frequency of Seasonal Ice Cream
consumption Shown By Gender
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Elaboration Analysis of Cross tabs

• Analysis of the basic cross-tab for each level of
  another variable, such as subgroups of the same
  sample
• Percentage 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
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Calculating Rank Data

• Please place in rank order the following
  varieties of cookies (1 most preferred to
  4least preferred)
• __ Chocolate chip
• __ Marshmallow
• __ Oatmeal
• __ Oreo

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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 4
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
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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

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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
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Measures of dispersion

• What is the tendency for measures to depart from
  the central tendency?
• Range simplest measure of dispersion
• Deviation 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

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MEASURES OF VARIABILITY

• Variability is the degree of spread or dispersion
  in a set of scores
• Rangedifference between highest and lowest score
• Standard deviationaverage difference of each
  score from mean

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THE MEAN AND THE STANDARD DEVIATION
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STANDARD DEVIATIONS AND OF CASES

• The normal curve is symmetrical
• One standard deviation to either side of the mean
  contains 34 of area under curve
• 68 of scores lie within 1 standard deviation
  of mean