An Investigation of Reaction Time and the Effect of Task Complexity and the Effect of Relaxed and Heavy Audio on Task Performance.
Alan Cummins Student No: 1165236 Course: PSY283 Lecturer: Dr. Garry Prentice
Laboratories II PSY283 Alan Cummins 1165236 Page 2 of 26
Abstract
This experiment seeks to determine whether reaction time is affected by task complexity. In
addition audio in the form of relaxed and heavy music is used to determine if reaction time can
be affected positively or negatively in terms of reaction time on a given task. Participants were
asked to take part in a card-sorting experiment. Two different tasks were tested: Simple card
shuffling into two equal piles and a complex task involving sorting cars by their suits into four
equal piles. While carrying out the two tasks differing relaxed and heavy music was played so
that in all each participant carried out four independent tasks of card sorting. This is an
extension of work carried out by Bellamy, 1993 which focused on task complexity as the
independent variable. Fifteen participants took part in repeated measures within subjects
designed experiment in order to test the hypotheses. The independent variables of music and
task difficulty were varied and the dependent variable of reaction time to complete the various
tasks was measured. It was found that reaction time is affected by task complexity with a
significant result of z=-3.408, p < 0.05, 2-tailed when comparing simple versus complex tasks.
However the null hypothesis was not rejected with regard to audio having an effect on reaction
time across the simple and complex tasks with z = -1.392, p > 0.05, 2-tailed for comparison of
the simple task under varying audio and z = -0.57, p > 0.05, 2-tailed for comparison of the
complex task under varying audio conditions. This experiment did not take account of what
constituted as relaxing or heavy audio but can be extended in the future to incorporate other
factors such as sleep deprivation, Childs, 2008 or audio cues could be learned and practised as
in Yingling, 1962.
Laboratories II PSY283 Alan Cummins 1165236 Page 3 of 26
Contents Abstract ......................................................................................................................................................... 2
Introduction .................................................................................................................................................. 4
Method ......................................................................................................................................................... 9
Materials: .................................................................................................................................................. 9
Participants: ............................................................................................................................................ 10
Design: .................................................................................................................................................... 10
Procedure: ............................................................................................................................................... 10
Results ......................................................................................................................................................... 13
Discussion.................................................................................................................................................... 19
References .................................................................................................................................................. 22
Appendix A – Record Sheet ......................................................................................................................... 25
Appendix B – SPSS Output .......................................................................................................................... 26
Laboratories II PSY283 Alan Cummins 1165236 Page 4 of 26
Introduction
The brain has two major roles, namely that of physiological functions such as heart beat and
body movement. Body movement involves brain activity. The brain must take in sensory
information, process and interpret that information and coordinate muscle movement output
in response to that sensory input if required. This series of steps takes time. Body reaction time
is the amount of time required for the nervous system to receive and integrate these incoming
sensory details and then cause the body to respond. Most actions, excluding reflex reactions,
monosynaptic responses, and knee-jerk, involve a large amount of brain activity. This receiving
and processing of information, integrating and interpreting of such and control of muscle
activity use many neuron to neuron interactions. As Carlson, 2004 describes neurons (See Figure
1) communicate by sending an action potential from the cell body of one neuron via the axon to
the terminal buttons.
A: Human Brain B: Neuron C: Neuron Synaptic Communication
Terminal Button
Dendrites
Axon
Hundreds of millions of neurons
Presynaptic Neuron
Postsynaptic Neuron
Synaptic Gap, transmitter substance
Figure 1 - Brain, Neuron and Synaptic Gap
Laboratories II PSY283 Alan Cummins 1165236 Page 5 of 26
The terminal buttons of the pre-synaptic neuron release a neurotransmitter that crosses the
synaptic gap causing either excitatory or inhibitory effects in the post-synaptic neuron. Guyton,
1991 details that it takes 0.5 milliseconds for these signals to cross a synapse. Thousands of
neurons are involved in the mechanism and combined cause the body to move in response to a
sensory input. While travelling through the network of neurons signals are either convergent or
divergent. Convergence requires that many neurons incorporate their action potentials and
pass this to a single neuron. Divergence requires that a single neuron passes its action potential
through to several other neurons. The more convergence that is required the more time it
takes to process the sensory input. Neurons must await all signals both inhibitory and
excitatory in order to sum their effects and continue on to form further potentials for the
subsequent neuron and so on. This discrimination time increases with increased complexity of a
task. A complicated task involves more decision making which in turn requires more neuron to
neuron communication.
