Assuming the correctness of this explanation, it would follow that _any change in the average is due to some change in the producing conditions_; and this derivative law is applied as a help in the observation and explanation of social facts. Statistics are collected and classified: averages are struck: and changes in the average are referred to changes in the concomitant conditions.
With the help of this law, we may make a near approach to the precision of the Method of Difference. A multitude of unknown or unmeasured agents may be at work on a situation, but we may accept the average as the result of their joint operation. If then a new agency is introduced or one of the known agents is changed in degree, and this is at once followed by a change in the average, we may with fair probability refer the change in the result to the change in the antecedents.
The difficulty is to find a situation where only one antecedent has been changed before the appearance of the effect. This difficulty may be diminished in practice by eliminating changes that we have reason to know could not have affected the circumstances in question. Suppose, for example, our question is whether the Education Act of 1872 had an influence in the decrease of juvenile crime. Such a decrease took place _post hoc_; was it _propter hoc_? We may at once eliminate or put out of account the abolition of Purchase in the Army or the extension of the Franchise as not having possibly exercised any influence on juvenile crime. But with all such eliminations, there may still remain other possible influences, such as an improvement in the organisation of the Police, or an expansion or contraction in employment. "Can you tell me in the face of chronology," a leading statesman once asked, "that the Crimes Act of 1887 did not diminish disorder in Ireland?" But chronological sequence alone is not a proof of causation as long as there are other contemporaneous changes of condition that may also have been influential.
The great source of fallacy is our proneness to eliminate or isolate in accordance with our prejudices. This has led to the gibe that anything can be proved by statistics. Undoubtedly statistics may be made to prove anything if you have a sufficiently low standard of proof and ignore the facts that make against your conclusion. But averages and variations in them are instructive enough if handled with due caution. The remedy for rash conclusions from statistics is not no statistics, but more of them and a sound knowledge of the conditions of reasonable proof.