Quantitative Data Analysis

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Quantitative Data Analysis

• Social Research Methods 2109 6507
• Spring, 2006
• March 6 2006

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Quantitative Analysis convert data to a
numerical form and statistical analyses

• quantification (??) the process of converting
  data to a numerical format (??????????)

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Quantification of Data

• Develop codes and a codebook
• Coding data (????)
• Data entry (????)
• Data file construction (??????)
• Statistical Analyses

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Quantitative Data Analyses

• Univariate analyses (?????) a single variable
• Distributions, central tendency, dispersion,
  subgroup comparisons
• Bivariate analyses (?????) the analysis of two
  variables
• Multivariate analyses (?????) analyzing more
  than two variables simultaneously

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Univariate Analysis

• Distributions (??)
• Frequency distribution (can use a graph)
• Central tendency (the form of an average) (????)
• The arithmetic mean (?????)
• The mode (the most frequently occurring
  attribute) (??)
• The median (the middle attribute in the ranked
  distribution of observed attributes) (???)

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Univariate Analysis

• Dispersion (??) the way values are distributed
  around some central value (ex an average)
• The simplest measure the range
• Standard deviation an index of the amount of
  variability

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Examples of Dispersion
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Please note some calculations are not suitable
to all variables

• Continuous variables (quantitative variables)
  (????) a variable whose attributes form a steady
  progression
• Ex age
• Discrete variables (qualitative variables)
  (????) a variable whose attributes are separate
  from one another, or discontinuous
• Ex gender
• Nominal or ordinal variables

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Bivariate Analysis

• Explanatory bivariate analyses consider causal
  relationships (???????????)
• Explanatory or Independent Variables vs.
  Response or Dependent Variables

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Measures of association

• The basic idea proportionate reduction of error
  (PRE) (???????)
• If you know the relationship between the two
  variables, you will make fewer errors in guessing
  values of one variable if you know values of the
  other.
• Today focus on correlation (????)

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A Scatterplot (???) display the relationship
between two quantitative variables measured on
the same individuals (???????????)
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Looking at a scatterplot

• Look for direction, form, and strength of the
  relationship
• Direction (??)
• Positive association (???)
• Negative association (???)

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Looking at a scatterplot

• Form (??) what shape or pattern?
• ??? ??? ??? ???
• Strength the points in the scatterplot lie to a
  simple form (a line or a curve?) (??????????????)
  

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Outlier (???) an individual obs. falling outside
the overall pattern of the graph
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The correlation coefficient (r)

• Correlation (r) a measure of the strength and
  direction of the linear relationship between two
  quantitative variables (???????????????)
• r can take on values from -1 to 1

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Facts about correlation

• A positive value of r a positive association
• A negative value of r a negative association
• r closer to 1 or -1 stronger association
• r 0 no association
• r measures the strength of linear association
• r (y, x) r (x, y)
• r sensitive to outliers

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Examples of correlations
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More about correlations

• How big is a correlation?
• No hard and fast rule
• In general abs(r) gt0.7--- strong association
• But in social sciences, r is usually not strong
  in terms of its value (lt 0.7)

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Formula of the correlation coefficient
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To get r in SPSS

• ??(A) ???(C) ????

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Conclusions about correlation

• Scatterplots the first step when considering the
  association between two quantitative variables
• r summarize the strength of linear association
• Distinct (but related) to the slope of the
  regression line