What does this mean? Simply that just because there is a positive trend between two variables, it does not imply that one causes the other.
Lisa Simpson put it best here (At 4:14)
In case you don't feel like watching The Simpsons (there must be something wrong with you), a transcript of the scene is below.
Later, a full-force Bear Patrol is on watch. Homer watches proudly.
Homer: Not a bear in sight. The Bear Patrol must be working like a
Lisa: That's spacious reasoning, Dad.
Homer: Thank you, dear.
Lisa: By your logic I could claim that this rock keeps tigers away.
Homer: Oh, how does it work?
Lisa: It doesn't work.
Lisa: It's just a stupid rock.
Lisa: But I don't see any tigers around, do you?
[Homer thinks of this, then pulls out some money]
Homer: Lisa, I want to buy your rock.
[Lisa refuses at first, then takes the exchange]
What one must do to simply dispel this argument, is see how likely the situation is anyway. Using Lisa's example, the chance of a tiger being present on Evergreen tce is quite small, thus, more likely than not, there would not be a tiger present with or without the use of the magic rock.
Of course in this case, it is simple to see the rock has no effect because of the very absurdity of the proposition.
However sometimes it is not so simple to see the logical fallacies, especially if they are covered up with a mirage of scientific sounding (although unsubstantiated) claims.
Homeopathy, reflexology, and almost all forms of "alternative medicine" succumb to this fallacy. Even the hypothesis of 'global warming caused by human actions', has arguments made in its favor that are completely based on logic which follows that a correlation equals causation.
With homeopathy, reflexology etc, there are other factors at work (such as the placebo effect) that yield positive results. This would show a correlation between the alternative therapy and patient outcome, but not indicate that it is the actual therapy which is leading to the positive trend. An explanation for the positive trend would be that patients think that is is going to work, and because of the placebo effect, the patients think that they are healing, and thus report positive results.
The way to prove if a treatment is legitimate is to examine scientifically, the theory behind the mechanism that the therapy is based on. For example, in homeopathy, that water has a memory, and this memory can be used to turn water into medicine. This claim has to be examined scientifically to prove or disprove the theory.
For the record, homeopathy is bullshit. There have been no robust scientific studies ever conducted ever that show homeopathy to have any legitimate scientific basis.
However, other studies have been conducted that show people (on average) treated with homeopathic remedies have more positive outcomes than those not treated at all.
This is why people are tricked. The above claim seems to show that homeopathy works, but it does not show this.
When the same studies are conducted comparing homeopathic remedies to placebos (in a blind test, where the subjects do not know if they are receiving the homeopathic remedy or the placebo), there is no difference (on average) between the two groups.
So remember, when you see an explanation for something, stop and think. Is this a legitimate explanation, or am I just being shown a trend, and being told that because they correlate, one is causing the other.