Hiho all, complexmelody's dad here, dropping in with an update on my daughter's project.
Thanks for the welcome you gave my daughter to the forum and the encouragement and advice you gave her for her project. It really got her thinking about a number of issues associated with refining her ideas and designing her experiment, as I had hoped when I suggested that she post here. As a result she came up with a design that considered a number of elements that I don't think she had put much thought into previously, such as:
-Formulating a rigorous problem statement
-Developing a specific, measurable hypothesis
-The purpose of a control group
-Appropriate sample size
-Design that provided a consistent test each time
-What kind of conclusions she could legitimately draw from the data.
She started formulating the idea a few months ago when we were listening to Brian Dunning's Skeptoid podcast discussion about Emily Rosa's experiments with Therapeutic Touch. She has long been interested in science (and is a big fan of the Mythbusters show,) reads the Junior Skeptic, and describes herself as a skeptic. But Rosa's story inspired her to attempt some sort of paranormal research project of her own. We brainstormed a bunch of ideas and telekinesis with dice seemed a good subject to bite off for her upcoming science fair.
As a number of you pointed out, the overall objectives here were not to undertake any groundbreaking original scholarly research. She's in Middle School. The goal was to come up with a fun, original problem statement, develop a hypothesis, design an experiment to test the hypothesis, analyze the data, and draw whatever appropriate conclusions could be drawn. Her target test audience were children her own age, for whom cash or other prizes would definitely be a better incentive than the "fame" associated with performing some paranormal trick. Besides, she was more interested in the aggregate data - overall, how well did people with an incentive to roll sixes perform over pure chance? - than in any one or two outstanding performances that would indicate some sort of special gift. Of course they had to throw the dice themselves.
The design she settled on was this. She read a script to each of 42 test subjects to assure it was consistently explained. They would roll 4 dice in a cup six times. She would total up the number of sixes they rolled, and for each six, her subject would get either a Starburst or Hershey's Kiss (their choice.) If they rolled ten or more sixes they would get a $5 iTunes gift card. If they rolled 20 or more sixes, they would get a $20 iTunes gift card. (The idea of giving cash was nixed pretty quickly by her science teacher, who already had some fears of backlash about letting her play dice games in school - the idea of cash prizes just made it more morally objectionable to some of the powers that be. Besides, my daughter thought that the prizes she offered were a greater incentive than cash anyway.)
The challenging part for me was to help her model a "pure chance" result as a basis for comparing her experimental data. We couldn't use any advanced statistics that was beyond her abilities. We couldn't, then, use terms like "confidence level," "variance," or "standard deviation." I did teach her about the concept of a normal distribution and outliers, and the general notion of regression toward the mean as a way of explaning the importance of sufficient sample sizes. It was hard for me to refrain from taking over and crunching all the data myself and tell her whether or not the null hypothesis should or shouldn't hold, but it was more important for me to give her a way to look at the data and determine if there was anything interesting or unusual about it as the basis for her conclusions, and the groundbreaking proofs of anything would have to wait until she was better at statistics.
So I developed an Excel-based model with the computer randomly generating dice rolls in the exact pattern of her human experiment. We ran three sets of 42 trials and created frequency histograms of each, and compared it to that of her experimental data.
Interestingly, the mode of her data set (more people got five sixes than any other number) was generally higher than the modes in the computer generated models (three, four and five). Also in her experiment, one lucky girl rolled nine sixes out of 24 (fortunately one short of my having to cough up the $5 for an iTunes gift card
) and nobody got zero sixes, where in the computer results we had a couple of zeros, and the highest number of sixes was eight.
Even though we didn't go into any high-school level math, the idea of comparing the frequency of events between one case and another was rather abstract. At times I wonder if she really grasped it. I suppose we will find out if the judges ask her what it all means. But she had a lot of fun (I think) working on it, and wrote it all up and laid it out on the project board last night for submission today.
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