## SSS Research: Card Flipping experiment, part 1

One of the important parts of my “Statistics Sports and School (SSS)” course will involve students creating a research question that can be answered with data collection, and designing a plan to properly collect data.  Anybody who has taught statistics understands the challenges of having kids narrow down their wonders to a question that can be answered with the limited amount of time, resources, focus, and energy available to them.

To put myself in their shoes, I designed my first mini experiments with a tinge of “sportiness” to them. Hopefully future questions will involve me doing something where I don’t sit on my ass.

Here was my first research question: Can I toss individual playing cards into a bowl (from about 5-6 feet away) better with my dominant(left) hand than my non-dominant (right) hand?

While my husband was watching some movie entitled “Revenge of Mordor,” or something like that, I decided to mess up the living room.

I challenged myself to come up with a question in about 20 minutes. I liked this one because:

• The question is authentic ( I think I’d be better with my left hand, but I’m not totally sure: I throw frisbee better with my right hand, and tossing cards is like throwing a frisbee. …but is that the same type of dexterity?)
• The question involves some reasonable complexity (lots of variables impact whether a card goes in: practice, mild winds, degree of focus, fatigue, distance to the target)
• The question required systematic, but achievable data collection (I messed this experiment up about three times before executing all the steps and recording data with a reasonable degree of consistency)
• The question allowed for many approaches to analyze the problem
• The question reveals more questions to pursue
• The plan to collect data could be executed in a reasonable about of time (about 2 hours, including screw-ups)

Here was my protocol:

1. I took a deck of plastic poker cards (plastic ones bend less, and are less likely to crease, tear, or be distorted my normal weak than paper ones).

2. I shuffled the 52 cards to determine which hand would throw the card in each trial.  Black = left hand.  Red = right hand.

3.  I sat down on the couch with my deck, and threw each card, aiming for a large, deep salad bowl with a diameter of about 14 inches.

4. I recorded the following variables after each trial:

X1: the hand I used (l = left (dominant) hand. r = right(non dominant) hand.
X2: Did the card land in the bowl (y=yes, n=no)
X3: trial number (1 = first throw, 2 = 2nd throw, etc…)
X4: round number (1 = first round of 52 cards, 2= 2nd round of 52 cards. After tossing the entire deck once, I had to collect all the cards, check my work, reshuffle, and re-seat myself after the first set of 52 throws was completed. I wanted to account for the fact that conditions affecting my success rate might be different in the two rounds.

Here is an Excel File of the card flipping experiment.

Here is a Google Docs File of the card flipping experiment.

If you convert this into a .csv file, you can easily import this into Fathom, or your favorite tool for data analysis.  I’m not a huge fan of Excel for statistical analysis, but hey, knock yourself out.

Challenge to the reader:  What can you do with this?

Maybe the folks studying data and Statistics at PCMI  would be interested in playing with this data.

Are you convinced that this evidence shows that  I am a more accurate card thrower with my left hand than with my right hand?  Support with the existing data, please.

I’d love to hear what you would do to answer this question with my data. I’d also like to know what other questions/ wonders that crop up.

More on my analysis in a bit.

… of course, to increase your accuracy, you can always do this.

I have been a math/statistics teacher for 25 years. I currently teach at an independent school in southern California. I also coach teaching fellows for Math for America - Los Angeles chapter. I love my career, my colleagues, and my friends & family.
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### 5 Responses to SSS Research: Card Flipping experiment, part 1

1. Sendhil Revuluri says:

Oh great. Now I have this song in my head: http://www.youtube.com/watch?v=RrxePKps87k … But seriously, nice example of a problem that’s authentic and “not too big, not too small”!

• Nice! … I just had to keep thinking “RIGHT on RED” so I wouldn’t screw up the experiment – It took me about four or five times not to miscount or screw up the treatments.

So now … what do you think? Do I have enough evidence to be convinced?

2. Glenn says:

If we look at evidence vs. convincing evidence, then yes, we have evidence, and no we do not have convincing evidence. The chi-square test of independence says no.

But, the real question is how to make the case without that level of stats knowledge. You made more (20) with your left than with your right (14). Is the 38.5% really that much better than the 26.9%? A simulation would show you could achieve this through random sampling. How many more times would you have to do it to help?

And the question I had was did practicing help? You went from 5 with the right hand to 9. Did you get better through practice?

• Thanks for the feedback: Glenn, what program did you use to execute the analysis?
That’s a nice visual display. Fathom does something a bit less effective than that.

Stay tuned for part 2, where I will include a video of my simulation in Fathom.
A “low tech” simulation is easy with two decks of cards.
We know 37 cards went in the bowl, the rest didn’t…
Suppose my ability to toss cards in the bowl is the same for both hands…

Yeah: The practicing question is a good one to analyze with the existing data. Also thinking about consistent practice over time (does the fine dexterity skills carry over frmm day to day, or is it more like the movie “Groundhog Day?”)