# Research Spotlight: Sample Variance

*How many blue M&M's should you expect to get from a bag?*

Our 2022 holiday party at Advantage Research included a spirited game of Wits & Wagers, a party game that involves both trivia and wagering based on odds. (We are numbers nerds after all!) One of the questions that came up during the game was "What percent of M&M's are blue?"

What would you guess is the correct answer? Take a minute and come up with a number before scrolling any further.

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The answer? **24%!** This set off a round of spirited discussion, some arguing that this seemed too high, others feeling that 24% was spot-on. So who was right?

The next day we conducted a little experiment (again, nerds) by opening two bags of plain M&M's and sorting them by color:

In the first bag, 9 out of 55 M&M's (16%) were blue; in the second bag, 11 out of 57 (19%) were blue. So why didn't we find 24% blue M&M's in these bags? The answer has to do with **sample variance**, and it's an important concept in market research.

M&M's are probably made one color at a timeāthe machines make a whole bunch of one color, then a whole bunch of another color, etc. Once enough of each color have been made, the different colors are mixed together into a large container so they can be dispensed into individual bags.

Instead of counting each M&M that goes into each bag to ensure the exact same amount of each color, the company allows the sample to "fall out naturally". Picture someone reaching into that large container with a scoop and taking whichever M&M colors happen to be within the area of that scoop. Thus, while 24% of all M&M's made might be blue, the actual number that end up in each bag will be different each time.

Think of this concept when it comes to recruiting for a research study. If the study only requires that all candies selected be M&M's, then sampling will be easy: just scoop out as many as you need! If we only want blue M&M's, we will need to take multiple scoops to get enough, and thanks to sample variance we won't know how many blue M&M's will be in each scoop until after we've collected them. Now take that even further: if we only want blue M&M's that are exactly 1 cm in diameter and have a perfectly centered "m" printed on them, how much time and effort will it take to find those? Conclusion: the more rare the desired audience, the more difficult and costly it will be to find them.

Advantage Research has been helping organizations like yours plan for how many "blue M&M's" they will need for research projects and what it will take to find them since 1992. When planning your next research study, reach out to us!