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Lecture

# Quantitative data analysis

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Western University

Sociology

Sociology 2206A/B

Georgios Fthenos

Winter

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Quantitative DataAnalysis
Lecture #7
March 11, 2014
The big mistake in quantitative research is to think that data analysis
decisions can wait until after the data has been collected
o Must be fully aware of what analysis techniques will be used before the
data collection begins
o Questionnaire, observation schedule, and coding frame should be
designed/ thought about with the data analysis in mind
o The statistical techniques that can be used depend on how a variable is
measured
o Inappropriate measurement may make it impossible to conduct certain
types of data analysis
o The size and nature of the sample also imposes limitations on the kinds of
techniques that are suitable for the data set; hard to interview 1000 people
unless you have a lot of time
**Types of variables**
Nominal/ dichotomous: the only difference that exists between participants is
being in one category or another; no rank order of categories
o No arithmetic or mathematical operations with the categories
o I.e.: gender: categories ‘male and ‘female’; male doesn’t come before,
female doesn’t come before (no rank order). Sexual orientation (gay,
straight), relationship status (single, married), race/ethnicity, occupation,
religion.
Ordinal: The categories of the variable can be rank ordered
o E.g., high enthusiasm; moderate, low (Likert scale)
o Agree, neutral, disagree
o Distance or amount of difference between categories may not be equal
o Cannot be arithmetic or mathematical operations with the categories;
cannot find mean or standard deviation. Can find mode or median
Interval/ ratio: Distance or amount of difference between categories is uniform;
there is intervals
o I.e., 0 siblings, 1 sibling, 2 siblings, 3 siblings
o Can do arithmetic and mathematical operations with the categories;
can find mean and standard deviation. (I.e., 1 sibling + 3 siblings =4
siblings)
o Ratio variables have a ‘0’starting position
o Interval variables DO NOT have a ‘0’starting position
o i.e., Income, hours of TV watched, hours you work per week, age
o ** Distances must be uniform throughout each interval, or it becomes
ordinal** figure 13.1 UnivariateAnalysis
Analysis of one variable at a time
The first step is often to create frequency tables for the variables of interest
o Frequency table show the number of times a particular variable shows up
in the population, expressed as an actual number and as a percent of the
whole population.
E.g., 36% of participants…(made more than $50,000)
When interval/ratio categories are shown in frequency tables, some of the
categories may be combined as long as they don’t overlap
(E.g., age groups of 20-29, 30-39, …)
Combining categories makes the data more manageable and easier to comprehend
Diagrams can be used to illustrate frequency distributions
Use bar charts and pie charts for displaying a nominal or ordinal variable
Use histograms for an interval/ratio variable
Measures of central tendency
An average or typical score for the group
I want to calculate mean, median, or mode because..
Mode: the score that shows up the most in a particular category
o Can be used with all variable types
o Most applicable to nominal data; are most people in a certain religion?
Median: the middle score when all scores have been arrayed in order (if even
number of scores it is the mean of the two middle scores)
o Can be used with ordinal or interval/ratio data. Cannot rank nominal
variables because there is no ‘middle’
Mean: sum of all scores, divided by the number of scores
o Can be used with interval/ ratio data
o Vulnerable to outliers (extreme scores); results can be skewed
Measures of dispersion
The amount of variation in a sample
Range: the highest score minus the lowest score
o Shows the influence of an outlier
Standard deviation: Measures the amount of variation around the mean
o I.e., if mean is 10, and sd is 5; 5-10, 10-15
o Influenced by outliers
Bivariate analysis Determines whether there is a relationship between two variables
Note; determination of a relationship DOES NOT prove causality
Contingency tables/ two way tables (cross-tabulations); SPSS
o Allows simultaneous analysis of two variables
o Identify patterns of association
o Can be used for any variable type
o Normally used for nominal or ordinal data
Pearson’s r: normally used with interval/ ratio data’quantitative data
o Values from 0 (indicate no relationship)
o To +1 (indicates perfect positive relationship)
o Or -1 (indicates perfect negative relationship)
o The relationships between the variables should be relatively linear if
Pearson’s r is to be used in a study
o .7; relatively strong
o Can be established using a scatter plot
o Figures 13.6-13.9
Kendall’s tau-b: shows correlation between pairs of ordinal variables. Or with
one ordinal and one interval/ ratio variables
o Like Pearson’s r, values range from 0- +/- 1
Spearman’s rho: shows correlation between pairs of ordinal variables
o Like Pearson’s r, values range from 0- +/-1
Cramer’s V:

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