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III. DESCRIBING A SINGLE VARIABLE: Univariate Analysis

OCTOBER 8:
FREQUENCY DISTRIBUTIONS 

SPSS Guide, Ch. 2: "Using Frequencies to Obtain Detailed Data Descriptions," only pp. 15-21.

You should know the nature of your data before trying to analyze them. The most elementary method for summarizing data is to construct a distribution of the frequency of occurrence for every value in a set of observations. Frequencies is the SPSS procedure for constructing such a distribution.  Your reading in the SPSS Guide describes this procedure, but it uses data from world95, a data file contained on your SPSS 10 CD and one that should be stored in the same folder with your SPSS program.

If you wish, you can open world95 and follow the Examples in the SPSS Guide, reproducing the results displayed in the book. That's a good way to learn, but it doesn't stretch you enough. In general, I will assign tasks that employ different data sets than those in the SPSS Guide, presuming that you'll learn more if you have to figure out what to do yourself.

Assignment: Enter SPSS, call up the states2000 file, go to the Analyze Menu, choose Descriptive Statistics, then click on Frequencies. Then create frequency distributions and graphs for each of these variables in that file: division, Bush2000, and Presvote.

Interpret the results. In light of the early lecture and readings on measurment, what kinds of variables are division, Bush2000, and Presvote?


OCTOBER 9:
MEASURES OF CENTRAL TENDENCY

SPSS Guide, Ch. 2: "Using Frequencies to Obtain Detailed Data Descriptions," only pp. 21-23.

Frequency distributions are informative but clumsy. The essential information in frequency distributions can often be summarized with two types of statistics: (1) measures of central tendency and (2) measures of dispersion or variation. Each type of statistic tells something about the nature of the full distribution. We begin with the simpler summary statistics: measures of central tendency.

Assignment: Call up the states2000 file and run Frequencies to obtain the Mean, Median, and Mode for these variables: pctwomen, pctblack, and these variables for voting in the 2000 election: bush2000, gore00, and nader00.

Because these three variables are all continuous, you will not want to print the frequency counts, so remove the check next to "Display Frequency Tables" box in the Frequencies dialog box, and in the "Statistics" dialog box, check Mean, Median, and Mode in the area titled, "Central Tendency."

Study the output and be sure you understand what you have computed, that is, understand the differences among the mean, median, and mode as measures of central tendency. For example, why do the data show that Bush won a higher percentage of the states' votes than Gore?


OCTOBER 11:
MEASURES OF DISPERSION

SPSS Guide, Ch. 2: "Using Frequencies to Obtain Detailed Data Descriptions," only pp. 23-28..

Variability in observations lies at the heart of statistical analysis and social analysis. Most research seeks to understand why some person, group, or nation differs on some variable from other persons, groups, or nations. Indeed, if the cases did not differ, then we would not be observing a variable. Fundamental to variability in statistical analysis is the concept of variance. Be certain you know it well-- along with the related concept, standard deviation. This is definitely knowledge to be tested on examinations.

Assignment: Rerun Frequencies for the same variables as yesterday, but this time check these under the "Disperson" area of the "Statistics" dialog box: std. deviation, variance, range, minimum, and maximum. Also ask for "skewness" and "kurtosis" in the "Distribution" area. Also, go to the "Chart" menu and select "Histograms" and "With normal curve." Which variable--pctwomen, pctblack, and bush2000--is closest to a normal distribution?

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