Chapter 15: Quantative data analysis
Numerical representation and manipulation of observations for the purpose of
describing and explaining the phenomena that those observations reflect
Quantitative data analysis is almost always constructed using computer software
You have to codify your data in a numerical form so the program could read them
You don’t need to codify income or weight for instance since they would be in
Numerical representation can be assigned to any number of variables,
Example: gender, for male and female, you change value to “1” and “2” for instance
Elementary Quantitative Analysis
The analysis of a single variable, for purpose of description. Frequency distributions,
averages, and measures of dispersion would be examples of univariate analysis, as
distinguished from bivariate and multivariate analysis which are more explanatory.
Focuses on describing units of analysis.
Most basic format for presenting univariate data is a one-way distribution
This is often laid out in a table that records the number of cases observed for each of
the attributes of some variable
Example: Check table 15-1 p.416 because I can’t actually summarize the example.
Frequency distribution: a description of the number of times the various attributes of
a variable are observed in a sample.
Example: The report that 53% of a sample were men and 47% were women; or that
20.4% of people attend religious services and 12.1% and so forth in a sample...
It’s sometimes easier to see a frequency distribution in a graph, so check figure 15-2
You can present you data in the form of average (in mean, mode or median form)
instead of simply reporting the overall distribution of values that are often referred as
“marginal frequencies” or “marginals”. So you reduce the raw data into a more
Average: an ambiguous term generally suggesting typical or normal; it’s a central
tendency. The mean, median, and mode are specific examples of mathematical averages. Mean: An average computed by summing the values of several observations and
dividing by the number of observations.
Example: Let’s say you have A in Sociological Inquiry, B in History and B in English.
To calculate the mean, you convert the letter grades into their numerical representations
and divide the values by the total of cases. So (4.0 + 3.0+3.0)/3=3.33 and so your GPA
(or mean) is B+
Mode: An average representing the most frequently observed value of an attribute
Example: If a sample contains 1000 Protestants, 275 Catholics, and 33 Jews, Protestant
is the modal category since it’s the category with the most people in it
Median: An average representing the value of the “middle” case in a rank-ordered set
Example: If the ages of five men were 16, 17, 20, 54, 88, the median would be 20
For the median, when the total number of subjects is an even number, there is no
middle case, so you calculate the mean of the two values on either side of the midpoint of
the ranked data
Example: 16, 17, 20, 54, 88, 90 (20+54)/2=37. So the median is 37
For a visual example of mean, mode, and median also check figure 15-3 page 419. The
example involves teenagers as subjects, their age ranges from 13 to 19. We want to
calculate the average. The easiest way is to calculate the mode, which is 16. We can also
choose to calculate the mean by multiplying each age by the number of subjects who
have that age, total the results of all those multiplications, and divide that total by the
number of subjects. We can also choose to find the median by checking the middle value
where half the values are above it and half the values are below it.
The three measures of central tendencies often produce slightly different values
Which measure of central tendency you choose depends on the nature of your data and
the goal of your analysis, so it’s important to be familiar with the distribution of your data
Example: You want to check the average family wealth in a community where few
families have great wealth: $100 000, $100 000, $109 000, $114 000 and
$30 000 000 (Paris Hilton’s forgotten mansion). IT IS MISLEADING IF YOU
CALCULATE THE MEAN since it would NOT represent the average wealth of the the