Laboratories II PSY283 Alan Cummins 1165236 Page 6 of 26
Pile A
Pile B
Processing requiring
many neurons
Spades Pile
Clubs Pile
Diamonds Pile
Hearts Pile
A: Simple Task: Sorting Cards into Two Equal Piles
B: Complex Task: Sorting Cards into Piles of Suits
Spades
Clubs
Diamonds
Hearts
Input Processing Output
Figure 2 - Diagram of Schematic Neural Processes Simple and Complex Task
This experiment seeks to investigate the reaction time of the brain and its correlation with task
complexity. Building on work by Bellamy, 1993 two sets of tasks, simple and complex are
carried out by participants. Figure 2 illustrates the basic processes involved in each of the tasks.
Laboratories II PSY283 Alan Cummins 1165236 Page 7 of 26
Task A is the most simplistic and asks the participants to deal cards into two equal piles,
whereas Task B asks the participants to deal cards into 4 piles according to their suits. This more
complicated task involves more processing where visual information must be incorporated with
a sorting task in order to correctly carry out the experiment. Experimentation by Schweizer,
(1998) has already indicated that the reaction time increases with task complexity. This
experiment is then extended out to consider what effect other factors may have in influencing
discrimination time. Factors such as distraction, attention, learning, stress, competition, gender,
sleep deprivation and substance use can effect this discrimination time. Audio is played at both
a relaxed (Classical music) and heavy pace (Dance music) in order to determine if discrimination
time is affected. Audio at differing tempos has been shown to affect the performance of
participants in a repetitive task as indicated in Smoll, 1975. Nelson, 1963 also carried out work
tying the type of music to athletic performance but failed to find any relationship. This
experiment will look solely at reaction time as compared to task complexity to determine if any
relationships exist. Equally music may effect mood and as a consequence performance.
Hayakawa, 2000 has carried out tests in order to determine how music affects mood. Hunter,
2008 gives indication of how mood and type of music are tied. Ernst, 1996 has linked mood to
cognitive appraisal. Jones, 2006 has investigated classical music, namely that of Mozart and its
effect on spatial reasoning. The investigated experiment takes a combination of these varying
effects of music and links them into task complexity and reaction time. The audio chosen does
not have any lyrics as this has been shown by Stratton, 1994 to have an effect on mood.
This experiment seeks to investigate specifically the following two hypotheses.
Laboratories II PSY283 Alan Cummins 1165236 Page 8 of 26
Alternate Hypothesis One: There will be a significant difference between the average task
completion times of a simple card shuffling task as compared to the average task completion
times of a complex card shuffling task.
Alternate Hypothesis Two: There will be a significant difference between the average
completion times of a task when carried out while relaxed audio is played as compared to when
the identical task is carried out while heavy audio is played.
Laboratories II PSY283 Alan Cummins 1165236 Page 9 of 26
Method
Materials:
The materials used for the experiment were as follows:
• Playing Cards: Six sets of playing cards were used. With four used for each of the
differing tasks for each participant.
• Music: Two sets of music were used, heavy audio in the form of dance music and
relaxed audio in the form of classical music. Neither type of music had any lyrics and was
purely instrumental.
• Shuffler: An automatic shuffler was used to shuffle each deck of cards.
• Record Sheet: A basic Record Sheet was used to record completion times per task. See
Figure 7.
• Stop-watch: With ability to record number of milliseconds.
• Office Equipment: Chair and table to lay the cards into bundles.
• Pen: To note the time recorded.
• Bag and Named Slips: Participants were randomly chosen by being drawn from a bag.
• Instruction Sheet: Containing exact instructions to be read out to each participant.
• Laboratory: As sound was being used and concentration required on behalf of the
participants a quiet laboratory was used.
Laboratories II PSY283 Alan Cummins 1165236 Page 10 of 26
Participants:
The total sample size was fifteen participants taken randomly from Psychology students from
Dublin Business School (n=15). The order in which these participants took part was randomly
chosen by drawing names from a hat.
Design:
The design method used for this experiment was a ‘repeated measures within subjects’ design.
