# Experimental Design Help

My kids and I are wanting to test whether or not different collored skittles taste differently. I want to have them do an experiment. I’ll blindfold them and give them 2 skittles and ask them if they taste the same or not. I’ll keep track of the truth and their responses.

It’s been too long for me to quite remember the right way to analyze the data. I think my null hypothesis should be that their guesses are completely random. How would I calculate the test statistic on this. How big of a sample size am I going to need?

Thanks for the help.

Interesting experiment. Could the results depend on what information you give your kids? If you are choosing skittles at random and your kids know that, they maximize their correct guesses by guessing “different” evey time.

Who knows what that means for experimental design?

I’ll have excel randomize whether I give them the same or different. I’m not going to bother trying to control the individual colors - just pick two that are the same or two that are different.

The wald method is probably the easiest, and there is nothing wrong with that. It essentially uses a normal approximation.

You could also calculate a confidence interval exactly. I wouldn’t bother with that unless learning about confidence intervals is part of the “experiment.” That might be too advanced.

I’d probably just be inclined to use the wald method, and make sure they pay attention to what happens to the estimate every time the data doubles. Make sure they see each additional measurement adds less than the one before it.

I would use two colors of Skittles, get results, then try two different colors as some may taste similar enough and some may taste distinctly different by person.

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I just did what I described above. I have 3 kids, and did 15 trials each.

Oldest got 9 right. Second got 10. Youngest got 6. Altogether, 25 out of 45.

Looking at the binomial distribution - they would have needed to get at least 28 right for a 95% confidence result. Looks like we can’t reject the hypothesis that they taste the same.

Maybe some other day we’ll get some more and try some other tests.

A simpler experiment that might give you good enough results would be to just give them one Skittle at a time and see if they can correctly identify the flavor.

If they can correctly identify grape vs cherry vs lemon vs lime vs orange then I think it’s safe to say that the flavors must be sufficiently different to not taste the same.

I don’t think you’d need to use as many Skittles either. With five flavors, two at a time means 25 combinations just to go through each possibility once.

I’d suggest re-doing the experiment and make it a double-blind study.

Have the Mrs. set up the collection of pairs with “same” or “different” colors by putting them in a closed container (I’m thinking like one of those “condiment cups” with opaque lids). And she gives it to you.

You choose which child gets the cup.

There’s likely to be more that needs to go into the logistics here, but this should get the ball rolling in terms of making it a double-blind.

Mind sharing the age range and gender distribution of the kiddos?

Might also get neighbor kids involved . . . perhaps set up a “science fair project” that could at least get all y’all on the local (loca?) news.

15, 12, 8. All boys.

If my 8 year old needs to do a science fair project this year we might do something on a larger scale.

Another good exercise might be to repeat the experiment, but have them roll a 6 sided die. Greater than/equal 4 and they pick them identical, otherwise different.

Help them understand how that doesn’t look very different from your results.

You could even do that a couple times. Like MC generation, old school!

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Could have another kid do the “odd/even” selection as well.

Another option might also to make the selection not 50/50 to see how that would look.

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Don’t forget that if you are running this experiment multiple times, you increase the risk of a false significant alpha, just due to chance.

Fisher’s Exact Test.

Make sure you publish the raw data. Don’t want to get in trouble with the peer reviewers.

Here you go:

J M R
Actual Result Correct? Actual Result Correct? Actual Result Correct?
1 S D 0 D D 1 D S 0
2 S D 0 S D 0 D D 1
3 D D 1 S S 1 S D 0
4 D D 1 D D 1 S D 0
5 D D 1 S D 0 S S 1
6 S D 0 S S 1 S D 0
7 D S 0 S S 1 D D 1
8 D D 1 S S 1 S D 0
9 S S 1 S S 1 D S 0
10 D S 0 D D 1 S S 1
11 D D 1 D S 0 S D 0
12 D D 1 S D 0 S S 1
13 S S 1 D S 0 D S 0
14 D D 1 D D 1 S D 0
15 D S 0 D D 1 S S 1
9 10 6

First letters of my kids names for header. S = “Same color”, D = “Different colors”

Which one had COVID? I’m gonna guess “R”.

Pretty easy to calculate the p value based on the binomial distribution.

Be sure to pick the alpha before you do so though!

Yeah - I finally remembered that and figured it out.