# Experimental Study of Human Reaction Time

This lab is designed to align with AAOT science outcome #1: Gather, comprehend, and communicate scientific and technical information in order to explore ideas, models, and solutions and generate further questions.

## Materials:

• 12″ (30 cm) Ruler
• digital device with spreadsheet program
• digital device with internet access

## Objectives

1. Apply a kinematic equation to predict the time required for on object to free-fall a certain distance.
2. Apply a method to determine human reaction time and acquire experimental data on human reaction time.
3. Analyze data to determine the average reaction time of a certain population.
4. Analyze data to estimate the uncertainty in the average reaction time measured using this method.
5. Analyze data to determine if reaction time depends on the number of tests a person attempts.

## MEthods

### Experimental Methods

2)  Repeat this experiment 10 times, recording your measured reaction time for each trial in a spreadsheet, which should look like the one below. Enter your drop distances in units of meters. Label the other columns as seen below but leave them blank for now.

 Trial Fall Distance (m) Reaction time (s) Distance Uncertainty (m) Max time (s) Minimum time (s) Time Uncertainty (s) 1 2 3 4 5 6 7 8 9 10

### Modeling Methods

3) Find a kinematic equation that relates fall distance and time. Remembering the object was dropped from rest, rearrange the equation to isolate the time. Show your work below.

4) Apply the equation you found above within a spreadsheet formula to determine the ruler fall time for each drop distance in your dataset and fill in the column (don’t do all of the calculations by hand, we want to learn how to use the spreadsheet features). This fall time is how long it took you to see the ruler falling and close your fingers to catch it, which we will define as your reaction time in this study.

### Analysis Methods

5) Graph the reaction time vs. trial number in a scatterplot. Give the graph a name and label the axes, including units.

6) Your fingers are wide, squishy, and do not have sharp edges so the uncertainty in measuring the location of your fingers is not determined simply by precision of your ruler.  Estimate the actual uncertainty in reading off the location of your fingers and explain your reasoning.

9) The uncertainty in the location of your fingers leads to an uncertainty in the reaction time measurement. We will estimate that time uncertainty by calculating the range of possible fall times that correspond to the fall distance + and – the uncertainty. To start, use a formulas in the spreadsheet to calculate the measured fall distances plus the uncertainty (max distances) and also the fall distances minus the uncertainty (min distances) and fill in those columns.

10) Now apply a spreadsheet formula that calculates the difference between the fall time for the max distance and the fall time for the minimum distance. We will use this as the time uncertainty. Use the spreadsheet formula to fill in the last column in your spreadsheet.

11) Add vertical error bars to you graph to represent the uncertainty in reaction time for each trial. You can use the custom error bar option to select the uncertainty column and automatically assign the correct uncertainty to each data point on the graph.  The videos in the lab manual introduction demonstrate how to do this.  There was no uncertainty in the trial number because there was no measurement made, you simply counted the trials, so we will not add horizontal error bars (use the fixed size option and set the size to zero).

12) Calculate the average, standard deviation, and standard error of the mean (SEM) of your 10 reaction time values. You may use the built-in functions of the spreadsheet to perform these calculations. The videos in the lab manual introduction demonstrate these calculations.

13) The standard deviation tells us about variation in the data (how close together the value are). In other words, the standard deviation represents the lack of consistency in your reaction time from one trial to the next. Due to the lack of consistency, we would not be very certain that a small number of reaction time measurements would be representative of your average reaction time. However, the uncertainty in the measurement of an average value can be reduced by averaging many individual measurements. That uncertainty is often estimated by the SEM (based on the assumption that the variation in the values is random). Using the SEM as an estimate of the uncertainty in your average reaction time, report your average reaction time with uncertainty in the standard format: average + uncertainty in the average.

14) Calculate a percent uncertainty in the average. Report your average reaction time with % uncertainty in the standard format: average + percent uncertainty in the average (%).

15) Apply a trendline to the plot of the data and display the trendline equation and R2 value on the graph, and record each here:

16) Do the data suggest that there is a trend (correlation) in the reaction time vs. trial data?  Explain in terms of the error bars, the trendline equation, and the R2 value.

## Conclusions

17) If a significant amount of the variation in the data is actually caused by a real trend in the data (such as getting faster or slower with more trials) then you did not actually attempt to measure the same thing 10 times (reaction time), you measured 10 different things one time each (reaction time after different amounts of practice).  In that case the variation is caused by the trend, not by measurement error or random inconsistency in your reaction time so we cannot trust that the SEM is  representative of the uncertainty in the average value we found.  Based on your previous answer, do you feel that the SEM is a good estimate of the uncertainty in your average reaction time?

18) Are you confident that the average reaction time value you measured is representative of your actual typical reaction time? Explain your reasoning, which should incorporate your answers above and the SEM value.

## Further Questions

19)  Verification/replication of scientific results is an important part of the scientific process. Use this online reaction time tester to quickly make another 10 reaction time measurements. Find the average, standard deviation, and SEM of those 10 results and record below.

20) Contrast the online tester results with those of your fall-time experiment. Were the average reaction times measured by each method in agreement?  Explain. (Do the average + SEM of each result overlap?)

21) Find a peer-reviewed research article on human reaction time and compare the result of that study to your result and the online reaction tester result. Does your result seem reasonable in comparison? Explain. Do any of the average results agree within the combined uncertainty in your measurement and theirs? (Do the average + uncertainty of the result overlap?) Explain.

21) Do your results suggest that the fall-time method is a reasonable way to test reaction time? Explain by referencing specific results of this lab and comparisons with other methods.