# 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:

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

## Objectives

1. Apply a kinematic equation to predict the distance travelled by an object in free-fall for a given time interval.
2. Create an apparatus to measure 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

1) Calculate the distance an object would fall in 0.02 seconds, assuming it was dropped from rest and ignoring air resistance. Show your work below.

3) Create a column in a spreadsheet with time values separated by 0.02 s. Use the formula feature of the spreadsheet software to repeat the calculation of fall distance for each of the time values in the table and convert units to cm.  You should get a table like this, but with many more rows, and the question marks replaced with values calculated by your formula:

 Time (s) Drop Distance (cm) 0.02 ?? 0.04 ?? 0.06 ??

Use the first 0.02 s calculation that you did by hand to verify that the formula is working correctly. Fill the table until the drop distance you calculate are larger than the total length of your ruler. Check with your instructor if you are unsure about your spreadsheet results.

4) Are the distances in your spreadsheet evenly spaced? Explain why or why not. [Hint: Look back at the equation you used to calculate the distances.]

6)  Repeat this experiment 10 times, recording your measured reaction time for each trial in a spreadsheet, which should look like this.

 Trial Reaction Time (s) Time Uncertainty (s) 1 2 3 4 5 6 7 8 9 10

### Analysis Methods

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

8) 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. Even though you are assuming same uncertainty in each distance measurement, that does not mean the time uncertainty is the same for each trial (because fall time and distance are not linearly related). However, we can use your spreadsheet of fall times and distances to estimate the time uncertainty for each trial.  For each drop distance you measured, look the distances above and below that fall within the finger location uncertainty you explained above. Then look at the range of fall times that correspond to that range of distances. That is the uncertainty in the fall time that corresponds to the location uncertainty. Do this for each trial and record the time uncertainty in another column to the right of your experimental reaction time data.

10) 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 error 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).

11) 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.

The standard deviation tells us about variation in the data (how close together the value are). We often use the standard deviation calculated from a set of measurements an estimate of the uncertainty in making that particular type of measurement, assuming we were measuring the same quantity each time.  However, it is likely that your reaction time was actually different each time, so we can’t really assume the standard deviation represents the uncertainty for a single reaction time measurement. Instead, the standard deviation represents the lack of consistency in your reaction time from one trial to the next.

12) 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 average value can be reduced by averaging many values. 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.

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

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

15) 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 a certain amount of practice).  In that case the variation is caused by the trend, not by measurement error or random inconsistency in your reaction time and the SEM is not necessarily representative of the uncertainty in the average value.  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

16) 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 answer above and the SEM value.

## Further Questions

17) 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? Do the values agree within the combined uncertainty in your measurement and theirs?

18) 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.

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

20) Do you feel that the fall-time method is a reasonable way to test reaction time? Explain. 