As I suggested earlier, this result could raise a question about how we interpret a null
hypothesis test. Whether we take the traditional view of hypothesis testing or the view put
forth by Jones and Tukey (2000), we can conclude that the difference is greater than
chance. If the pattern of responses had come out favoring the effectiveness of therapeutic
touch, we would come to the conclusion supporting therapeutic touch. But these results
came out significant in the opposite direction, and it is difficult to argue that the effective-
ness of touch has been supported because respondents were wrongmore often than ex-
pected. Personally, I would conclude that we can reject the effectiveness of therapeutic
touch. But there is an inconsistency here because if we had 157 correct responses I would
say “See, the difference is significant!” but when there were 157 incorrect responses I say
“Well, that’s just bad luck and the difference really isn’t significant.” That makes me feel
guilty because I am acting inconsistently. On the other hand, there is no credible theory that
would predict participants being significantly wrong, so there is no real alternative expla-
nation to support. People simply did not do as well as they should have if therapeutic touch
works. (Sometimes life is like that!)An Example with More Than Two Categories
Many psychologists are particularly interested in how people make decisions, and they
often present their subjects with simple games. A favorite example is called the Prisoner’s
Dilemma, and it consists of two prisoners (players) who are being interrogated separately.
The optimal strategy in this situation is for a player to confess to the crime, but people often
depart from optimal behavior. Psychologists use such a game to see how human behavior
compares with optimal behavior. We are going to look at a different type of game, the uni-
versal children’s game of “rock/paper/scissors,” often abbreviated as “RPS.” In case your
childhood was a deprived one, in this game each of two players “throws” a sign. A fist rep-
resents a rock, a flat hand represents paper, and two fingers represent scissors. Rocks break
scissors, scissors cut paper, and paper covers rock. So if you throw a scissors and I throw a
rock, I win because my rock will break your scissors. But if I had thrown a paper when you
threw scissors, you’d win because scissors cut paper. Children can keep this up for an aw-
fully long time. (Some adults take this game very seriously and you can get a flavor of what
is involved by going to a fascinating article at http://www.danieldrezner.com/archives/
002022.html. The topic is not as simple as you might think. There is even a World RPS
Society with its own web page.)
It seems obvious that in rock/paper/scissors the optimal strategy is to be completely un-
predictable and to throw each symbol equally often. Moreover, each throw should be inde-
pendent of others so that your opponent can’t predict your next throw. There are, however,
other strategies, each with its own advocates. Aside from adults who go to championship
RPS competitions, the most common players are children on the playground. Suppose that
we ask a group of children who is the most successful RPS player in their school and we
then follow that player through a game with 75 throws, recording the number of throws of
each symbol. The results of this hypothetical study are given in Table 6.3.144 Chapter 6 Categorical Data and Chi-Square
Table 6.3 Number of throws of each symbol in
a playground game of rock/paper/scissors
Symbol Rock Paper Scissors
Observed 30 21 24
Expected (25) (25) (25)