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Quantitative Data Analysis
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Definitions
Examples of a data set
Creating a data set
Displaying and presenting data – frequency
distributions
• Grouping and recoding
• Visual presentations
• Summary statistics, central tendency, variability
What do we analyze?
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Variable – characteristic that varies
Data – information on variables (values)
Data set – lists variables, cases, values
Qualitative variable – discrete values,
categories.
– Frequencies, percentages, proportions
• Quantitative variable- range of numerical values
– Mean, median, range, standard deviation, etc.
Creating a data set
• Enter into a statistical package (program)
• Program does calculations and displays
results
• Examples: census data
Data on CD (GSS 2004)
http://www.d.umn.edu/~sjanssen/Intro%20to
%20SPSS%20exercise.htm
Creating a data set
• May involve coding and data entry
• Coding = assigning numerical value to
each value of a variable
– Gender: 1= male, 2 = female
– Year in school: 1= freshman, 2= sophomore,
etc.
– May need codes for missing data (no
response, not applicable)
– Large data sets come with codebooks
Displaying and Presenting Data
• Frequency distribution – list of all possible
values of a variable and the # of times
each occurs
– May require grouping into categories
– May include percentages, cumulative
frequencies, cumulative percentages
Displaying and Presenting Data
• Ungrouped frequency distribution
– Usually qualitative variables
• Grouped frequency distribution
– Values are combined (grouped) into
categories
– Use for quantitative variables
– Many separate values
Grouping into categories
• May use meaningful groupings
• May use equal intervals (more common)
– Equal width
– Mutually exclusive
– Exhaustive
• Class interval = category, range of values
• Midpoint = exact middle of interval
• Limits = halfway to next interval
Summary statistics
• Percent = relative frequencies;
standardized units.
• Cumulative frequency or percent =
frequency at or below a given category (at
least ordinal data required)
Visual Presentation of Data
• Bar graph (column chart, histogram): best
with fewer categories
• Pie chart: good for displaying percentages;
easily understood by general audience
• Line graph: good for numerical variables
with many values or for trend data
Summary statistics:
central tendency
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“Where is the center of the distribution?”
Mode = category with highest frequency
Median = middle category or score
Mean = average score
Summary Statistics:
Variability
• “Where are the ends of the distribution?
How are cases distributed around the
middle?”
• Range = difference between highest and
lowest scores
• Standard deviation = measure of
variability; involves deviations of scores
from mean; most scores fall within one
standard deviation above or below mean.