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As we discussed in class, standardized z-scores convert any original units of measurement

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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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