High Speed Hupotheses

8/3/2019 High Speed Hupotheses

1/3

High-speed hypotheses!

Lawrence M. Lesser

The University of Texas at El Paso, Texas, USA.

e-mail: [email protected]

Abstract This article presents engaging interactive hypothesis tests which can be conducted

with students very efficiently.

Keywords: Teaching; Hypothesis tests; P-value.

Introduction

With class time at a premium, it helps to have

handy a repertoire of engaging classroom-tested

activities or experiments that can each be done

within 5 minutes from collection of data to

computation of the p-value! Such activities

support the American Statistical Associations

(ASA; 2010) recommendations to use real

data and foster active learning in the class-

room, illustrate the statistical problem solving

process (ASA 2007) and likely tap the potential

benefits of using fun in the statistics classroom

(Lesser and Pearl 2008). A representative

variety of common basic hypothesis tests are

spanned with the activities which follow.

Activity one: who has ESP?

Background: Because it is discussed in popular

culture, students are already familiar with and

interested in the idea of having extra-sensory

perception (ESP). Some textbooks (e.g. Utts

2005) have used it in case study examples. ESP

experiments commonly involve predictions from

a smaller set of items (with maybe 4 or 5

choices), but this can be modified for pedagogi-cal purposes, as it is here.

Topic: (One-tailed) hypothesis test for a pro-

portion p

Procedure: You bring in a standard 52-card

deck of cards (make sure students are familiar

with the breakdown of suits and values on the

cards) and have students commit in writing

their predictions for, say, a dozen cards about

to be drawn with replacement. Under the null

hypothesis of no ESP, the probability of a

correct prediction (i.e. of both suit and denomi-

nation) would be 1/52, or about 1.9%. While

you draw the cards, every student in the room

is participating by independently trying to make

a correct prediction. Because almost all stu-dents will experience no more than two suc-

cesses, it is very quick to tabulate the results

of the hypothesis test for these cases. When

asked in advance Do any of you have ESP?,

no student seriously answers Yes, so it can

be noted that by chance alone, a sufficiently

large class can be expected to have at least

one student who obtains a personal p-value of

less than 5%, therefore falsely rejecting the

null hypothesis.

Teachers interested in adding a magic trick

component (e.g. using marked cards) can ensure

obtaining a significant p-value by being (almost

surely) the only one in the room to make all

predictions correctly or (to make it not quite so

suspicious) even to make most of the predictions

correctly (by deliberately missing a few). Lesser

and Glickman (2009) offer related discussion on

the use of magic in statistics. Teachers wanting to

vary the success probabilities involved could have

students predict only the suit or only the denomi-

nation. A website students can use to further

explore and assess their psychic abilities

(to predict cards, pictures, locations, lottery

numbers, etc.) is http://www.gotpsi.org.

Activity two: take your seats

Background: There is some literature about

where students prefer to sit in various types of

classrooms (e.g. Kaya and Burgess 2007) and

gender is a variable that is considered of poten-

tial importance in this context. For this activity,

we assume that the classroom seating arrange-

ment is a rectangle made up of rows of individual

seats, but modifications can be made for other

arrangements.

Practical activities

2011 The AuthorTeaching Statistics 2011 Teaching Statistics Trust, 34, 1, pp 101210


2/3

Topic: Test of the equality of two proportions (or

done as a chi-squared test of independence)

Procedure: Walk into the classroom where stu-

dents have already freely chosen their seats.

Have the class agree on an operational definition

of front half of the room and back half of theroom, for the part of the room where students

are sitting. The class can fill in the table below in

less than 1 minute and then go on to test the null

hypothesis that males and females are equally

likely to sit in the front half of the room. The

teacher could have students identify the two

populations in this activity and then discuss

whether or not the males and females in the

room can be considered as random samples

from those respective populations.

Activity three: hold a note

Background: Some published literature

(e.g. Cheng 1991) suggests that you can sing

more fully in a standing position than in a sit-

ting position, while other literature suggeststhat the more important consideration is sim-

ply good posture whether you are sitting or

standing.

Topic: Testing the equality of two means

Procedure: Each student flips a coin to

determine whether he/she will be in the sitting

(tails) or standing (heads) group. An online

stopwatch (e.g. http://www.shodor.org/

interactivate/activities/Stopwatch/) is projected

onto a screen where it is within view of every-

one. After a 3-2-1 countdown by the teacher, the

stopwatch will be started and everyone in the

room will start to sing a note. (For consistency,

suggest that everyone use a common syllable

such as ohhhhhhh; also suggest to everyone to

choose a pitch in the middle of their singing

range, which should be easier to maintain for the

duration of their singing). Each student is asked

to watch the stopwatch and notice the amount of

elapsed time at the instant he/she ran out of air

and was unable to continue singing. Almost

everyone will be done after about 18 seconds, so

the total time needed is very minimal. The

teacher now displays a spreadsheet or software

package for data analysis. The data can be

entered either by having students one at a time

call out their time (and whether they were sitting

or standing) or, in case more privacy is desired,

by having students fill out and turn in a simple

slip of paper without their name on it that indi-

cates the time duration (in seconds) andwhether they were sitting or standing.

