Exercise 6
To demonstrate that the point at which one transforms scores makes a difference, try the following:
Methodology A
Calculate mean z-scores for autonomy, by country, using appropriate weighting. Then transform the country means produced using the equations shown above (do the last in Excel).
- Weight data by design weight.
- Find the mean, minimum and maximum values of each country on the autonomy variable.
- Copy the table from the output and paste it into an Excel sheet.
- Compute each country’ transformed score:
Methodology B
Next use SPSS to compute transformed autonomy scores for each individual (using the same formula). Then produce a mean transformed score for each country, using appropriate weighting.
How different are the two sets of scores?
Solution and SPSS syntax
The scores we calculated are shown here, in rank orders:
| Country | Transformed scores |
|---|---|
| DK | 5.93 |
| AT | 5.71 |
| NO | 5.61 |
| NL | 5.57 |
| FI | 5.54 |
| IE | 5.34 |
| CH | 5.33 |
| BE | 5.24 |
| SE | 5.21 |
| SI | 5.08 |
| GB | 5.07 |
| ES | 5.03 |
| EE | 4.98 |
| FR | 4.93 |
| HU | 4.92 |
| BG | 4.91 |
| DE | 4.90 |
| SK | 4.90 |
| CY | 4.86 |
| PL | 4.84 |
| PT | 4.73 |
| UA | 4.52 |
| Country | Transformed scores |
|---|---|
| DK | 6.13 |
| AT | 5.91 |
| NO | 5.79 |
| FI | 5.75 |
| NL | 5.74 |
| IE | 5.50 |
| CH | 5.49 |
| BE | 5.44 |
| SE | 5.38 |
| GB | 5.26 |
| SI | 5.25 |
| ES | 5.22 |
| FR | 5.16 |
| EE | 5.14 |
| BG | 5.14 |
| HU | 5.12 |
| DE | 5.09 |
| SK | 5.06 |
| CY | 5.04 |
| PL | 5.00 |
| PT | 4.91 |
| UA | 4.71 |
As you can see, the rank orders are almost the same, but there are quite big differences in the actual scores. If you have problems replicating these, check out the SPSS syntax for methodology A and methodology B. The ‘min’ score was -2.5690 and the max score was 1.5155 (both to four decimal places).
* methodology A.
* methodology B.