Saucers of Mud

I wanted to post about the Rain Probability Gauge from Science Made Stupid by Tom Weller (out of print, hosted with Weller’s permission at https://drive.google.com/file/d/0B241HCXaGuT8TzZhYXNJS25EWEk/view?resourcekey=0-G5WyeyFZRFpq0CFMEkHiLQ), but the text is too long for me to alt-text on Twitter, so here it is in what I hope is accessible form!

Testing Rain for Probability

You’ve probably heard the weatherman predict a “30% chance” or a “70% probability” of rain. You can check the chance of rain having fallen for yourself with a back-yard rain probability gauge.

Let’s say it rained during the night. What were the chances of that rain occurring?

1. Check the gauge—which is marked in inches just like a regular rain gauge—for the level of rainwater, and mark it down. This represents the level of actual rainfall (which will always be the same as the level of probable rainfall.)

2. Next, check the level of nonprobable rainfall (which you can also think of as probable nonrainfall). Since nonprobable rain is lighter than probable rain, the nonrain will float on top of the rainwater.

Probabilites, of course, are invisible. To render them measurable, the rain probability gauge contains a probability float to mark the level of nonprobable rain. A probability float can be made of any material less probably than rain, and hence lighter. Except in very dry parts of the world, this presents no problem; an entry stub from the Publishers Clearing House Sweepstakes will do nicely. Alternatively, a few drops of statisticians’ ink can be added to the column to make it visible.

3. To the two levels, apply the formula actual rain divided by total probable & nonprobable rain = % chance

In the illustration, 3 inches of rain divided by 10 inches of norain gives .30, telling you that the three inches of rain that fell did so as a result of a 30% chance of rain.

[Illustration: a tube with markings. Water filling up the bottom three markings are labelled “Actual Rain.” Seven more empty markings are labelled “Non-Probable Rain.” A stub of paper at the top is labelled “Probability Float.”]

If it has not rained, and the gauge is dry, proceed as follows:

1. Mark down the level of the probability float.
2. From a watering can or garden hose, slowly add water to the column until the probability float starts to rise.
   This approach is based on the fact that the bottom of the gauge contains a certain level of probable rain, just as before, but without any actual water to make it visible. Since real rain must contain equal volumes of water and the probability of water, the probability in the bottom of the column will absorb just its own volume of the water you add, and no more.
3. Measure the level of water and the new level of the float.
4. Subtract from the water level a volume of water equal to the rise in the probability float, as this represents water in excess of the probability level.
5. Divide this figure by the total capacity of the gauge, thus deriving the odds from which your dry spell resulted.