To perform the test of means of the two

independent samples, students will need to

agree on whether to have the software do a t

test or a z test, and whether to assume the

unknown variances are equal. Beyond the cal-

culations, students can also be asked to do the

following:

(1) discuss whether this experiment is best

classified as single-blind, double-blind or nei-

ther; (2) discuss what would be changed to

have each person try both the sitting and the

standing conditions; (3) consider a third condi-

tion (e.g. singing with arms held straight up

towards the ceiling, or maybe singing right

after doing 20 jumping jacks) which would

make this activity a vehicle to test the equality

of more than two means (i.e. to use analysis of

variance).

Even though singing can be a personal form

of expression, the beauty of this activity is that

it simply is a single note (so that the ability to

keep rhythmic time, for example, is not

needed) and that everyone is doing it at the

same time and so no one will be able to easilyhear anyone (or hear when they drop out)

except for the very last couple of people, and

by that naked end of the window, students

have already moved beyond any initial moment

of self-consciousness. To make the activity feel

safe and fun, I demonstrate the procedure

by holding a note all by myself first while I run

the stopwatch, then I point out that each voice

will be camouflaged by doing it all together,

and I also mention that anyone who feels

uncomfortable for any reason is not required to

participate. To the extent that humming may

feel safer than singing, this activity works

just as well having each student humming

(with closed lips, mmmmmm). In several

implementations of this activity, I have not

noticed any students reticence or non-

participation. If anything, there seems to be a

positive communal experience about doing

something this unusual in statistics class in

general, as well as the particular pleasantness

of being enveloped by the sound vibrations of

everyones simultaneous notes and how they

collectively and spontaneously formed interest-

ing harmonies.

Number

of males

Number

of females

Front half of the classroom

Back half of the classroom

High-speed hypotheses! 11



3/3

Activity four: which hand is quicker?

Background: Anderson-Cook and Sundar (2001)

describe a class demonstration to compare the

reaction times of ones dominant and non-

dominant hands. In the demonstration, there isa 3-2-1 countdown and then one of nine boxes

lights up and the time (to the hundredths of a

second) is recorded for how long it takes to

move the computer mouse (with a designated

hand) over to that highlighted box and click on

it. As time permits before the demonstration,

teachers can first discuss the principles of

experimental design and critique the flawed

first draft of the experimental design offered in

that article. If time is limited, however, teachers

can just go to and use the final version of the

applet at http://www.amstat.org/publications/

jse/java/v9n1/anderson-cook/GoodExpDesign

Applet.html.

Topic: Test of means from two dependent

samples

Procedure: Teacher projects onto a screen the

website at the URL just mentioned and person-

ally takes the test with each hand to demon-

strate to the class how the applet works,

explaining what dominant and non-dominant

mean and how the traffic light countdown

graphic and Reset! and Start! buttons work.

Then, a reasonable number of students (as few

as 5 or 6 is sufficient to illustrate the concept,but more can be allowed if there is time and

interest) each come up one at a time to try the

applet. Each data observation takes just a

second (literally), so the entire data collection

can go very quickly. Then the Compile Info!

button can be hit to reveal the t value of the

paired t test.

References

American Statistical Association (2007). Guide-

lines for Assessment and Instruction in Statis-

tics Education (GAISE) Report: A Pre-K-12

Curriculum Framework. Alexandria, VA:American Statistical Association. http://

www.amstat.org/education/gaise/.

American Statistical Association (2010). Guide-

lines for Assessment and Instruction in Statis-

tics Education: College Report. Alexandria, VA:

American Statistical Association. http://

www.amstat.org/education/gaise/.

Anderson-Cook, C.M. and Sundar, D.-R. (2001).

An active learning in-class demonstration of

good experimental design. Journal of Statistics

Education, 9(1), http://www.amstat.org/

publications/jse/v9n1/anderson-cook.html.Cheng, S.C.-T. (1991). The Tao of Voice: A New

East-West Approach to Transforming the

Singing and Speaking Voice. Rochester, VT:

Destiny Books.

Kaya, N. and Burgess, B. (2007). Territoriality:

Seat preferences in different types of class-

room arrangements. Environment and Behav-

ior, 39(6), 859876.

Lesser, L.M. and Glickman, M. E. (2009). Using

magic in the teaching of probability and sta-

tistics. Model Assisted Statistics and Applica-

tions, 4(4), 265274.

Lesser, L.M. and Pearl, D.K. (2008). Functionalfun in statistics teaching: Resources, research,

and recommendations. Journal of Statistics

Education, 16(3), 111. http://www.amstat.

org/publications/jse/v16n3/lesser.pdf.

Utts, J.M. (2005). Seeing Through Statistics (3rd

edn). Belmont, CA: Thomson Brooks/Cole.

12 Lawrence M. Lesser


Documents

High Speed Hupotheses