Playing Games with a Purpose
Teaching Two-Sample Hypothesis Tests
We usually think of games as a pleasant
distraction—just something we do for fun.
However, growing evidence suggests that
games can do more than keep us entertained,
especially when it comes to learning in a
classroom setting.
“We shifted the focus away from statistical
calculations that aren’t tied to the context of
scientific research,” says Kuiper. “Our
materials provide an alternative to lectures and
textbook style problems, and incorporate
research-like experiences in the classroom.”
Because statistics is a topic that doesn’t come
easily to most and is often not thought of as
being fun, using properly designed games to
teach statistics can become a valuable tool to
spark interest and help explain difficult
concepts.
To incorporate research-like experiences into
their instruction, Kuiper, Cummiskey, and
Sturdivant had students use game-based labs.
“The labs leverage students’ natural curiosity
and desire to explain the world around them,
so they can experience both the power and
limitations of statistical analysis,” says
Kuiper.
What kinds of “properly designed” games are
we talking about? Not traditional board games
like Monopoly or Chutes and Ladders, but
interactive computer games—the types of
games younger generations have grown up
with.
For example, the trio used the online computer
game “Tangrams” to teach hypothesis testing,
and had students use statistical software like
Minitab to analyze data along the way.
Dr. Shonda Kuiper, associate professor and
chair of the mathematics and statistics
department at Grinnell College, Kevin
Cummiskey, assistant professor at the United
States Military Academy, and Colonel Rod
Sturdivant, associate and academy professor at
the United States Military Academy, have
been exploring the use of computer games in
their classrooms for many years.
Defining Hypothesis Testing
Of the many topics taught to students in
introductory-level statistics courses,
hypothesis testing is among the most
challenging to understand at the conceptual
level.
Hypothesis tests are statistical procedures that
evaluate two mutually exclusive statements
about a population.
These two statements are called the null
hypothesis and the alternative hypothesis.
They are always statements about
population attributes, such as the value of a
parameter, the difference between
corresponding parameters of multiple
populations, or the type of distribution that
best describes the population. A hypothesis
test uses sample data to determine which
statement is best supported by the data.
Examples of questions you can answer with
a hypothesis test include:

Is the average time to complete a
Tangrams game less than 2 minutes?
 Is the average completion time of a
game different for males and
females?
 Do science and engineering majors
complete games more quickly than
other majors?
Most hypothesis tests in Minitab are located
in the Stat > Basic Statistics menu,
although some, like the chi-square test, are
located in Stat > Tables > Cross
Tabulation and Chi-Square.
Teaching Hypothesis Testing with
“Tangrams”
In the Tangrams lab developed by Kuiper,
Cummiskey and Sturdivant, students are
introduced to hypothesis testing through a
web-based puzzle game. Players must solve
a puzzle in which they cover an image by
flipping, rotating, and moving a set of
shapes.
Figure 1. The web interface of the Tangrams puzzle
game.
The Tangrams website collects each player’s
information and automatically records their
completion times. The students can
download the data set for the entire class,
which is available for immediate use
through the website.
Students take on the role of a researcher by
selecting from a wide variety of independent
variables to explain why some students
complete the game faster than others. For
example, a student may decide to investigate
whether game completion times differ based
on the type of music played in the
background, and then translate this research
question into a testable hypothesis.
Next, students can analyze their data by
calculating summary statistics and plotting
histograms of the Tangrams completion
times in statistical software such as Minitab.
Because completion times tend to vary
significantly among the students, the data
sets tend to be “messy,” and do not follow a
normal distribution.
This makes the analysis engaging for
students, because they must discuss and
make decisions about data cleaning, such as
whether to remove outliers. Then they must
check assumptions, conduct appropriate
statistical significance tests, and state their
conclusions. “Many statistics courses
discuss model assumptions and removing
outliers or erroneous data,” Kuiper says,
“but students rarely face data analysis
challenges where they must make and
defend their own decisions.”
Application in the Classroom
To illustrate how to implement the
Tangrams lab in the classroom, we will
consider a class that chooses to investigate
the relationship between a student’s
academic major and the time it takes to
complete the puzzle. Specifically, the class
wants to answer the following research
question: Are students who major in math,
science, and engineering faster at
completing the puzzle than students
majoring in other subjects?
Prior to starting the game, the players enter
pertinent data about themselves into the
Tangrams web interface. For this example,
students entered type of major, either
“MSE” for math, science, engineering
majors, or “Other” for all other majors.