This consisted of one group of participants who carried out an experiment of sorting cards in a
simple and complex manner under differing circumstances of quiet or heavy audio. The
dependent variable was that of the reaction time, the time that was required by each
participant to complete each of the individual tasks. The independent variables were that of the
type of audio being played and the task difficulty. Audio played was classical relaxed music and
heavy dance music. The tasks were simple, sort four piles randomly from a deck of cards and
complex, sort a deck of cards into 4 bundles of suits correctly. Each task was carried out under
relaxed and heavy audio and each participant carried out four tasks in total.
Procedure:
The following procedure was used to carry out the experiment:
1. The experimenter took note of all the participants in the experiment.
2. From this list names were randomly drawn out of a bag to determine the order in which
the participants would carry out the experiment.
3. Once random allocation was decided the participants and experimenter went to the
laboratory.
Laboratories II PSY283 Alan Cummins 1165236 Page 11 of 26
4. Each participant was called in turn to carry out the experiment in isolation in the
laboratory.
5. Before carrying out the tasks each deck of cards was shuffled in the automatic shuffler
to ensure random card allocation.
6. Instructions were read out as follows: “You will be required to carry out several tasks
involving placing decks of cards into piles on the table in front of you. You must carry
out these tasks as quickly as possible without any error. In between each task we shall
pause and reshuffle the decks as required. Please do not start each task until indicated
to do so.”
7. As there were two differing tasks instructions were read out just prior to the participant
carrying out the individual tasks. Instructions for the simple task were read as follows:
“There is a deck of cards in front of you. Please place the cards into equal piles so that
you have four piles in total. If you have any questions about the task please ask. Do not
start until the audio has begun and you are indicated to start.” Instructions for the
complex task were read as follows: “There is a shuffled deck in front of you. Please sort
the cards into four piles, with each pile containing only the individual suits spades,
hearts, diamonds and clubs. If you have any questions about the task please ask. Do not
start until the audio has begun and you are indicated to start.”
8. Each participant upon entering the room was given the general instructions about the
experiment and also for each of the simple and complex tasks as they were carried out.
9. Alternate participants were started with either relaxed or heavy music playing in the
background.
Laboratories II PSY283 Alan Cummins 1165236 Page 12 of 26
10. Each participant carried out the tasks in one of two orders:
a. Simple with Relaxed, Simple with Heavy, Complex with Relaxed, Complex with
Heavy
b. Simple with Heavy, Simple with Relaxed, Complex with Heavy, Complex with
Relaxed
11. Each participant therefore carried out 4 individual tasks of sorting cards into piles.
12. After each task was carried out the time required to complete the task was noted on the
record sheet. See Figure 7.
13. Upon completion of the four tasks each participant was asked not to inform their fellow
participants about the nature of the tasks or any of the other details of the experiment,
procedures and instructions. The participants were then thanked for their participation.
14. Once all participants had carried out the experiment the data record sheet was input
into SPSS and the data analysed.
Laboratories II PSY283 Alan Cummins 1165236 Page 13 of 26
Results
The following are the results of analysis of time taken by each of the fifteen participants to
carry out the card shuffling tasks under varying conditions.
Figure 3 shows the average number of seconds it took each participant to carry out the simple
shuffling task under relaxed and heavy audio. There is a difference in the completion time with
(See Figure 8):
Difference: Simple Relax – Simple Heavy = 30.3533 – 30.1160 = 0.2373 seconds
This indicates that the simple task was carried out at a quicker rate when heavy audio was
played.
Figure 3 - Average Completion Time for Simple Task By Music Type
29.8
30
30.2
30.4
Simple Task Relax Audio Simple Task Heavy Audio
Task
Tim
e in
Sec
onds
Music Type
Average Completion Time for Simple Task By Music Type
Laboratories II PSY283 Alan Cummins 1165236 Page 14 of 26
However, looking at the Wilcoxon result (See Figure 9):
Wilcoxon Signed Rank Result: z = -1.392, p = 0.164, p > 0.05, 2-tailed
This indicates that there was no significant difference between the completion time of the
simple task under relaxed or heavy audio. It should be noted that there was a greater variation
in the standard deviation of completion time under heavy versus relaxed audio for the simple
task.
