Foundations of Sociological Inquiry
Quantitative Data Analysis
Today’s Objectives Quantitative Data Statistics Distributions Comparative Analysis Questions?
Quantitative Data the numerical representation and manipulation of
observations for the purpose of describing and explaining the phenomena that those observations reflect.
Examples of Quantitative Data Age
1 = 1 2 = 2 3 = 3 4 = 4 5 = 5
Sex Male = 1 Female = 2
Education Less than HS = 1 High School/GED = 2 Some College = 3 College Degree = 4
Region of Country West = 1 Midwest = 2 South = 3 Northeast = 4
Recommended Salary for Job Candidates:$4000 $70,000 $40,000 $80,000 $120,000 $135,000 $70,000 $50,000 $67,000.00 $500,000 $50,000 $75,000.00 $60,000 $150,000 $20,000 $50000.00 $70,000 $80,000 $62,000 $200,000 95,000 $75000 $70,000 $80000 $75,000 $45,000 a year $100,000 $250,000 $65,000.00 $45000.00 $75,000 $88,000 $80,000.00 $150,000 $55,000 $130,000 $60,000 $78,000 $150,000 $50,000 70000 $45,000-60,000 $80,000 $75,000 $55000 $40,000 95,000 $80,000 $30,000.00 $80000 $30000 $70,000 $50,000 $50,000 $65000 $80,000 $? $80,000 $50000 $50000 (I have no idea how much Marketing Executive gets paid usually) 150,000 $74,000 $60,000 $60,000 $65,00 $80,000 $65,000 $90,000 $70,000 $90,000 $80,000 $45000 $45000 $35000 $100,000 $85,000 $50,000 $60000 80000 $85,000 $58000 $60000 $70,000 $80,000 $70,000 $40000 $70,000 $80,000 $60,000 $200,000 $80,000 $50000 $60,000 - $75,000 $80,000 $60,000 $45,000 $50,000 $90,000 $30,000 $60,000 50000 $200,000.00 $40000.00 $60000 $50,000 $75,000 $60000 $180000 $120,000 $80000 $55,000 $50,000 85000 $145,000 $ $85,000 $55,000 $70000 $75, 000 $60,000 60000 $ 10,000 $100000 $65000 $85,000 $80,000 $60,000 $ 70,000 $80,000 $75,000.00 $100,000 $50000.00 $70,000 $95,000 $92,000 $70,000 $50,000 $68,000 $80,000 $40,000 $30,000 $50,000 $60,000 $40,000 $80,000 $65,000 $i dont know $90,000 $60,000 $70,000 $80,000 $65000 $70,000 $ $100,000 $72000 $70,000 $50,000 $110,000.000 $80000 $18,000 $110,000 $200,000 $100,000 $80000
Statistics are used to: Summarize data Make statements of inference
Statistics are used to: Summarize data
Measures of central tendency Distributions
Make statements of inference
Statistics are used to: Summarize data Make statements of inference
Frequentist interpretation: Under repeated sampling, how likely is it that you will find an
effect this large or larger? Bayesian interpretation:
What is a credible interval surrounding any measure of central tendency, correlation, or association?
Ways of looking at quantitative data Measures of Central Tendency Distributions/Dispersion
The _______ is computed by summing the values of several observations and dividing by the number of observations?
1 2 3 4
1% 0%6%
93%
1. frequency
2. mean
3. median
4. mode
Ways of looking at quantitative data Measures of Central Tendency
Mean – an average computed by summing the values of several observations and dividing by the number of observations.
Mode- an average representing the most frequently observed value or attribute.
Median – an average representing the value of the “middle” case in a rank-ordered set of observations.
Distributions/Dispersion
Recommended Salary for Job Candidates
Candidate 1
Candidate 2
Candidate 3
Candidate 4
Mean $94,225 $67,125 $77,012 $73,414
Mode $70,000 $80,000 $60,000 $80,000
Median $75,000 $65,000 $68,750 $70,000
N 40 37 41 43
Valid N 40 36 40 41
Recommended Salary for Job Candidates
A measure of dispersion describes
1 2 3 4 5
13%
1% 1%1%
84%1. where the data are clustered.
2. which data are the most important.
3. how the data are distributed around some central value.
4. which data are appropriate for analysis.
5. discrete data only.
Ways of looking at quantitative data Measures of Central Tendency Distributions/Dispersion
Maximum, Minimum Range Probability (Normal, Poisson, Binomial, Chi-square,
Student’s T, F)
Recommended Salary for Job Candidates
Candidate 1
Candidate 2
Candidate 3
Candidate 4
Min-Max $4000-500,000
$30,000-150,000
$30,000-200,000
$10,000-200,000
Range $496,000 $120,000 $170,000 $190,000
Std Dev $80,669 $23,222 $39,551 $30,523
N 40 37 41 43
Valid N 40 36 40 41
Recommended Salary for Job Candidates
Two factories (Apparel and Shoe) show annual average wages of $30,000. However, the range of salaries in the Apparel factory is $5,000, while the range of salaries in the Shoe factory is $15,000. Which of the factories has a larger variation in income?
1 2 3 4 5
14%
53%
26%
5%3%
1. apparel factory
2. shoe factory
3. neither
4. Both factories have equal variation in income.
5. The range is not the appropriate measure.
Comparative Analysis Describe subsets of cases, subjects or respondents. Compare empirical relationship between variables.
Determine logical direction of relationship (independent variable and dependent variable).
Analyze simultaneous relationships among several variables.
Questions?