Chapter 14: Quantitative Data Analysis

'Collapsing' Response Categories

If a table had a few too many numbers for an interpretations, try 'collapsing' response categories by combining for instance 'probably and definitely'

Quantitative analysis

The numerical representation and manipulation of observations for the purpose of describing and explaining the phenomena that those observations reflect.

Quantification

The process of converting data to a numerical format.

Standard deviation

-A more sophisticated measure of dispersion. -A measure of dispersion around the mean, calculated so that approximately 68% of the cases will lie within plus or minus one standard deviation from the mean, 95% will lie within plus or minus two standard deviations from the mean, and 99.9% will lie within three standard deviations. Thus, for example, if the mean age of a group is 30 and the standard deviation is 10, then 68% have ages between 20 and 40. The smaller the standard deviation, the more tightly the values are clustered around the mean; if the standard deviation is high, the values are widely spread out.

Elements of a codebook

-Each variable is identified by an abbreviate variable name (Religious services attendance = ATTEND) -Full definition of the variable (In a questionnaire, the definition consists of the exact wordings of the questions asked) -Indicates the attributes composing each variable ('extremely liberal', 'liberal', 'slightly liberal', etc...) -Each attribute has a numerical label (Extremely liberal= Category 1)

Univariate Analysis

-The simplest form of quantitative analysis. -Describes a case in terms of a single variable (specifically the distribution of attributes that it comprises) The analysis of a single variable (specifically the distribution of attributes that it comprises), for purposes of description. Frequency distributions, averages and measures of dispersion = examples of univariate analysis, as distinguished from bivariate and multivariate analysis. The most basic format reports all individual cases, that is, to list the attribute for each case under study in terms of the variable in question.

Two functions of codebook

1) Primary guide used in the coding process 2) Guide for locating variables and interpreting codes in your data file during analysis

Frequency distribution

A description of the number of times that the various of attributes of a variable are observed in a sample. A report that 53% of a sample were men and 47% were women = a simple example of a frequency distribution

Machine-readable form

A form that can be read and manipulated by computers and similar machines used in quantitative analysis.

Contingency table

A format for presenting the relationships among variables as percentage distributions. Values of the dependent variable are contingent on (depend on) values of the independent variable. No standardized model.

Discrete variables

A variable whose attributes are separated from one another, or discontinuous, as in the case of gender or religious affiliation. Contrast this with continuous variables, in which one attribute shades off into the next. Thus in age (a continuous variable), the attributes progress slowly from 21 to 22 to 23 and so forth, whereas there is no progression from male to female in the case of gender.

Continuous variable

A variable whose attributes form a steady progressions, such as age or income. Thus, the ages of a group of people might include 21, 22, 23, 24 and so forth and could even be broken down into fractions of years. Contrast this with discrete variables, such as gender or religious affiliation, whose attributes form discontinuous chunks.

Average

An ambiguous term generally suggesting typical or normal- a central tendency. The mean, median and mode are specific examples of mathematical averages.

Central Tendency

Beyond simply reporting the overall distribution of values (sometimes called marginal frequencies or marginal), you may choose to present your data in the form of an average (or measure of central tendency)

Two types of variables: continuous and discrete

Continuous variable (or ratio variable) increases steadily in tiny fractions. Ex. age, which increases steadily with each increment of time. Discrete variable jumps from category to category without intervening steps. Ex. gender, military rank and year in college (you go from being a sophomore to a junior in one step)

Quantification of Data (SPSS)

Data such as 'age, religious affiliation, political party and region of the country' are easy to quantify. However, something like 'occupation' is harder. Using established coding schemes gives you the advantage of being able to compare your research results with those of other studies. You should choose a coding scheme appropriate to the theoretical concepts being examined in your study (eg. for some studies, it's sufficient to code all occupations as either white-collar or blue-collar)

Handling 'Don't Knows'

Look at what percentage of respondents did answer the question. Then divide each subcategory by that 0.? Percentage (0.85). Just report your data with and without don't knows because otherwise they mad.

Bivariate Analysis

The analysis of 2 variables simultaneously, for the purpose of determining the empirical relationship between them. The construction of a simple percentage table or the computation of a simple correlation coefficient are examples of bivariate analysis (eg. subgroup comparisons constitute a kind of bivariate analysis because they involve 2 variables, in contrast to univariate analysis)(however, like univariate analysis, subgroup comparisons are largely descriptive in purpose and focus on describing people or other units of analysis under study while bivariate focuses/determines on the variables and their relationships)

Dispersion

The distribution of values around some central value, such as an average. The simplest measure of dispersion is the range (distance separating the highest from the lowest value). Thus, besides reporting that the mean age of a group is 37.9, we might also indicate that the range is from 12 to 80.

Codebook

The document used in data processing and analysis that tells the location of different data items in a data file. Typically, the codebook identifies the locations of data items and the meaning of codes used to represent different attributes of variables.

Median

The middle attribute in the ranked distribution of observed attributes An average representing the value of the "middle" case in a rank-ordered set of observations. If the ages of five men were 16, 17, 20, 54 and 88, the median would be 20 (and the mean would be 39)

Mode

The most frequently occurring attribute An average representing the most frequently observed value or attribute. (If a sample contains 1,000 Protestants, 275 Catholics and 33 Jews, then Protestants is the modal category)

(Arithmetic) mean

The result of dividing the sum of values by the total number of cases. -One way to measure central tendency or "typical" values -An average computed by summing the values of several observations and dividing by the number of observations

Developing Code Categories

Two approaches: 1. Start with a relatively well-developed coding scheme. 2. Generate codes from your data a. Code categories should be exhaustive and mutually exclusive b. Train (if any) coders- teach them definitions of code categories and show them how to use those categories properly c. Obtain verification of your own reliability as a coder (get someone to code your cases to check)

Bivariate analyses

Unlike univariate analysis that describe the units of analysis, bivariate analysis are primarily aimed at explanation. univariate (description) bivariate (explanation)