The Human Stopwatch Ten Second Experiment
Overview
The Human Stopwatch 10 second experiment is an experiment that can be carried out with online instruction. Students get experience in predicting a 10-second interval and can use descriptive statistics to learn about measurement accuracy and precision.
The Human Stopwatch Ten Second Experiment for Remote Teaching
Fred J. Rispoli
Stony Brook University
Abstract In this article we describe a simple experiment called the “Human Stopwatch Ten Second Experiment” which can be carried out during remote instruction. The analysis can be calculated by using descriptive statistics and hypothesis testing. Students also learn about the accuracy and precision of measurement.
Introduction
Teaching remotely has some new challenges to deal with that do not exist in a classroom. One of them that I struggled with is how to run an experiment while teaching via Zoom. I was interested in running a “hands-on” experiment and obtaining data that could be subjected to statistical analysis. My goal was to obtain experimental data that could be used in calculating meaningful means, standard deviations and running a hypothesis test. In this article I shall describe an experiment that I call the “Human Stopwatch Ten Second Experiment” that introduces students to concepts of accurate and precise measurements. The experiment is an extension of “The Human Stopwatch Experiment”, sometimes used in high school and middle school [1]. The experiment also demonstrates the values of basic statistics and the importance of information. I will also describe the implementation using Zoom.
The experiment consists of pairing up students into groups of two. If there is an odd number of students, create one group with three students. One student is called the “operator” and the other is called the “timer.” The operator uses a stopwatch which can be found on any smart phone. The operator says “Start” and starts timing with the stopwatch, and the timer must count out 10 seconds in their head, and then say “Stop” when they reach 10. The operator stops the stopwatch and records the actual time that has elapsed. In the first phase of the experiment the operator hides the time elapsed from the timers. The timer should not be able to see the stopwatch or any other clock. The pair repeats this process 9 times for a total of 10 measurements, and then the students switch roles, and repeat the process. If teaching with Zoom, the instructor can divide up the groups using breakout rooms to avoid distractions from other groups.
After everyone has finished the first phase, times are all reported to the instructor who records them on a spreadsheet. Times can be communicated either verbally or via an email. The instructor fills in a data collection sheet that looks like Table 1.
Precision vs. Accuracy
Before the experiment, students are given a brief lesson on measurement concerning precision versus accuracy. They should be aware that an average is used to measure accuracy, and the standard deviation provides a measure of precision. After I ran this experiment numerous times, a third measure evolved which has proven to be very useful and insightful. Since we are mostly interested in the timer being close to 10 seconds, it seemed reasonable to count “Hits”, which is the number of times the timer was between 9.5 and 10.5 seconds. This can be used as a defect indicator. In other words, a defect is whenever the timer is not between 9.5 and 10.5.
Once all of the times are recorded on the spreadsheet, it is very informative for the instructor to show the group how to calculate the averages and the standard deviation. Then we ask: “who is the most accurate?” Followed by “who is the least accurate?” We do the same type of thing with precision, reminding the group that we want to identify the person with the smallest standard deviation to identify the most precise timer. Usually, we will see different students being the most accurate and most precise. This is where the “Hits” measure becomes so useful. Hits counts the number of results that are between 9.5 and 10.5 seconds. It can help to determine who the best timer is in the class. Sample data is given in Table 1 on a data collection sheet.
Table 1 Phase 1 Data Collection Sheet
Phase 1 Trial | Michael | Heidi | Nikolas | Shreya | Lynette |
1 | 9.36 | 9.20 | 9.01 | 7.89 | 8.49 |
2 | 10.14 | 10.23 | 9.12 | 6.90 | 9.53 |
3 | 10.10 | 9.94 | 9.62 | 8.94 | 9.56 |
4 | 11.48 | 8.56 | 9.93 | 7.56 | 8.97 |
5 | 11.44 | 8.49 | 10.17 | 8.22 | 9.26 |
6 | 12.38 | 9.66 | 10.36 | 8.56 | 9.05 |
7 | 10.63 | 9.29 | 10.02 | 8.48 | 9.91 |
8 | 11.51 | 9.63 | 10.41 | 9.54 | 9.27 |
9 | 11.73 | 10.08 | 9.89 | 9.99 | 9.00 |
10 | 12.02 | 8.76 | 10.35 | 9.25 | 9.55 |
Average | 11.08 | 9.38 | 9.89 | 8.53 | 9.26 |
Standard Deviation | 0.97 | 0.63 | 0.50 | 0.94 | 0.40 |
Hits | 2 | 5
| 7 | 3
| 1 |
Team Statistics and Phase 2
It is also instructive to look at all of the times combined to determine a team average and a team standard deviation. From the above Phase 1, and a subsequent Phase 2, we get the following.
