Truth, damned truth and statistics

Over the weekend I had the opportunity occasionally to be flummoxed by maths puzzles set to a teenager.



However, enough of my brain cells have survived the rigours of decades of trade union activity that I still have a rough comprehension of statistics.



Those of us who are dealing daily with the disproportionate impact of Coalition spending cuts on disadvantaged groups certainly need such comprehension.



Let me illustrate with a maths puzzle of my own for you;



A section of the workforce of an employer consists of 70% BME (black and minority ethnic) employees and 30% white employees.



Restructuring proposals put 73% of the BME staff and 45% of the white staff at risk of redundancy.



The employer answers concerns about this disproportionate impact (which, given the numbers involved, is found to be "extremely statistically significant" using Fisher's Exact Test) as follows;



"the proportion of BME staff who may be at risk is broadly comparable with the proportion of BME staff in [that part of the organisation]".



Does this answer from the employer demonstrate;



(A) a misleading comparison between the proportion of a sub group in an overall population with the proportion of that sub group having a particular additional characteristic;



(B) a lack of comprehension of the meaning of an "extremely statistically significant" relationship between two characteristics;



(C) an inexpert attempt to downplay evidence of a potentially racially discriminatory outcome if the proposals proceed as planned, or;



(D) all of the above?



The first correct answer in the comments below will win an, as yet unannounced, prize.

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