Once indicators for the index were selected based on the State Just Jobs theoretical framework (see Methodology section), data was normalized and used to construct the composite Index. Equal weights were used for each dimension, and for each indicator within each dimension. To enable comparability of scores across dimensions and indicators, two normalization techniques were used - standardized z-scores and min-max rescale. A set of 2 scores were created for each dimension and indicator--1 score for standardization (z-score) and 1 score for min-max rescale (see Explore the Index page). In addition, sensitivity analysis was conducted to check for robustness and stability of the composite Index, with respect to each indicator.
A. Standardization (z-scores)
Standardization is the process of converting raw data of indicators into a scale with a mean of zero and standard deviation of one. The extreme values i.e. greater than 3 have a greater effect on the Index and hence this method generates outlier behavior. The formula used for the standardization method is given by:
The high refers to an indicator whose preferred value is high (e.g. labor force participation rates, literacy rates); low refers to an indicator whose preferred value is low (e.g. unemployment rates, share of own-account workers); “Equal to a” refers to an indicator whose preferred value is a specific preferred value (e.g. ratio of minimum wages to average wages, ratio of female to male employment rates).
B. Min-Max rescale
This method provides the linear transformation of raw data of an indicator in a given identical range from zero to one. The formula used for the min-max rescale method is given by:
The high refers to an indicator whose preferred value is high (e.g. labor force participation rates, literacy rates); low refers to an indicator whose preferred value is low (e.g. unemployment rates, share of own-account workers); “Equal to a” refers to an indicator whose preferred value is a specific preferred value (e.g. ratio of minimum wages to average wages, ratio of female to male employment rates).
Robustness and Sensitivity Tests
Sensitivity tests are performed to check the robustness of the composite index. The sensitivity test represents how much uncertainty in the index score for a given State is reduced if a particular indicator, or the source of uncertainty, is removed. The sensitivity test explores the effect of deleting each indicator, one at a time, and examining its impact on the relative ranking. The main aim of the sensitivity tests is to measure the relative shift in the position of a State in the ranking by eliminating a given indicator.
The formula used for the sensitivity test is:
In addition, we also use a sensitivity test to explore how the states’ rankings change when one normalization method is used over another.