Descriptive Statistics
Descriptive statistics are statistics that describe a variable’s central tendency (the ‘middle’ or expected value) and dispersion (the distribution of the variable’s responses). Be aware that SPSS will calculate statistics even if the measure of central tendency and dispersion are not appropriate. What do I mean by inappropriate descriptive statistics? The General Social Survey includes two attributes for the variable SEX: male or female. (Whether or not this is exhaustive is another discussion). Assume you have 25 people in your dataset: 15 have identified as male and 10 people have identified as female. Although you could add up all of the 1s (males) and 2s (females) and then divide by 25, the average, 1.4, makes no sense.
Central Tendency
The mean is a statistical average (the summation of all data values divided by the number of data). The median is the datum that is in the middle of the data when it is rank-ordered (from lowest to highest). The mode is the value that occurs most frequently. Here are the central tendencies that are appropriate for different levels of measurement:
Nominal: Mode
Ordinal: Median, Mode
Scale*: Mean, Median, Mode
*SPSS uses the term “Scale” for Interval and Ratio levels of measurement.
Dispersion
In addition to knowing the “center” of your data, you will also want to know its dispersion (how far it is spread out around your “center”). You can examine dispersion by using the following:
Nominal: None
Ordinal: Range, Interquartile Range
Scale*: Range, Interquartile Range, Variance, Standard Deviation
Nominal Variables
To obtain descriptive statistics for nominal variables, click Analyze, Descriptive Statistics, Frequencies. Move the nominal variables that you want to examine into the Variables box. Then click on the Statistics button. Check the following boxes:
Click Continue, OK. Here is the output for the variable “sex” from the 2008 GSS data set:
The second box above is called a “frequency distribution.” The frequency is the number of responses for each attribute (or category) of the variable. The percent is the attribute’s percentage of the total N. The valid percent adjusts for missing data. As you can see from the Statistics box, there are no missing data for this variable, therefore the percent and valid percent are the same.
Ordinal Variables
Ordinal variables are those variables that are ranked. One of the more common forms of ordinal variables are Likert scale responses. The variable “Happy” in the General Social Survey is one of these types of variables.
The process of obtaining descriptive statistics is very similar to the process for nominal variables: click Analyze, Descriptive Statistics, Frequencies. Move the ordinal variables that you want to examine into the Variables box. Then click on the Statistics button. Here is the difference from nominal variables. In contrast to what you do for nominal variables, you may choose the median, range, and interquartile range as additional statistics for ordinal variables. If you use all of these statistics, your statistics box will look like this:
Here is an the output for the variable “happy” from the 2008 GSS data set:
Notice that there were 1495 valid responses and 5 missing cases for this variable. S, the percent and valid percent in the frequency distribution differ slightly from one another.
Continuous Variables (called “Scale” by SPSS)
To obtain descriptive statistics from continuous variables, click Analyze, Descriptive Statistics, Descriptives. Move your variables into the Variable box. Click Options and make the following selections:
Click Continue, OK.
For the variable “age” in the 2008 GSS data set, your output will look like this:
There were 1491 respondents who gave their age in this survey, the youngest is 18 years old and the oldest is 89. The mean age is 47.57 and the standard deviation is 17.406.
HINT: Make sure that you always check your statistics when you change your variable. SPSS will not make the change for you!!
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SPSS eTutor by Dee Britton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