| Phase 1 | Phase 2 |
Team Average | 9.63 | 10.15 |
Team Standard Deviation | 1.10 | 1.01 |
Average Number of Hits/Person |
|
|
After Phase 1 is complete, a good question to ask is: “What can be done to improve the team accuracy?” Typical answers will be to fire the worst timer, or perhaps require training. You may also hear that it would help to provide the timer with their times, so they could try to correct during the process. Does this really help? This is what Phase 2 is all about.
In Phase 2 we repeat the experiment, except now the operator shows the timer their times. The analysis carried out is similar to Phase 1. But, in addition, now we run a 2-sample t-test to see if there is a significant difference in the average team scores between Phase 1 and 2.
Figure 2 Phase 2 Data Collection Sheet
Phase 2 Trial | Michael | Heidi | Nikolas | Shreya | Lynette |
1 | 8.28 | 9.50 | 9.20 | 7.47 | 9.26 |
2 | 9.31 | 10.16 | 10.60 | 10.22 | 12.67 |
3 | 10.01 | 9.80 | 11.11 | 8.99 | 9.13 |
4 | 10.25 | 11.22 | 10.22 | 9.96 | 10.93 |
5 | 10.07 | 10.50 | 10.18 | 12.19 | 9.16 |
6 | 9.73 | 10.40 | 9.70 | 11.60 | 11.23 |
7 | 10.37 | 11.16 | 10.25 | 9.05 | 9.44 |
8 | 9.68 | 10.30 | 10.38 | 9.50 | 9.62 |
9 | 10.07 | 11.10 | 10.17 | 8.41 | 11.83 |
10 | 9.69 | 10.38 | 10.00 | 12.27 | 10.63 |
Average | 9.75 | 10.45 | 10.18 | 9.97 | 10.39 |
Standard Deviation | 0.60 | 0.57 | 0.51 | 1.62 | 1.26 |
Hits | 8 | 7 | 7 | 3 | 1 |
Prior to running the t-test we run a two sample F test to determine if we have equal variances. The F-test indicates a one-tailed p-value of 0.27, so we conclude the variances are equal. Next, we check for normality. Times in both phases indicate that the data is normal using an Anderson Darling Test. The t-test yields a 2-tailed p-value of 0.016. So, we conclude that there is a significant difference in means. It turns out that the information made a significant difference. Using the data, we could also run a pairwise t test.
Conclusion
The idea of using humans as a stopwatch has been considered elsewhere. For an interesting summary see the article [2]. The article published by the Statistics Education Web online journal, [3], gives a 30 second version where the teacher asks the class to predict 30 seconds and class statistics are then considered. The experiment works very well inside a classroom, which is where I first began to run this. But I was pleasantly surprised how well this can still be run when teaching remotely. Students enjoy the exercise, especially when we look at the completed data collection sheet as a group. It is very entertaining to look at everybody’s times, and then determine who is good at this. I even use this as a team building exercise. I try to run this early in the course, often during a first meeting, if possible.
References
[1] Human Stopwatch published on Desmos.com https://teacher.desmos.com/activitybuilder/custom/59de914bdfeb6e0c086d4b34?collections=featured-collections%2C5da8a6474d5c010a4455b470).
[2] Do Humans Have a Biological Stopwatch? By Dan Falk, in the Smithsonian Magazine, January 2013
https://www.smithsonianmag.com/science-nature/do-humans-have-a-biological-stopwatch-164710819/