Dr David McGrath

Spine Physician

MB BS (Hons) FAFOM, RACP, FAFMM
Master of Pain Medicine

The headlines read "Social Services Fail to Act" implying that given the information, they should have removed children from delinquent parents.
But how fair is that statement ?
The mathematics makes the situation clear.

Social DiagnosisTrue State of Affiars	Children at Risk	Children Not at Risk
Family Dysfunction Diagnosed	a	b
No Family Dysfunction Diagnosed	c	d

In the example, the reporter is focused on cell "c". The reporter did not report the other cells.
No social worker can know with certainty, the relevence of their observations.
If we put in some realistic numbers for social observation, we will understand the dilemma of trying to be correct all of the time.

Cell "a" represents Correct Diagnosis
Cell "b" represents Incorrect Diagnosis
Cell "c" represents Incorrect Diagnosis
Cell "d" represents Correct Diagnosis

Suppose their are 100 families, 80% of which are not dysfunctional. Given a perfect system, we have the following numbers.

Social DiagnosisTrue State of Affiars	Children at Risk	Children Not at Risk
Family Dysfunction Diagnosed	20	0
No Family Dysfunction Diagnosed	0	80

Life is not so easy. More likely the situation would be like this:

Social DiagnosisTrue State of Affiars	Children at Risk	Children Not at Risk
Family Dysfunction Diagnosed	10	10
No Family Dysfunction Diagnosed	10	70

1. We are not likely to identify EVERY family at risk (50%)
2. We are likely to mis-classify normal families as dysfunctional (10 out of 80)

When we try to improve, moving to perfect, as in the first table, we usually, improve the sensitivity of detection, at the expense of specificity. By trying to reduce false negatives, we usually increase false positives. They tend to move in opposite directions. When we relax criteria, we do so for true's and non true's.

Social DiagnosisTrue State of Affiars	Children at Risk	Children Not at Risk
Family Dysfunction Diagnosed	15	20
No Family Dysfunction Diagnosed	5	60

Now we can identify 75% of dysfunctional families, but are still likely to be wrong around 50% of the time,as children not at risk,have been wrongly classified. In an extreme example, we could say all families are at risk, in which case we will intervene on all families, and be right only 20% of the time.
This is the dilemma of explanation. We cannot be right 100% of the time, without having a significant percentage of false positives.
I could state all people have muscle imbalance, and therefore identify all people with this condition, while being wrong most of the time. (a type of true by generalisation)