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Introduction to Data Analysis

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Introduction to Data Analysis Why do we analyze data? Make sense of data we have collected Basic steps in preliminary data analysis Editing Coding – PowerPoint PPT presentation

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Title: Introduction to Data Analysis


1
Introduction to Data Analysis
  • Why do we analyze data?
  • Make sense of data we have collected
  • Basic steps in preliminary data analysis
  • Editing
  • Coding
  • Tabulating

2
Introduction to Data Analysis
  • Editing of data
  • Impose minimal quality standards on the raw data
  • Field Edit -- preliminary edit, used to detect
    glaring omissions and inaccuracies (often
    involves respondent follow up)
  • Completeness
  • Legibility
  • Comprehensibility
  • Consistency
  • Uniformity

3
Introduction to Data Analysis
  • Central office edit
  • More complete and exacting edit
  • Best performed by a number of editors, each
    looking at one part of the data
  • Decisions on how to handle item non-response and
    other omissions need to be made
  • List-wise deletion (drop for all analyses) vs.
    case-wise deletion (drop only for present
    analysis)

4
Introduction to Data Analysis
  • Coding -- transforming raw data into symbols
    (usually numbers) for tabulating, counting, and
    analyzing
  • Must determine categories
  • Completely exhaustive
  • Mutually exclusive
  • Assign numbers to categories
  • Make sure to code an ID number for each completed
    instrument

5
Introduction to Data Analysis
  • Tabulation -- counting the number of cases that
    fall into each category
  • Initial tabulations should be preformed for each
    item
  • One-way tabulations
  • Determines degree of item non-response
  • Locates errors
  • Locates outliers
  • Determines the data distribution

6
Preliminary Data Analysis
  • Tabulation
  • Simple Counts
  • For example
  • 74 families in the study own 1 car
  • 2 families own 3
  • Missing data (9)
  • 1 Family did not report
  • Not useful for further analysis

Number of Cars Number of Families
1 75
2 23
3 2
9 1
Total 101
7
Preliminary Data Analysis
  • Tabulation
  • Compute Percentages
  • Eliminate non-responses
  • Note Report without missing data

Number of Cars Number of Families
1 75
2 23
3 2
Total 100
8
Preliminary Data Analysis
  • Cross Tabulation
  • Simultaneous count of two or more items
  • Note marginal totals are equal to frequency
    totals
  • Allows researcher to determine if a relationship
    exists between two variables
  • Used a final analysis step in majority of
    real-world applications
  • Investigates the relationship between two
    ordinal-scaled variables

Number of Cars Lower Income Higher Income Total
1 48 27 75
2 or More 6 19 25
Total 54 46 100
9
Preliminary Data Analysis
  • Cross Tabulation
  • To analyze the data
  • Calculate percentages in the direction of the
    causal variable
  • Does number of cars cause income level?

Number of Cars Lower Income Higher Income Total
1 64 36 100
2 or More 24 76 100
Total 54 46 100
10
Preliminary Data Analysis
  • Cross Tabulation
  • To analyze the data
  • Does income level cause number of cars?

Number of Cars Lower Income Higher Income Total
1 89 59 75
2 or More 11 41 25
Total 100 100 100
11
Preliminary Data Analysis
  • Cross Tabulation allows the development of
    hypotheses
  • Develop by comparing percentages across
  • Lower income more likely to have one car (89)
    than the higher income group (59)
  • Higher income more likely to have multiple cars
    (41) than the lower income group (11)
  • Are results statistically significant?
  • To test must employ chi-square analysis

12
Preliminary Data Analysis
  • Chi-square analysis
  • Allows the statistical testing of the
    independence of two or more nominally-scaled
    variables
  • Null hypothesis (HO) is that the variables are
    independent (i.e., no relationship exists)
  • Alternative hypothesis (HA) is that a statistical
    relationship exists among the variables
  • Present example
  • HO Income level will have no affect on the
    number of cars that a family owns
  • HA Income level will affect the number of cars
    that a family owns

13
Preliminary Data Analysis
  • Chi-square analysis
  • General Approach
  • Based on marginal totals compute the expected
    values per cell
  • Compare expected values to actual values to
    compute chi-square value (C2)
  • Compare computed C2 to critical C2
  • Table 4 on p. 442 in text

Number of Cars Lower Income Higher Income Total
1 75
2 or More 25
Total 54 46 100
14
Preliminary Data Analysis
  • Chi-square analysis
  • Compute Expected Values
  • E1 (75 54)/100
  • E1 40.5
  • E2 (75 46)/100
  • E2 34.5
  • Note E1 E2 75
  • E3 ?
  • E4 ?

Number of Cars Lower Income Higher Income Total
1 E1 E2 75
2 or More E3 E4 25
Total 54 46 100
15
Preliminary Data Analysis
  • Compute C2 value
  • C2 S (Oi Ei)2/Ei
  • C2
  • df (rows - 1) (cols. - 1) 1 1 2
  • a .05
  • Critical C2 5.99
  • 12.08 gt 5.99 Reject the Null Hypothesis

Cell Oi Ei Oi - Ei (Oi Ei)2 (Oi Ei)2/Ei
E1 48 40.5 7.5 56.25 1.39
E2 27 34.5 -7.5 56.25 1.63
E3 6 13.5 -7.5 56.25 4.17
E4 19 11.5 7.5 56.25 4.89
S C2 12.08
16
Preliminary Data Analysis
  • Conclusion
  • Income has an influence on number of cars in a
    family
  • BUT
  • Does family size matter??
  • Do a 3-way Cross-Tabulation
  • Is Income more important than Family Size?

17
Preliminary Data Analysis
  • Total Data

Income Level 1 Car or Less 2 or More Cars Total
Low 48 6 54
High 27 19 46
Total 75 25 100
18
Preliminary Data Analysis
  • Families with 4 Members or Less

Income Level 1 Car or Less 2 or More Cars Total
Low 44 2 46
High 26 6 32
Total 70 8 78
19
Preliminary Data Analysis
  • Families with 5 Members or More

Income Level 1 Car or Less 2 or More Cars Total
Low 4 4 8
High 1 13 14
Total 5 17 22
20
Preliminary Data Analysis
Families with 4 Members or Less
Income Level 1 Car or Less 2 or More Cars Total
Low 96 4 100
High 81 19 100
Families with 5 Members or More
Income Level 1 Car or Less 2 or More Cars Total
Low 50 50 100
High 7 93 100
21
Preliminary Data Analysis
Create New Table Look at those families with 2
or more cars by family size Families with 2 or
More Cars by Income and Size
Income Level/Size 4 or Less 5 or More Total
Low 4 50 11
High 19 93 41
Certainly Both family size and income level
contribute to the number of cars that a family
owns But family size seems to be the driver
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