Page 407 - Special Topic Session (STS) - Volume 4

STS2320 Mohamed A I.
to the small sample size (134 countries), but those variables with severe
skewness and/or severe kurtosis required statistical treatment before they
could be employed, see Groeneveld, R.A., and G. Meeden (1984). Variables
with one to five outliers were winsorized, whereby those values considered
outliers were assigned the next highest value until the skewness and kurtosis
were brought into acceptable ranges. However, five variables with more than
five outliers required additional calculation and were treated using logarithm
and the square root transformations, see Cornell University et al. (2017).
The value of a variable was considered an outlier if its instance fell outside the
range of the specific data fence defined as follows:

Lower bound = first quartile – 1.5 X interquartile range
Upper bound = third quartile + 1.5 X interquartile range

Outliers were treated by replacing each outlier with the second highest value
in the case of high values, or the second lowest value in the case of low values.

Normalization
The rescaling or ‘maximum–minimum’ method was used for normalization.
The values of variables were normalized into the 0–100 range, in which higher
values indicated better results. The normalization criterion depends on
whether the variable is good (has a positive relation with the overall Index) or
bad (has a negative relation with the overall Index). The good variables were
normalised using the following formula:

Normalized value = − × 100
−

In the case of bad variables (i.e. those with an inverse relation) the formula was
adjusted to:

Normalized value = − × 100
−

For survey data or composite indices, the original series’ range of values was
retained in the form of minimum and maximum values; for instance, in the
case of the 1–7 range for the World Economic Forum Executive Opinion Survey
variables.

Index weighting
It should be noted that weighting across the index components (indices,
pillars and sub-pillars) was not unified, and varied according to the nature of
the components and their relative importance. Weightings identified for the
seven constituent indices range from equal weighting and budget allocation

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