When Statisticians Have Too Much Time on Their Hands…They Convert

It’s Spring. El sol is preheating the Northern Hemisphere in its yearly cycle revving up for Summer. Nibs of green unfurl in branches on their way to maturing into full-blown leaves. The ever-welcome cacophony of harmonious chirps resounding sight unseen from every tree graces attentive ears. And it’s the time when a young man’s fancy turns to the fluttering heartwarming vibrations emanating from…hummingbirds!

I have a hummingbird feeder. In three years of putting it up, I’ve never seen one stinking hummingbird—though my neighbors unmercifully blather about this hummingbird and that family of hummingbirds strapping on the feed bags daily at their feeders. But, like Charlie Brown trying to kick that elusive football teed up by Lucy, I don’t give up!

I’ve tried the red stuff and the clear stuff sold commercially, but I read hummingbirds, like people, prefer fresh food. I mean, why would the discriminating palate waste its time gagging on sugar water that’s been aging in a dingy bottle stored on a shelf in a stuffy garage? Evidently, unlike wine, hummingbird food doesn’t mellow with age. So, I put my nimble fingers to the task and invoked the Google-god in a quest to find the perfect DIY hummingbird food recipe I could make fresh and preferably organic—after all, I do live in Ann Arbor. After much research, I found it!

The recipe was simple enough: One-part sugar to four-parts water, which obviously makes five-parts fresh, pure, natural, tantalizing hummingbird food. Yum! A culinary delight for my tiny long-beaked feathered friends. The problem is, my hummingbird feeder only holds four total ounces. If I used one ounce of sugar and four ounces of water, I’d have five ounces—too much for my feeder. I could discard the other ounce, but that would be wasteful. The recipe suggested one cup of sugar to four cups water and store the rest, but that would defeat my purpose to make it fresh every time. So, I did what any self-respecting, mathematically oriented, technically inclined, pocket-protector toting geek with too much time does. Make conversions.

Voila! A little sugar, water, and a few calculations, resulted in the following recipe. Feel free to use it, but I suggest you invest in some decent measurement equipment.

HUMMINGBIRD FOOD

1-part sugar to 4-parts water makes 5-parts hummingbird food

0.8 ounces sugar + 3.2 ounces water = 4.0 ounces hummingbird food

4.8 teaspoons sugar + [3 ounces + 1.2 teaspoons] water = 4.0 ounces hummingbird food

Conversions are useful in applications other than hummingbird food, too. Applications like analytical studies where the parameter of interest can’t be measured directly, but another parameter is measurable and it’s closely related to the parameter of interest. These are called “surrogate variables.” For example, you may not be able to measure directly when you fell asleep on the couch last night, but you did put a movie on at eight o’clock and can recall the last scene you saw. You find out the scene occurs forty-five minutes into the movie. Hence, you deduce you fell asleep around eight forty-five. Surrogate variables are particularly useful if a conversion factor exists to transform the measurable surrogate variable into a reasonable approximation for the unmeasurable parameter.

Whether it’s hummingbird food or unmeasurable factors in a study, conversion can fly in to produce a feast from your sweet ingredients.

Below are the calculations and conversions, in case you want to check the math. For those of you who follow the metric system (which is most of the world outside the U.S.A), I’ll let you join in the fun and do that conversion yourself!

Since 6 teaspoons = 1 fluid ounce, then:

Hence:

4.8 teaspoons sugar + [3 ounces + 1.2 teaspoons] water = 4.0 ounces hummingbird food