SPSS Exercise and Assignment 3
As we discussed in class, standardized z-scores convert any original units of measurement, e.g., weights, heights, minutes, pounds, etc., into a standard measurement with the mean being 0 and standard deviation being 1. A standardized score, z-score, tells us how many standard deviation units a case is above or below the mean. If a case’s standard score is 0, the value for that case is equal to the mean. If the standard score is 1, the value for the case is one standard deviation above the mean. If the standard score is
–1, the value for the case is one standard deviation below the mean.
z-score is also the statistics we need to calculate for locating the probability under the normal curve. If z = 1.69, p = .4545, found by consulting the z-table (illustrated below).
Finding z-scores
We can use the Descriptive Statistics procedure in SPSS to obtain standardized z scores for each case in the dataset and save them as a new variable.
Practice Problem
The following dataset records 68 tourists’ daily spending in a destination city (Note: this dataset is positively skewed. We use this set for demonstration purpose). Find standard z-score for each case.
$140 86 139 161 175 82 125 149 135 127 265 235 132 172 149 168 212 105 220 126 90 171 162 229 121 114 149 126 129 118 172 156 216 87 172 230 162 195 128 126 142 118 127 126 108 102 95 90 88 94 103 114 98 82 105 97 123 116 93 178 194 225 78 70 62 59 54 49
1. Enter data in Data View
2. Name the variable spending
3. Keep 2 decimal points
4. Label the variable Tourist Daily Spending ($) in Variable View
5. Click Analyze
6. Click Descriptive Statistics
7. Click Descriptives … Descriptives dialog box comes up.
8. Move the Tourism Daily Spending ($) to the Variable[s]: text box
9. Select Save standardized values as variables at the bottom of the dialog box
10. You can select some summary statistics by clicking the Options … menu
11. Select Mean, Std. deviation, Maximum and Minimum. Click Continue.
12. Click OK
A summary table is generated as follows:
13. Switch back to Data View. You will see that a new variable, the standard score for spending, has been created, and the new variable, zspendin (the standardized scores), has been saved in the Data Editor (see partial screenshot below).
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