# 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).

1. Weight data by design weight.
2. Find the mean, minimum and maximum values of each country on the autonomy variable.
3. Copy the table from the output and paste it into an Excel sheet.
4. 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:

Table 2.3. Transformation scores, methodology A
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

Table 2.4. Transformation scores, methodology B
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.

WEIGHT BY DWEIGHT.

MEANS TABLES=autonomy BY CNTRY
/CELLS MEAN COUNT STDDEV.

WEIGHT BY COMWEIGHT.

DESCRIPTIVES
VARIABLES= autonomy
/STATISTICS=MIN MAX.

* methodology B.

COMPUTE t_autonomy = 5+(5*autonomy*(1.5155+2.569))/(autonomy*(1.5155-2.569)+2 *1.5155*2.569).
EXECUTE.

WEIGHT BY DWEIGHT.

MEANS TABLES=t_autonomy BY CNTRY
/CELLS MEAN COUNT STDDEV.
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