SSS Card Tossing Experiment, Part 2: is the evidence convincing?

So time to analyze some results: Do I have convincing evidence that my ability to toss playing cards into a bowl is better with my left hand than my right hand? 

Let’s look at my actual performance:

Here is my two way table of card tossing results

Here is my two way table of card tossing results

Here is a bar chart of my card tossing results. My left hand got six more in than my right hand.

Here is a bar chart of my card tossing results. My left hand got six more cards in the bowl in than my right hand did.

I had an overall  success rate of 34/104, about 32.7%. For my left hand, my success rate was 20/52 (about 38.4%). for my right hand, 14/52 (about 26.9%.)  That’s over an 11% percentage-point difference.  If this were a presidential election, this big a difference would be considered a landslide.

Question I would pose to students: 

Why were my results so different?  What could have caused it?   

Remember from my post in part 1  that the hand I used was determined my random assignment (picking a red card or a black card).  This evens out the impact any other factors that may determine whether the card went in the bowl or not  (wind, distraction, a badly planned throw, a weird playing card).

Eventually, I would hope for students to settle into one of two competing explanations:

Explanation 1:    My ability to throw cards is no better with my left hand than with my right hand, and the results were due to chance, or luck.

Explanation 2:  I really am a better card thrower with my left hand, and the data reflect this.

I ran a simulation to determine if I can rule out explanation #1.  How can we do this?  

(I’d give students about 10 minutes to discuss a good simulation here. Hopefully they would converge onto something like this).

1.   We know that 34 cards went in the bowl, and 70 did not. I could  take two decks of cards, shuffle them thoroughly together, and deal out 34 cards – those will be my throws that “went in the bowl.”

2. I now want to assume that explanation 1 is true, and see what could plausibly happen by chance. How do I simulate this?

 I will look at the color of each of the 34 “in the bowl” cards I dealt out.  Red = Right Hand,  Black – Left Hand.  Because the cards are shuffled thoroughly, my left and right hands are equally able to “get in the bowl.”

I’ll record a statistic:  “# left cards in the bowl” – “# right cards in the bowl.”  For example, if, in my simulation,  I get 17 red (right) cards and 15 black (left) cards Then my statistic will be:

15-17 = -2

3.  I wil repeat this process, and record  “# left cards in the bowl” – “# right cards in the bowl.” over and over, until I build up a sampling distribution for my statistic.  I can do this by generating a dot plot of results by hand.

4. I will look back and my real data from the actual experiment.  I will compare my value  “# lefties in” – “# righties in”   to the range of plausible values in my sampling distribution.  what could plausibly happen by chance.

So how did it go?   Here’s a dot plot of 1000 runs of the simulation:

In the actual experiment I had 6 more lefty successes than righty successes. If I were "completely ambidextrous" in my ability, a +6 or higher can happen by chance about 14% of the time (about 1 in 7 simulations)

In the actual experiment I had 6 more lefty successes than righty successes. If I were “completely ambidextrous” in my ability, a +6 or higher can happen by chance about 14% of the time (about 1 in 7 simulations)

So what do you think?  Is my “+6”  convincing evidence? How big a difference between my lefty and righty results would be convincing?

Most people would not be convinced that I’m a better card tosser with my left hand.  The results in the actual experiment are not that unusual: something as/more unusual happens about 14% of the time by random chance.

Here is a video of how I ran this simulation in Fathom.

You can also run a simulation like this in a great Website called StatKey.   Here’s how the results turned out there:

Again, based in 1000 simulations, a “+6” or higher occurred about 15% of the time by chance.

So no convincing evidence my left hand is better than my right hand throwing cards.

How could I get more convincing evidence in my next experiment?   

About roughlynormal

I have been a math/statistics teacher for 20 years. I currently teach at a college prep 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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