Experimental Design · Lesson 5

Precision, repeated trials and sources of error

Repeat a measurement and you rarely get the same number twice. That scatter is random error: one disk has a few more bubbles, one press of the stopwatch is a little slow. The spread of a set of trials (largest minus smallest) shows how much scatter there was; a small spread means precise results. Averaging several trials lets the high and low readings offset each other, so the average is steadier than any single trial.

Systematic error is different: it pushes every reading the same way by the same amount. A thermometer that reads 3 °C high, or a stopwatch that starts 2 s late, makes every trial wrong in the same direction. Averaging those trials keeps the error, because there is nothing for it to cancel against.

To work out an error’s effect, ask which way it pushes the recorded value. A stopwatch that starts late records too little time, so the true time is longer. A scale that reads high records too much, so the true mass is smaller. Then move the recorded value the other way.

Two kinds of error
Random errorSystematic error
What it looks likeTrials scatter above and belowEvery trial off the same way
ExampleReaction-time wobble on a stopwatchA dial that reads 3 °C high
Do more trials help?Yes: the average gets steadierNo: the bias stays in every average

Floating Disks

Potato cells contain catalase, an enzyme that breaks hydrogen peroxide down into water and oxygen gas. Students used this reaction to study how temperature affects catalase.

The students soaked small paper disks in potato extract. For each trial, they warmed a cup of 3% hydrogen peroxide solution in a water bath set to the test temperature, dropped in one disk, and pressed the stopwatch button the moment the disk touched the bottom of the cup. As oxygen bubbles formed on the disk, it rose, and the stopwatch was stopped when the disk reached the surface. Each temperature was tested in 4 trials, and Table 1 lists every time and the average.

Table 1
Temperature (°C)Trial 1 (s)Trial 2 (s)Trial 3 (s)Trial 4 (s)Average (s)
102219252021.5
201513161214
30101091110
401311141012
Table 1 lists the time for a disk to rise in 4 trials at each temperature, and the average. 10 °C: 22, 19, 25, 20 s (average 21.5 s). 20 °C: 15, 13, 16, 12 s (14.0 s). 30 °C: 10, 10, 9, 11 s (10.0 s). 40 °C: 13, 11, 14, 10 s (12.0 s). The fastest rise is at 30 °C.

Worked example Easy

Show the whole passage

Floating Disks

Potato cells contain catalase, an enzyme that breaks hydrogen peroxide down into water and oxygen gas. Students used this reaction to study how temperature affects catalase.

The students soaked small paper disks in potato extract. For each trial, they warmed a cup of 3% hydrogen peroxide solution in a water bath set to the test temperature, dropped in one disk, and pressed the stopwatch button the moment the disk touched the bottom of the cup. As oxygen bubbles formed on the disk, it rose, and the stopwatch was stopped when the disk reached the surface. Each temperature was tested in 4 trials, and Table 1 lists every time and the average.

Table 1
Temperature (°C)Trial 1 (s)Trial 2 (s)Trial 3 (s)Trial 4 (s)Average (s)
102219252021.5
201513161214
30101091110
401311141012
Table 1 lists the time for a disk to rise in 4 trials at each temperature, and the average. 10 °C: 22, 19, 25, 20 s (average 21.5 s). 20 °C: 15, 13, 16, 12 s (14.0 s). 30 °C: 10, 10, 9, 11 s (10.0 s). 40 °C: 13, 11, 14, 10 s (12.0 s). The fastest rise is at 30 °C.

At which temperature were the 4 trial times most spread out?

  1. 10 °CAnswer
  2. 20 °C
  3. 30 °C
  4. 40 °C

How to solve it

  1. For each row of Table 1, subtract the shortest trial time from the longest.
  2. 10 °C: 25 − 19 = 6 s. 20 °C: 16 − 12 = 4 s. 30 °C: 11 − 9 = 2 s. 40 °C: 14 − 10 = 4 s.
  3. The largest spread, 6 s, is at 10 °C: choice A. Spread comes from the trial columns, not from the Average column.

Why each choice is right or wrong

  • A. Correct. At 10 °C the times run from 19 s to 25 s (Table 1), a spread of 6 s, the largest of the four temperatures.
  • B. Incorrect. At 20 °C the times run from 12 s to 16 s, a spread of 4 s, less than the 6 s at 10 °C.
  • C. Incorrect. At 30 °C the times run from 9 s to 11 s, a spread of only 2 s, the smallest in Table 1.
  • D. Incorrect. At 40 °C the times run from 10 s to 14 s, a spread of 4 s, less than the 6 s at 10 °C.

Worked example Medium

Show the whole passage

Floating Disks

Potato cells contain catalase, an enzyme that breaks hydrogen peroxide down into water and oxygen gas. Students used this reaction to study how temperature affects catalase.

The students soaked small paper disks in potato extract. For each trial, they warmed a cup of 3% hydrogen peroxide solution in a water bath set to the test temperature, dropped in one disk, and pressed the stopwatch button the moment the disk touched the bottom of the cup. As oxygen bubbles formed on the disk, it rose, and the stopwatch was stopped when the disk reached the surface. Each temperature was tested in 4 trials, and Table 1 lists every time and the average.

Table 1
Temperature (°C)Trial 1 (s)Trial 2 (s)Trial 3 (s)Trial 4 (s)Average (s)
102219252021.5
201513161214
30101091110
401311141012
Table 1 lists the time for a disk to rise in 4 trials at each temperature, and the average. 10 °C: 22, 19, 25, 20 s (average 21.5 s). 20 °C: 15, 13, 16, 12 s (14.0 s). 30 °C: 10, 10, 9, 11 s (10.0 s). 40 °C: 13, 11, 14, 10 s (12.0 s). The fastest rise is at 30 °C.

Why did the students run 4 trials at each temperature and report the average?

  1. To make the disks rise faster at the lower temperatures
  2. To correct for a water bath that ran 2 °C warmer than its setting in every trial
  3. To reduce the effect of chance differences from one disk to the nextAnswer
  4. To test more temperatures than a single trial would allow

How to solve it

  1. Look at any row of Table 1: the four times at one temperature are not identical (at 10 °C they range from 19 s to 25 s). That trial-to-trial scatter is random error.
  2. Averaging several trials lets the high and low readings offset each other, so the average is steadier than any single trial.
  3. Averaging cannot fix an error that pushes every trial the same way, and it does not change the reaction itself. The answer is C.

Why each choice is right or wrong

  • A. Incorrect. Repeating a trial does not change how fast a disk rises; the times in Table 1 depend on temperature, not on how many trials were run.
  • B. Incorrect. A bath that runs 2 °C warm affects every trial the same way, and averaging trials that share the same error leaves that error in place.
  • C. Correct. The trials at each temperature differ by up to 6 s (10 °C, Table 1). Averaging 4 trials lessens the effect of these chance differences and gives a more reliable value for each temperature.
  • D. Incorrect. The number of temperatures (four) and the number of trials at each one are separate choices; extra trials add no new temperatures.

Trap More trials don’t fix a biased measurement

It is tempting to think that enough trials will wash out any mistake. They wash out only the random kind. If every reading is pushed the same way, by a dial that reads high or a timer that starts late, then 4 trials, 12 trials or 100 trials all carry the same bias, and so does their average.

When a question describes an error that affects every trial, the fix is to correct the instrument or the reading, not to repeat the experiment.