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

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**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**• 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”**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**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.