Foundations of Sociological Inquiry

Statistical Analysis

Today’s Objectives Why use Statistics? Descriptive Statistics Inferential Statistics Multivariate Techniques Questions?

The formula Y = f(X) tells us that

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17%

62%

4%

12%

4%

1. X is the dependent variable.

2. Y is the dependent variable.

3. f is the dependent variable.

4. need to know what Y, f, and X represent to determine the dependent variable.

5. None of these choices is correct.

Why Use Statistics?

Statistics enable us to construct simplified representations of a complex social world.

Why Use Statistics?

Statistics enable us to construct simplified representations of a complex social world.

Begin with a sociological questionIdentify data to answer the question (collect, observe, record)Analyze data (statistics help)Present your findings (statistics help)Situate your findings in relation to what we think we already know (statistics help)

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

Descriptive Statistics (summary) Statistical computations describing either the

characteristics of a sample or the relationship among variables in a sample Data reduction Measures of association Regression analysis Other forms of multivariate analysis

Recommended Salary for Job Candidates

Male Respondents

Female Respondents

Mean $77,277 $78,837

Std. Dev $37,904 $56,897

N 96 65Source: Data were collected from students enrolled in Sociology 300.

Recommended Salary for Job Candidates

Difference in Means

Is the difference in mean salary recommended by men and women statistically significant?

Difference in Means

Is the difference in mean salary recommended by men and women statistically significant?

Conduct a t-test

t = 0.20, df = 154, p-value = .84

95 percent confidence interval (-13392, 16512)

Difference in Means

Is the difference in mean salary recommended by men and women statistically significant?

Conduct a t-test

t = 0.20, df = 154, p-value = .84

95 percent confidence interval (-13392, 16512)

We should not reject the null hypothesis that the true difference in means is equal to zero

Recommended Salary for Job Candidates

Multivariate Analysis Is the difference in mean salary recommended by men

and women statistically significant, controlling for parental status of applicant?

Multivariate Analysis Is the difference in mean salary recommended by men and

women statistically significant, controlling for parental status of applicant?

Conduct a regression analysis of recommended salary

Variable Estimate t-value P-value

Male Respondent -1452 -0.18 0.86

Parent Applicant -14018 -1.77 0.08+

Intercept 85846 13.18 <.001***

Multivariate Analysis Is the difference in mean salary recommended by men and women

statistically significant, controlling for parental status of applicant? Conduct a regression analysis of recommended salary

Variable Estimate t-value P-value

Male Respondent -1452 -0.18 0.86

Parent Applicant -14018 -1.77 0.08+

Intercept 85846 13.18 <.001***

We should not reject the null hypothesis that the true difference in recommended salaries, controlling for parental status of applicant, is equal to zero

Inferential Statistics The body of statistical computations relevant to

making inferences from findings based on sample observations to some larger population. Sampling error Non-sampling error

_____ indicate the likelihood that the relationship observed between variables in a sample can be attributed to sampling error only.

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4%11%

19%

66%

1. Ex-post facto hypothesizing

2. Tests of statistical significance

3. Disconfirmation

4. Disambiguation

Statistical Significance Statistical Significance is a general term referring to

the likelihood that the relationship observed in a sample could be attributed to sampling error alone.

Statistical Significance Statistical Significance is a general term referring to

the likelihood that the relationship observed in a sample could be attributed to sampling error alone.

Tests of Statistical Significance are a class of statistical computations that indicate the likelihood that the relationship observed between variables in a sample can be attributed to sampling error alone.

Statistical Significance Statistical Significance is a general term referring to the

likelihood that the relationship observed in a sample could be attributed to sampling error alone.

Tests of Statistical Significance are a class of statistical computations that indicate the likelihood that the relationship observed between variables in a sample can be attributed to sampling error alone.

Level of Significance, in the context of tests of statistical significance, the degree of likelihood that an observed, empirical relationship could be attributed to sampling error.

_____ are statistical measures used for making inferences from findings based on sample observations to a larger population.

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11%

3%

27%

59%1. Descriptive

statistics

2. Inferential statistics

3. Both of the above

4. Neither of the above

A statistical significance level of .05 means that

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31%

19%

9%

4%

38%

1. the probability that a relationship as strong as the observed one can be attributed to sampling error alone is 5 percent.

2. we can be 5 percent sure that the relationship is real and not due to sampling error.

3. there is an .05 percent chance that a relationship as strong as the observed one can be attributed to sampling error.

4. the difference we observed in the table is 5 percent different.

5. there is a 5 percent standard error in the observations.

Questions?