Experimental Design · Lesson 1

Independent, dependent and controlled variables

Every experiment is built from three kinds of variables. The independent variable is the factor the researchers change on purpose. The dependent variable is what they measure as the result. The controlled variables are everything they deliberately keep the same, so that the independent variable is the only thing that differs from trial to trial.

The passage tells you which is which if you read for signal words. Different, varied and changed mark the independent variable (“Each beaker received a different concentration”). Each, every, all and kept at mark controlled variables (“All beakers were kept at 25 °C”). Measured, counted and recorded mark the dependent variable, which is usually the y-axis of a graph or the last column of a table.

When a passage has two studies, map each one separately. A factor can be the independent variable in Study 1 and a controlled variable in Study 2, so a question about “the factor that varied between trials in Study 2” needs the Study 2 paragraph, not Study 1’s.

Map each study in three blanks
BlankQuestion to askWhere to look
Changed (independent)What did they set differently on purpose?Setup words different, varied; the first column or x-axis
Measured (dependent)What did they record as the result?Counted, measured; the last column or y-axis
Kept the same (controlled)What did every trial share?Each, every, all, kept at in the setup

Duckweed Growth

Duckweed is a tiny floating plant that multiplies by producing new leaflike fronds. Students studied how two growing conditions affect how quickly a duckweed population grows.

Study 1

Students placed 20 duckweed fronds in each of 4 beakers holding 200 mL of pond water with 10 mg/L of added nitrate. All beakers were kept at 25 °C. Each beaker received a different number of hours of lamp light per day. After 10 days, the students counted the fronds in each beaker (see Figure 1).

Study 2

The students set up 4 new beakers, each with 20 fronds in 200 mL of pond water at 25 °C, and gave every beaker 14 hours of light per day. Each beaker received a different concentration of added nitrate. After 10 days, the fronds were counted again (see Table 1).

Figure 1
Figure 1Figure 1 (Study 1) plots the number of fronds after 10 days against hours of light per day for the Study 1 series: 34 fronds at 6 h, 52 at 10 h, 71 at 14 h and 78 at 18 h. The count rises with light, more slowly above 14 h.0102030405060708090468101214161820Light per day (h)Fronds after 10 days (fronds)
  • Study 1
Show the data as a table
Figure 1: data
Light per day (h)Study 1 (fronds)
634
1052
1471
1878

Figure 1 (Study 1) plots the number of fronds after 10 days against hours of light per day for the Study 1 series: 34 fronds at 6 h, 52 at 10 h, 71 at 14 h and 78 at 18 h. The count rises with light, more slowly above 14 h.

Table 1
Added nitrate (mg/L)Fronds after 10 days (fronds)
048
563
1071
2074
Table 1 (Study 2) lists the added nitrate concentration and the number of fronds after 10 days: 48 at 0 mg/L, 63 at 5 mg/L, 71 at 10 mg/L and 74 at 20 mg/L. The count rises with nitrate, then levels off.

Worked example Easy

Show the whole passage

Duckweed Growth

Duckweed is a tiny floating plant that multiplies by producing new leaflike fronds. Students studied how two growing conditions affect how quickly a duckweed population grows.

Study 1

Students placed 20 duckweed fronds in each of 4 beakers holding 200 mL of pond water with 10 mg/L of added nitrate. All beakers were kept at 25 °C. Each beaker received a different number of hours of lamp light per day. After 10 days, the students counted the fronds in each beaker (see Figure 1).

Study 2

The students set up 4 new beakers, each with 20 fronds in 200 mL of pond water at 25 °C, and gave every beaker 14 hours of light per day. Each beaker received a different concentration of added nitrate. After 10 days, the fronds were counted again (see Table 1).

Figure 1
Figure 1Figure 1 (Study 1) plots the number of fronds after 10 days against hours of light per day for the Study 1 series: 34 fronds at 6 h, 52 at 10 h, 71 at 14 h and 78 at 18 h. The count rises with light, more slowly above 14 h.0102030405060708090468101214161820Light per day (h)Fronds after 10 days (fronds)
  • Study 1
Show the data as a table
Figure 1: data
Light per day (h)Study 1 (fronds)
634
1052
1471
1878

Figure 1 (Study 1) plots the number of fronds after 10 days against hours of light per day for the Study 1 series: 34 fronds at 6 h, 52 at 10 h, 71 at 14 h and 78 at 18 h. The count rises with light, more slowly above 14 h.

