1. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Analysis & Interpretation: Individual Variables Independently Chapter 12, Student Edition MR/Brown & Suter 1

2. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objectives MR/Brown & Suter2 1. Distinguish between univariate and multivariate analyses 2. Describe frequency analysis 3. Describe descriptive statistics 4. Discuss confidence intervals for proportions and means 5. Overview the basic purpose of hypothesis testing

3. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objectives MR/Brown & Suter3 1. Distinguish between univariate and multivariate analyses 2. Describe frequency analysis 3. Describe descriptive statistics 4. Discuss confidence intervals for proportions and means 5. Overview the basic purpose of hypothesis testing

4. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objective 1 MR/Brown & Suter4  Is the variable to be analyzed by itself or in relationship with other variables?  Analysis involving individual variables is univariate analysis  Analysis involving multiple variables is multivariate analysis

5. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objectives MR/Brown & Suter5 1. Distinguish between univariate and multivariate analyses 2. Describe frequency analysis 3. Describe descriptive statistics 4. Discuss confidence intervals for proportions and means 5. Overview the basic purpose of hypothesis testing

6. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objective 2 MR/Brown & Suter6  Frequency Analysis  A count of the number of cases that fall into each of the response categories GenderNumberPercent Valid Percent Cumulative Valid Percent Male4519%20% Female17777%80%100% Total22296%100% Missing94% Overall231100%

7. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objectives MR/Brown & Suter7 1. Distinguish between univariate and multivariate analyses 2. Describe frequency analysis 3. Describe descriptive statistics 4. Discuss confidence intervals for proportions and means 5. Overview the basic purpose of hypothesis testing

8. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objective 3 MR/Brown & Suter8  Descriptive Statistics  Statistics that describe the distribution of responses on a variable  The most commonly used descriptive statistics are the mean and standard deviation  The mean (pronounced x bar) is a measure of central tendency  The standard deviation (s) is measure of dispersion

9. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objectives MR/Brown & Suter9 1. Distinguish between univariate and multivariate analyses 2. Describe frequency analysis 3. Describe descriptive statistics 4. Discuss confidence intervals for proportions and means 5. Overview the basic purpose of hypothesis testing

10. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objective 4 MR/Brown & Suter10  Confidence intervals for proportions – a projection of the range within which a population parameter will lie at a given level of confidence based on a statistic obtained from a probabilistic sample  Sampling has an impact on analysis  Drawing a probability sample allows for the appropriate calculation of confidence intervals

11. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objective 4 MR/Brown & Suter11  Confidence intervals are p - sampling error ≤ π ≤ p + sampling error  p = the relevant proportion obtained from the sample  sampling error considers the desired degree of confidence (z) and the number of valid cases overall for the proportion (n) in addition to p  π = population proportion

12. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objective 4 MR/Brown & Suter12  Confidence intervals for means – a projection of the range within which a population mean will lie at a given level of confidence  Confidence intervals are x - sampling error ≤ μ ≤ x + sampling error  x = the sample mean  sampling error considers the desired degree of confidence (z), the sample standard deviation (s), and the number of valid cases overall for the sample (n)  μ = population mean _ __

13. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objectives MR/Brown & Suter13 1. Distinguish between univariate and multivariate analyses 2. Describe frequency analysis 3. Describe descriptive statistics 4. Discuss confidence intervals for proportions and means 5. Overview the basic purpose of hypothesis testing

14. © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Objective 5 MR/Brown & Suter14  How can we tell if a particular result in the sample represents the true situation in the population or simply occurred by chance? This is the essence of hypothesis testing.  Null Hypothesis (H 0 ): The hypothesis that a proposed result is not true for the population  Researchers typically attempt to reject the null hypothesis in favor of some alternative hypothesis  Alternative Hypothesis (H A ): The hypothesis that a proposed result is true for the population