Chapter 14 Quantitative Data Analysis

Quantitative Analysis The technique by which researchers convert data to a numerical form and subject it to statistical analysis. Quantification: The process by which data becomes numerical Example: A computer cannot read the answer “strongly agree” so the researches assigns the numerical value 1…and so forth.

Quantification Continued Most times quantifying is important is with ordinal-level data. Why? Nominal-level data: The numbers you may assign have no particular value. Women=1 and Men=0 doesn’t mean anything statistically. Interval-level data: The numbers are already assigned in the data. Annual income is $50,000, or your age is 27. You’re not going to assign other numbers.

Ordinal Quantification Making sure that you’re properly representing the data by giving it the correct numerical status. We are winning the War in Iraq. 1 = Strongly Disagree 2 = Disagree 3 = Agree 4 = Strongly Disagree

Fool-Proof…certainly not! There can still be flaws. To use the previous example: We are winning the War in Iraq. 1 = Strongly Disagree 2 = Disagree 3 = Agree 4 = Strongly Disagree There may be a bigger difference between 1 and 2, than between 2 and 3, which would jeopardize our analysis of reality.

Where do we find all this? When downloading a dataset, there is often a codebook. The codebook will list all of the questions, all of the answers, and how each of the answers were coded into numerical form.

Baby Steps Univariate Analysis: The analysis of ONE variable for the purpose of description. You are simply trying to “describe” that one variable What is the average, the frequency, the distribution, and so on.

Distribution (or Marginals) A description of the number of times the various attributes of a variable are observed. Religious Attendance 57 never attend 67 attend once/month 83 attend once/week

Central Tendency Mean: The average, done by summing all values and dividing by the number of observations. Median: Represents the value of the “middle” case in a rank-ordering. Mode: Represents the most frequently observed value.

Dispersion The distribution of values around some central value. Can be very important, particularly in the case of “outliers”. Example: 20 observations of $20,000/year (avg. $20,000) 19 observations of $20,000/year AND 1 observation of $200,000/year (avg. $29,000)

Dispersion Range: The distance between the lowest and highest observed value. Standard Deviation: More complex measure in which 68% of observations are 1 standard deviation and 95% of cases are within 2 standard deviations of the average. Lower std. deviation means the data is bunched. Higher means it is more dispersed.

Collapsing Categories Moving responses and observations into more general categories. Done occasionally to counteract high standard deviation. Can be very tricky and should always have justification (theoretical or statistical) Example: Moving “very liberal”, “liberal” and “somewhat liberal” into the same category.

Don’t Knows In all surveys you have a group of people who reply “Don’t Know”. How do they fit into the statistical analysis? When reporting percentages and marginal's you should report them, but it gets much more complicated in terms of average and standard deviation.

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

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.

Multivariate Analysis Analysis of more than two variables simultaneously.

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

Ethics and Quantitative Data Analysis There is always the danger of defining and measuring variables in ways that encourage one finding over another. Quantitative analysts must guard against this. The quantitative analyst has an obligation to report both formal hypotheses and informal expectations that didn’t pan out.