Std Dev Simple Relaxed: 4.5297 versus Std Dev Simple Heavy: 6.71585
Figure 4 shows the average number of seconds it took each participant to carry out the complex
shuffling task under relaxed and heavy audio. There is a difference in the completion time with
(See Figure 8):
Difference: Complex Relax – Complex Heavy = 47.2060 – 46.1027 = 1.1033 seconds
This indicates that the complex task was carried out at a quicker rate when heavy audio was played.
Laboratories II PSY283 Alan Cummins 1165236 Page 15 of 26
Figure 4 - Average Completion Time for Complex Task By Music Type
However, looking at the Wilcoxon result (See Figure 9):
Wilcoxon Signed Rank Result: z = -0.57, p = 0.955, p > 0.05, 2-tailed
This indicates that there was no significant difference between the completion time of the
complex task under relaxed or heavy audio. It should be noted that there was a greater
variation in the standard deviation of completion time under heavy versus relaxed audio for the
complex task.
Std Dev Complex Relaxed: 13.72268 versus Std Dev Complex Heavy: 9.78983
45.4
45.6
45.8
46
46.2
46.4
46.6
46.8
47
47.2
47.4
Complex Task Relax Audio Complex Task Heavy Audio
Task
Tim
e in
Sec
onds
Music Type
Average Completion Time For Complex Task By Music Type
Laboratories II PSY283 Alan Cummins 1165236 Page 16 of 26
Comparing the simple task under both music conditions against the complex task under both
music conditions, Figure 5, it can be seen that the complex task took a greater amount of time
under both relaxed and heavy audio in comparison to the simple task.
Figure 5 - Average Completion Time for Simple and Complex Tasks By Music Type
It should be noted also that the spread in standard deviation comparing task complexity under
the various audio conditions was much greater for the complex task.
Std Dev Spread Simple Task: Heavy – Relaxed Audio = 6.71585 – 4.597 = 2.11885 seconds
Std Dev Spread Complex Task: Heavy – Relaxed Audio = 9.78983 – 13.72268 = -3.93285 seconds
0
5
10
15
20
25
30
35
40
45
50
Simple Task Relax Audio
Complex Task Relax Audio
Simple Task Heavy Audio
Complex Task Heavy Audio
Task
tim
e in
Sec
onds
Tasks
Average Completion Time for Simple and Complex Tasks By Music Type
Simple Task Relax Audio
Complex Task Relax Audio
Simple Task Heavy Audio
Complex Task Heavy Audio
Laboratories II PSY283 Alan Cummins 1165236 Page 17 of 26
Also the standard deviation in task completion time was reversed when comparing simple and
complex tasks under the varying audio conditions. For the simple task the standard deviation
was greater under the heavy audio task whereas for the complex task the standard deviation
was greater under the relaxed audio task (See Figure 8).
A comparison was finally made of the average completion time across both audio conditions,
purely comparing simple versus complex tasks, see Figure 6. This indicates that there is a larger
average completion time for the complex task versus the simple task.
Figure 6 - Average Completion Time across Task Complexity for Relaxed and Heavy Music
Looking at the Wilcoxon signed ranks test result:
Wilcoxon Signed Rank Result: z = -3.408, p = 0.001, p < 0.05, 2-tailed
0
5
10
15
20
25
30
35
40
45
50
Simple Complex
Task
Tim
e in
Sec
onds
Task
Average Completion Time Across Task Complexity for Relaxed and Heavy Music
Laboratories II PSY283 Alan Cummins 1165236 Page 18 of 26
This indicates that there is a significant difference between the average completion times for
simple versus complex tasks. Furthermore it can be noted that there is a much larger standard
deviation in the average completion time of the complex task under both audio conditions than
for the simple task under both audio conditions.
Std Dev: Simple Task (both audio conditions): 4.86566
Std Dev: Complex Task (both audio conditions): 11.40808
Laboratories II PSY283 Alan Cummins 1165236 Page 19 of 26
Discussion
It was found that there was support added to the work carried out by Bellamy, 1993.
The hypothesis that there would be a significant difference between the completion times of a
simple task as compared to a complex task was experimentally. This was found to be the case.
This mirrored the results found by Bellamy indicating that higher order complex tasks do indeed
take longer to process, interpret and react to. However with regard to the second hypothesis
that there would be a significant difference between the completion times of those carrying out
a task with relax audio as compared to those carrying out the same task with heavy audio the
null hypothesis was failed to be rejected. This suggests that the experiment as designed does
not give weight to audio having a positive or negative effect on carrying out tasks, either of
simple or complex in nature.
