1. SPSS Session 1: Levels of Measurement and Frequency Distributions

2. Learning Objectives Measurement of data Levels of measurement
Measures of Central Tendency
Measures of Dispersion

3. Review from Lecture 7
Identified and defined levels of measurement and measures of central tendency
Described situations in which different levels of measurement and measures of central tendency were useful and appropriate
Calculated frequency, percentage, range, measures of central tendency
Critiqued and justified their use for the exercise problems

4. Levels of Measurement
The level of measurement used in collecting data determines the statistical techniques which can be used in analysis.
Levels of measurement:
Nominal
Ordinal
Interval/Ratio

5. Nominal Level Measurement
Classifying items into groups
No implied value of the groups as in a hierarchy or quantitative value
In the dataset from our child protection study, nominal variables include
Gender of the respondent and child
male or female
General Health Questionnaire elevated scores
Subclinical score or clinically elevated score

6. Ordinal Level Measurement
Classifying values of a variable in an order
Quantitatively ordered items with an implied qualitative order
An example is a Likert scale question with possible responses:
1. Never, 2. Sometimes, 3. Occasionally, 4. Often, 5. Always
An example in our child protection study of an ordinal variable:
Previous_Involvement - Have Social Services been involved with this child/ family previously?
1. Yes – Long standing involvement
2. Yes – Occasional involvement
3. No – No previous involvement

7. Interval/Ratio Level Measurement
Interval/Ratio level variables have equal units between variables and offer a range of possible values in that variable
Age, time, and weight are examples
Examples in our child protection study of interval/ratio variables are:
GHQ-12 total score
FES scores
WAI scores
Age of child
Other total scores from standardized measures

8. Frequency Distributions and SPSS

9. Frequency Distributions
A distribution provides a summary of how the data exists on a range of possible or actual scores.
A frequency distribution combines all of the like values of a variable and graphical groups them.
Which is to say how many times a value was recorded in a variable
Charts such as a histogram provide a visual display of a frequency distribution where the frequencies of similar values in a variable are grouped

10. Frequency Distributions
In our child protection study:
Gender of the child
Age of the child
Previous involvement with social services
Gender of the child is a nominal variable
Previous Involvement with social services is an ordinal variable
Age of the child is an interval/ratio variable
Use the Analyze Menu in SPSS to find “Frequencies”

12. Select the variables from the list on the left and place in the “Variable(s)” list on the right.

13. Click on “Statistics” and select “Mean”, “Median”, “Mode”, “Standard Deviation”, “Minimum”, and “Maximum”
Click “Continue”

14. Click on “Charts”, and select “Histograms” with “Show normal curve on histogram”
Click “Continue”

15. Frequency Distributions
Click “OK” for the Frequency Distributions and the descriptive statistics for these three variables.
The results will appear in a new Output window

16. In the first table, the descriptive statistics for the three variables are displayed.

17. Frequency Tables and Histograms
The next three slides give the Frequency Table and Histogram for each of the three variables we selected.
When comparing the tables to the histograms, look to see how similar values are combined and visually displayed in the chart.
Also, compare the distribution in the histogram to the curve of that the distribution would be if the variable were normally distributed.

21. Measures of Central Tendency
Mean – summing all the scores in a dataset and dividing by the total number of scores. Provides an average score.
Median – The middle most score in a list of scores
Mode – The most frequent or common score in a list of scores

22. Measures of Central Tendency
From these results, we can see that the mean of the children in the study was 7.69 years.
Remember that it is inappropriate to take means (averages) of nominal or ordinal variables, thus the Means and Std. Deviation scores for Child Gender and Previous Involvement should be ignored.