Figure 2. Students input pertinent data about themselves
using the web interface of the Tangrams game.
After each student plays the game, their data
is matched with their puzzle completion
time. When the last student completes the
puzzle, the class’s data is immediately
available for analysis.
Before delving into data analysis, the
students need to translate the research
question into testable hypotheses. In this
case, they want to see if the difference
between the means of two populations—
MSE majors and other majors—is
statistically significant.
The null (H0) and alternative (Ha)
hypotheses would be:
H0: MSE majors have the same Tangrams
average completion time as students in other
majors.
Ha: MSE majors and other majors do not have
the same Tangrams average completion time.
Now the students input their data into a
Minitab worksheet to calculate basic
summary statistics.
Histogram of Other Majors
Mean = 90.7
12
10
Frequency
8
6
4
2
0
Figure 3. Students can input class data from the
Tangrams lab into a Minitab worksheet.
In Minitab, students use Stat > Basic
Statistics > Display Descriptive Statistics
to identify the sample mean and standard
deviation of the completion times of the
MSE majors and other majors. They can
also select to view other summary statistics,
such as median, mode, variance, and many
others.
Figure 4. Minitab’s Display Descriptive Statistics function
shows the sample mean and standard deviation of the
completion times of the 96 MSE majors and 32 other
majors that played Tangrams.
To view the distribution of the data, students
use Graph > Histogram > Simple to create
a histogram:
20
40
60
80
100
120
140
Puzzle Completion Times of Other Majors
160
Figure 5. This histogram makes it easy to see the
distribution of the completion times for other majors,
including the high and low times, as well as the mean
completion time.
The students also use Graph > Boxplot >
Multiple Y’s > Simple to view the data
distribution for both populations and to
easily identify outliers.
Next, to determine if there is a statistical
difference between the means of MSE
majors and other majors, the students
conduct a two sample hypothesis test in
Minitab. Because there are two independent
populations and the students want to
determine if the average completion times
are the same, they should choose a twosample t-test (Stat > Basic Statistics > 2Sample t) to compute the p-value.
Results
In this case, for type of major, the p-value for
the two-sample t-test was 0.26, which is not
significant at the 95% confidence level
(
Therefore, the class would fail to reject the
null hypothesis and conclude that there is no
significant difference between the two
population means.
The results of the hypothesis test will likely
surprise students, who may note that the
average completion times for MSE majors is
22% faster than the other majors. This seems
to imply that MSE majors outperformed other
majors. However, students would be ignoring
the large standard deviation in the completion
times, which decreases overall confidence in
the location of the population means.
Following the hypothesis test, students can
validate the basic assumptions of the t-test.
One important assumption is that the sample
of students participating in the research is a
random sample. This exposes students to the
challenges researchers come across when
conducting experiments. In practice, obtaining
a random sample is difficult. There are many
reasons why the sample for this classroom
example is not random. In this case, only four
sections of this particular statistics class
participated.
Reactions from Students
So what do students think about this approach
to learning statistics?
Through the National Science Foundation
supported grants, NSF DUE #0510392 and
NSF DUE #1043814, Kuiper and others
developed materials that can be used as
projects within an introductory statistics
course or to synthesize key elements learned
throughout a secondary statistics course.
The materials can be used to form the basis of
an individual research project and to help
students and researchers in other disciplines to
better understand how statisticians approach
the scientific process.
Sample materials and datasets, including those
for the Tangrams lab discussed in this article,
are freely available at
http://web.grinnell.edu/individuals/kuipers/st
at2labs/.
Read more about Cummiskey, Kuiper, and Sturdivant’s
research in the paper, “Using classroom data to teach
students about data cleaning and testing assumptions,”
Frontiers in Quantitative Psychology and
Measurement, September 2012. The paper can be
downloaded for free at:
http://www.frontiersin.org/Quantitative_Psychology
_and_Measurement/10.3389/fpsyg.2012.00354/abstr
act.
Many of Cummiskey’s students responded
very favorably to the game-based lab,
commenting that they liked being involved in
the data collection process because it made the
data “real” to them.
“As a group, students enjoyed playing the
games,” says Cummiskey. “The labs seemed
to truly engage students and many commented
that they saw how statistical procedures are
actually used by people outside the statistics
classroom.”
Visit www.minitab.com for more
information about statistics.