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:
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:
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?