The hypothesis regarding task complexity and speed of reaction time falls within
expected results. There is a discernible and quantifiable difference in the complexity of task
carried out and as such a clear and quantifiable set of tasks were easily measured and
evaluated. The second hypothesis regarding audio and its affect on task performance, however,
is much more difficult to quantify. Classification of the audio as relaxing or heavy is subjective in
nature. Rubin-Rabson, 1940 has suggested that age plays an important factor on participants
reaction to particular types of music. It gives credence to the criticism of what constitutes
relaxed and heavy audio as it relates to the age of participant. The reaction-time experiment
does not give any weight to age or familiarisation with the audio in use. This may have an affect
on the results obtained. Chen, 2008 suggests that musicians use differing parts of their brain from
Laboratories II PSY283 Alan Cummins 1165236 Page 20 of 26
non-musicians when carrying out tasks involving music so this could be a factor in differing
completion times on the various tasks. The experiment could be extended out to incorporate
level of experience with music as a whole. Work carried out by Martin, 2008 suggests that
motivation and engagement of musical and sporting participants is similar having affect on
adaptive cognitions, adaptive behaviours, impeding/maladaptive cognitions, and maladaptive
behaviours. The experiment could be enhanced to determine if the participants were from a
sporting or musical background and how this may affect reaction time and also how much
audio may cause a beneficial or aversive effect. Childs, 2008 investigated sleep deprivation in
collaboration with the effect of caffeine energy tablets on task performance. The reaction time
experiment could be modified to determine if relaxed or heavy audio will have a greater effect
on sleep-deprived participants in carrying out simple and complex tasks. Prolonged exposure to
audio cues may have an affect on the reaction-time experiment results. Yingling, 1962 suggests
that prolonged exposure and training in music appreciation causes increased intellectual
response over and above emotional response. These findings could be extended into reaction-
time measurement to determine if music appreciation can cause participants to use different
cognitive abilities as compared to a control group of untrained participants. Rockstroh, 2004
has linked test practise to increased performance. This finding should be considered in relation
to the reaction-time experiment. Participants should be questioned on their pre-test abilities
with card shuffling. The experiment could be further extended to include forcing the
participant to carry out a mental arithmetic task while carrying out a more physical task. Other
factors such as practice, attention/distraction, learning, age, stress, competition, visual acuity,
gender, length of arms, sleep deprivation, caffeine, day-of-week and drugs could be varied and
Laboratories II PSY283 Alan Cummins 1165236 Page 21 of 26
compared to a control group carrying out the simple and complex tasks without any other
distraction or performance aid.
Despite failing to reject the null hypothesis with regard to audio and its affect on task
completion the experiment has merit in terms of extension into further more specific and
tightly controlled experimentation in an effort to link audio cues to increased reaction time.
This could have benefit for many areas including but not limited to sports and education.
Laboratories II PSY283 Alan Cummins 1165236 Page 22 of 26
References
Bellamy, M.L. (1993). Reaction time and neural circuitry. Neuroscience Laboratory and
Classroom Activities, The Society for Neuroscience and the National Association of
Biology Teachers.
Carlson, N.R. (2004) Physiology of Behavior, 8th Ed, Pearson Education Inc.
Chen, J.L., Penhune, V.B., Zatorre, R.J. (2008). Moving on time: Brain network for auditory-
motor synchronization is modulated by rhythm complexity and musical training.
Journal of Cognitive Neuroscience, 20(2), Feb 2008. 226-239, MIT Press.
Childs, E., de Wit, H. (2008). Enhanced mood and psychomotor performance by a caffeine-
containing energy capsule in fatigued individuals. Experimental and Clinical
Psychopharmacology, 16(1), Feb 2008. 13-21, American Psychological Association.
Ernst, J.M. (1996). The effect of mood on cognitive appraisal. Dissertation Abstracts
International: Section B: The Sciences and Engineering, 56(10-B), Apr 1996. 5832,
ProQuest Information & Learning.
Guyton, A.C. (1991). Textbook of medical physiology. 8th ed. Philadelphia, PA: W.B. Saunders
Company; Harcourt Brace Jovanovich, Inc.
