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?