Narrative · Common cause
Ice cream and drowning
Ice-cream sales and drownings rise and fall together. Is the one causally relevant to the other? As long as the weather is not recorded, the table contains cases that agree in all recorded factors and differ in the effect.
Chapter 1
Two curves that rise together
In months in which a lot of ice cream is sold, more people drown. The connection can be found in many statistics, and it is real: the two quantities rise and fall together.
IC ice-cream sales high · DR drowning frequent.
No one believes that ice cream causes drowning. But what exactly distinguishes this connection from a causal one? The hypothesis “IC is causally relevant to DR” is drawn in the diagram as an arrow. The following chapters test it against a table of cases.
Chapter 2
The table contradicts itself
The table records six cases. In cases 1 and 2 ice-cream sales are high and drowning is frequent; in case 6 ice-cream sales are just as high, but drowning is not frequent (Vol. III, §7.2).
Two cases that agree in all recorded factors and differ in the effect form a contradictory configuration.
The same holds for cases 3, 4 and 5: the same ice-cream sales, a different effect. The table contains two contradictory configurations (Vol. III, §7.2).
A contradictory configuration shows that an unrecorded circumstance was at work in the one case and not in the other. The field of cases is not homogeneous for this factor set. The theory then pronounces no causal verdict. It requires the set of recorded factors to be extended.
Chapter 3
The weather
If the weather is included, the contradictions disappear. In all six cases drowning is frequent exactly when the weather is hot. Whether a lot of ice cream is sold as well makes no difference to this: case 5 has hot weather and little ice cream, case 6 cool weather and a lot of ice cream (Vol. III, §7.2).
HW hot weather.
Volume III extends the factor set by two further factors: whether the sales stands are open and whether the weather invites bathing. The minimal theory of drowning is then:
For ice-cream sales, hot weather with open stands, HW * VO, is a cluster. It is not the only one: in case 6 a lot of ice cream is sold on a cool day. The further cluster is not recorded in the survey (Vol. III, §7.2).
VO sales stands open · SW bathing weather.
Chapter 4
No arrow between the effects
Ice-cream sales occur in no cluster of a minimal theory of drowning. They are therefore not causally relevant to drowning. The hypothesis of the first chapter falls.
This does not deny the correlation. Hot weather is part of a cluster of ice-cream sales and of the cluster of drowning; where it is present together with open stands and bathing weather, both effects occur. The connection between the effects arises without a causal connection between them. It is the pattern of the Manchester hooters, only with other names: two effects of a common cause.