Hayakawa, Y., Miki, H., Takada, K., Tanaka, K. (2000). Effects of music on mood during bench
stepping exercise. Perceptual and Motor Skills, Vol 90(1), Feb 2000. 307-314,
Perceptual & Motor Skills.
Hunter, P.G., Schellenberg, E.G., Schimmack, U. (2008). Mixed affective responses to music
with conflicting cues. Cognition & Emotion, 22(2), Feb 2008. 327-352.
Laboratories II PSY283 Alan Cummins 1165236 Page 23 of 26
Jones, M.H., West, S.D., Estell, D.B. (2006). The Mozart Effect: Arousal, Preference, and Spatial
Performance. Psychology of Aesthetics, Creativity, and the Arts, S(1), Aug 2006, 26-32,
American Psychological Association.
Martin, A.J. (2008). Motivation and engagement in music and sport: Testing a multidimensional
framework in diverse performance settings., Journal of Personality, 76(1), Feb 2008.
135-170, Wiley-Blackwell Publishing Ltd..
Nelson, D.O. (1963). Effect of selected rhythms and sound intensity on human performance as
measured by the bicycle ergometer. Research Quarterly, 34(4), 484-488.
Rockstroh, S., Schweizer, K. (2004). The Effect of Retest Practice on the Speed-Ability
Relationship. European Psychologist, Vol 9(1), Mar 2004. 24-31., Hogrefe & Huber
Publishers.
Rubin-Rabson, G. (1940). The influence of age, intelligence, and training on reactions to classic
and modern music. Journal of General Psychology, 22, 413-429, Heldref Publications.
Salloway, S.P., Blitz, A. (2002). Introduction to functional neural circuitry., Brain circuitry and
signaling in psychiatry: Basic science and clinical implications. Kaplan, Gary B. (Ed);
Hammer, Ronald P. Jr. (Ed); 1-29, American Psychiatric Publishing, Inc.
Schweizer, K. (1998). Complexity of information processing and the speed-ability relationship,
Journal of General Psychology, 125(1), Jan 1998. 89-102., Heldref Publications.
Smoll, F. L. (1975). Preferred tempo in performance of repetitive movements., Perceptual and
Motor Skills, 40(2), Apr 1975. 439-442, Perceptual & Motor Skills.
Stratton, V.N., Zalanowski, A.H. (1991). The effects of music and cognition on mood.
Psychology of Music, Vol 19(2), 121-127, Sage Publications.
Laboratories II PSY283 Alan Cummins 1165236 Page 24 of 26
Stratton, V.N., Zalanowski, A.H. (1994). Affective impact of music vs. lyrics. Empirical Studies of
the Arts, 12(2) 173-184, Baywood Publishing.
Yingling, R.W. (1962). Classification of reaction patterns in listening to music. Journal of
Research in Music Education, 10(2), 105-120, National Assn of Music Education.
Laboratories II PSY283 Alan Cummins 1165236 Page 25 of 26
Appendix A – Record Sheet
Participant No. Simple Task
Relaxed Audio
Completion Time
Simple Task
Heavy Audio
Completion Time
Complex Task
Relaxed Audio
Completion Time
Complex Task
Heavy Audio
Completion Time
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Figure 7 - Record Sheet
Laboratories II PSY283 Alan Cummins 1165236 Page 26 of 26
Appendix B – SPSS Output
Descriptive Statistics
N Mean Std. Deviation
simple task with relax audio 15 30.3533 4.52970
complex task with relax
audio 15 47.2060 13.72268
simple task with heavy
audio 15 30.1160 6.71585
complex task with heavy
audio 15 46.1027 9.78983
simple 15 30.2347 4.86566
complex 15 46.6543 11.40808
Valid N (listwise) 15
Figure 8 - Descriptive Statistics for Card Shuffling Task
Wilcoxon Signed Ranks Test
simple task with
heavy audio -
simple task with
relax audio
complex task with
heavy audio -
complex task with
relax audio
complex -
simple
Z -1.392(a) -.057(b) -3.408(b)
Asymp. Sig. (2-tailed) .164 .955 .001
a Based on positive ranks.
b Based on negative ranks.
c Wilcoxon Signed Ranks Test
Figure 9 - Wilcoxon Signed Rank Test for Card Shuffling Tasks