Quantitative Analysis

1. Quantitative Analysis Define Quantitative Analysis Describe the coding process Identify two functions of codebooks Practice doing a codebook format Describe ways to enter data Give examples of univariate analysis Explain central tendency and issues that surround it Distinguish discrete from continuous variables Differentiate the goals of univariate, bivariate, and multivariate analyses Identify the goal of subgroup comparisons Differentiate dependent from independent variables Show how bivariate data are presented and analyzed Show how multivariate data are presented and analyzed

2. Assignment for 4/1 • Qualitative Article Review • 2-3 page review describing the relevant components of the research • Critique of whether or not the study has been done right • What improvements, if any, are needed? If none needed, what are the strengths of the study?

3. Quantitative analysisNumerical representation and manipulation of observations for the purpose of describing and explaining the phenomena that those observations reflect.

4. Sources of Quantitative Data • Questionnaires • Rating forms • Measurements • Open-ended questions • Field observations

5. Terminology • Attribute – A characteristic of a person or thing. • Variable – A logical grouping of attributes.

6. Variables • Independent • Variable with values that are not problematical in an analysis , but are simply taken as given—it causes or determines a dependent variable • Dependent • Variable assumed to depend on or be caused by another (D=income, I=educ) • (Intervening)

7. Continuous variableIncreases steadily in tiny fractions. • Discrete variableJumps from category to category without intervening steps.

8. Levels of Data • Nominal • Ordinal • Interval • Ratio • Important when determining codes for independent and dependent variables

9. What level of data are they? Age Sex Blood pressure IQ Income Job title Finish place in race Ethnicity # of work-outs per week Test score Job responsibility classification Temperature Height Satisfaction level (Likert scale)

10. Developing Code Categories Two basic approaches: • Beginning with a coding scheme derived from the research purpose. • Generate codes from the data. Coding: • Code categories should be exhaustive and mutually exclusive. • Reliability

11. Student Responses That Can Be Coded “Financial Concerns”

12. Codebook Construction Purposes: • Primary guide used in the coding process. • Document that describes the locations of variables and lists the assignments of codes to the attributes composing those variables.

13. Entering Data • Data entry specialists enter the data into an SPSS data matrix or Excel spreadsheet. • Optical scan sheets. • PDAs. • Part of the process of data collection.

17. Transforming and Missing Data • Transform – A specific function in SPSS that can recode variables • Age into age categories • Missing or misrepresented responses?

18. Types of Analyses • Univariate • Bivariate • Multivariate

19. Univariate analysisDescribes a case in terms of a single variable - the distribution of attributes that comprise it. • Frequency distribution (f =)Description of the number of times that the various attributes of a variable are observed in a sample.

20. Descriptive Statistics Frequencies Percentages Central tendency Mean Median Mode Dispersion measures Range Variance Standard deviation

21. Graphical Representation - Frequencies Pie Charts Bar Graph Histogram

22. SPSS Analysis: GSS Attendance at Religious Services, 2000

23. AverageMeasure of central tendency. • Mean (x bar)Result of diving the sum of the values by the total number of cases.

24. ModeThe most frequently occurring attribute. • MedianMiddle attribute in the ranked distribution of observed attributes.

25. DispersionRefers to the way values are distributed around some central value. • Range = X(max) – X(min) • Interquartile range • Standard deviationIndex of the amount of variability in a set of data.

26. Basketball Example Team #1 0 1 10 14 20 Team #2 8 8 9 10 10

27. Calculating Std. Deviation and Variance • Calculate the mean • Subtract the mean from each score (this is your deviation score) • Square the deviation scores • Add the squared deviation scores • Divide this number by n-1 • Take the sq. root of this number • Square the number

28. What do the data look like?(Distribution Curves) • Normal distribution • 68/95% rule • Skewness • Positive • Negative

29. Univariate Analysis • Describing a case in terms of the distribution of attributes that comprise it. Example: • Gender - number of women, number of men.

30. Presenting Univariate Data Goals: • Provide reader with the fullest degree of detail regarding the data. • Present data in a manageable from.

31. Subgroup Comparisons • Describe subsets of cases, subjects or respondents. Examples • "Collapsing" response categories. • Handling "don't knows."

32. Bivariate analysisAnalysis of two variables simultaneously. Focus is on the variables and the empirical relationships. • Descriptive, univariate • Inferential, bivariate & multivariate

33. Bivariate Analysis • Describe a case in terms of two variables simultaneously. • Example: • Gender • Attitudes toward equality for men and women

34. Contingency tablesValues of the dependent variable are contingent on values of the independent variable.

35. Constructing Bivariate Tables • Divide cases into groups according to the attributes of the independent variable. • Describe each subgroup in terms of attributes of the dependent variable. • Read the table by comparing independent variable subgroups in terms of an attribute of the dependent variable.

36. Construct a contingency Table • 150 Fathers favor year-round schools and 50 oppose it; 100 Mothers favor year-round schools and 300 oppose it

37. So what’s the deal on significance? • Statistical significance = unlikeliness that relationships observed are due to chance • Significance level= .05 (based on probability) • Type I Error • Type II Error **The key is how meaningful the results are- not necessarily if statistically significant.

38. Tests of Associations • Chi-square (nominal, ordinal data) • Expected vs. observed • Phi (2x2) • Cramer’s V (larger tables) • Correlations (Pearson, Spearman) • Depends on level, sample size • +1 and –1 (perfect correlations) 0= none • Used to determine reliability • Correlation does not equal to causation • Gives p value but the corr statistic more useful

39. Tests of Difference (Parametric) • Parametric- compares means • Non-parametric- compares ranks (median based) • T-test (grouped data with 2 values) • Indep usually nominal/ordinal & dep usually interval/ratio • Indep t-test (2 groups) • matched pairs t-test (same group at 2 times) • Reports as a t statistic (check Lavene’s) • Check means to determine differences

40. Tests of difference… con’t • Analysis of variance (2+ groups on indep with nominal/ord and int/ratio dep) • Post hoc to determine which groups differ • F statistic (like the t statistic) • Check for meaningfulness

41. Test of Difference (non-parametric) • Mann-Whitney U test (like indep t-test) • Sign test (like matched t-test) • Wilcoxin Signed Ranks test- like t-test when dependent has more than 2 ranked values • Kruskal-Wallis (like oneway) • Friedman Analysis of variance (repeated measures)

42. Multivariate Analysis • Analysis of more than two variables simultaneously. • Can be used to understand the relationship between two variables more fully.

43. Things to remember about stats… • Pay attention to levels of your data • Identify independent and dependent variables • Know when to choose parametrics/ non-parametrics and the appropriate test • P< .05 • Check for meaningfulness • Sometimes not finding significance is more important

44. Quantitative Analysis • Univariate - simplest form,describe a case in terms of a single variable. • Bivariate - subgroup comparisons, describe a case in terms of two variables simultaneously. • Multivariate - analysis of two or more variables simultaneously.