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Quantitative data analysis

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Western University
Sociology 2206A/B
Georgios Fthenos

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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