SPSS Session 1:

Levels of Measurement and Frequency Distributions

Learning Objectives

• Measurement of data• Levels of measurement• Measures of Central Tendency• Measures of Dispersion

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

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

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

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

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

Frequency Distributions and SPSS

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

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”

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

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

• Click on “Charts”, and select “Histograms” with “Show normal curve on histogram”– Click “Continue”

• Click “OK” for the Frequency Distributions and the descriptive statistics for these three variables.

• The results will appear in a new Output window

Frequency Distributions

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

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.

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

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.