Investigating Science 11–12 · Year 12
Reaction time from a falling ruler: reliability, sample size and outliers
Module 5: Scientific Investigations
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The idea
One measurement of reaction time is unreliable; repeated trials and larger samples shrink the uncertainty of the mean, and each outlier has to be judged against a stated rule rather than deleted.
What you need
- a 30 cm or 50 cm ruler, a table edge to rest the forearm on
- record sheet or spreadsheet, a reaction-timer app for the technology comparison
- consent form and anonymous participant codes
How to do it
- The tester holds the ruler with zero between the catcher’s open thumb and finger and drops it without warning; record the catch distance to the nearest 0.5 cm.
- Convert each distance to a time, t = √(2d/g).
- Do 20 trials per person; calculate the mean, standard deviation and standard error for the first 5, 10 and all 20 trials.
- Decide on an outlier rule before looking at the data (for example, a time under 0.10 s means the catcher anticipated) and apply it.
- Pool anonymised class data and compare groups only where their means differ by more than about two standard errors.
- Evaluate the method: sample selection, sample size, ethics and the ruler against the app.
What you should see
Catch distances of 15, 20 and 30 cm mean reaction times of 0.175, 0.202 and 0.247 s (g = 9.80 m/s²). With a trial-to-trial standard deviation of 0.03 s the standard error of the mean is 0.013 s for 5 trials and 0.007 s for the 20 trials in the procedure, so two people whose 5-trial means differ by less than about 0.04 s (two standard errors of the difference, 2 × √2 × 0.0134 = 0.038 s) cannot be told apart. The learner shows the standard error shrinking as 1/√n in their own data.
What changes
- What you change
- number of trials (and hand used, or app against ruler)
- What you measure
- reaction time and its standard error
- What you keep the same
- same ruler and drop position
- forearm resting on the table
- no warning before the drop
- same outlier rule for everyone
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- One careful measurement is enough.
- Outliers should always be removed.
- A bigger sample removes bias as well as random error.
Safety card
Hazards
- minor finger knocks
Controls
- use a plastic ruler
Note
No chemicals or heat. Human participants: obtain informed consent, allow anyone to withdraw, and record results against codes, not names.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Investigating Science Stage 6 Syllabus (2017), NESA; currentINS12-12INS11/12-1INS11/12-2INS11/12-3
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.
- www.nsw.gov.au/education-and-training/nesa/curriculum/science/investigating-science-stage-6-2017
- education.nsw.gov.au/content/dam/main-education/teaching-and-learning/curriculum/key-learning-areas/science/s-6/investigating-science/Investigating-Science-Module-5-guide.docx
- fi.edu/en/science-and-education/science-recipes/reaction-time
- instructional-resources.physics.uiowa.edu/1c3055-reaction-times