Table 1
Added nitrate (mg/L)Fronds after 10 days (fronds)
048
563
1071
2074
Table 1 (Study 2) lists the added nitrate concentration and the number of fronds after 10 days: 48 at 0 mg/L, 63 at 5 mg/L, 71 at 10 mg/L and 74 at 20 mg/L. The count rises with nitrate, then levels off.

In Study 2, which factor did the students vary from beaker to beaker on purpose?

  1. The hours of lamp light each beaker received per day
  2. The concentration of nitrate added to the pond waterAnswer
  3. The number of fronds counted after 10 days
  4. The temperature at which the beakers were kept

How to solve it

  1. Find the signal word in the Study 2 paragraph: “Each beaker received a different concentration of added nitrate.”
  2. Check Table 1: its first column, Added nitrate (mg/L), changes from row to row (0, 5, 10, 20), so nitrate is the independent variable.
  3. Light (14 h), temperature (25 °C), water (200 mL) and starting fronds (20) were the same in every Study 2 beaker, and the frond count is the result. The answer is B.

Why each choice is right or wrong

  • A. Incorrect. Light was fixed at 14 hours per day in every Study 2 beaker. Light was the factor that varied in Study 1 (Figure 1), so this mixes up the two studies.
  • B. Correct. Table 1 gives a different added nitrate concentration for each Study 2 beaker, 0, 5, 10 and 20 mg/L, so nitrate is the independent variable.
  • C. Incorrect. The number of fronds (48 to 74 in Table 1) is what the students counted after 10 days. It is the dependent variable, the result, not a factor they set.
  • D. Incorrect. Every Study 2 beaker was kept at 25 °C, so temperature was a controlled variable.

Worked example Medium

Show the whole passage

Duckweed Growth

Duckweed is a tiny floating plant that multiplies by producing new leaflike fronds. Students studied how two growing conditions affect how quickly a duckweed population grows.

Study 1

Students placed 20 duckweed fronds in each of 4 beakers holding 200 mL of pond water with 10 mg/L of added nitrate. All beakers were kept at 25 °C. Each beaker received a different number of hours of lamp light per day. After 10 days, the students counted the fronds in each beaker (see Figure 1).

Study 2

The students set up 4 new beakers, each with 20 fronds in 200 mL of pond water at 25 °C, and gave every beaker 14 hours of light per day. Each beaker received a different concentration of added nitrate. After 10 days, the fronds were counted again (see Table 1).

Figure 1
Figure 1Figure 1 (Study 1) plots the number of fronds after 10 days against hours of light per day for the Study 1 series: 34 fronds at 6 h, 52 at 10 h, 71 at 14 h and 78 at 18 h. The count rises with light, more slowly above 14 h.0102030405060708090468101214161820Light per day (h)Fronds after 10 days (fronds)
  • Study 1
Show the data as a table
Figure 1: data
Light per day (h)Study 1 (fronds)
634
1052
1471
1878

Figure 1 (Study 1) plots the number of fronds after 10 days against hours of light per day for the Study 1 series: 34 fronds at 6 h, 52 at 10 h, 71 at 14 h and 78 at 18 h. The count rises with light, more slowly above 14 h.

Table 1
Added nitrate (mg/L)Fronds after 10 days (fronds)
048
563
1071
2074
Table 1 (Study 2) lists the added nitrate concentration and the number of fronds after 10 days: 48 at 0 mg/L, 63 at 5 mg/L, 71 at 10 mg/L and 74 at 20 mg/L. The count rises with nitrate, then levels off.

Which factor was held constant in Study 1 but varied in Study 2?

  1. The number of hours of light per day
  2. The temperature of the pond water
  3. The concentration of added nitrateAnswer
  4. The number of fronds counted at the end

How to solve it

  1. List the Study 1 constants from its setup: 20 fronds, 200 mL of pond water, 10 mg/L of added nitrate, 25 °C. Study 1 varied light (Figure 1).
  2. List the Study 2 constants: 20 fronds, 200 mL, 25 °C, 14 h of light. Study 2 varied nitrate (Table 1).
  3. The factor on the Study 1 list that becomes the varied factor in Study 2 is nitrate: choice C. Light is the reverse case, varied in Study 1 and constant in Study 2.

Why each choice is right or wrong

  • A. Incorrect. This reverses the studies: light varied in Study 1 (6 to 18 h in Figure 1) and was held at 14 h in Study 2.
  • B. Incorrect. Both studies kept the water at 25 °C, so temperature was constant in Study 2 as well.
  • C. Correct. Study 1 gave every beaker 10 mg/L of added nitrate, and Study 2 gave the beakers 0, 5, 10 and 20 mg/L (Table 1).
  • D. Incorrect. The frond count was measured in both studies (Figure 1 and Table 1). It is the dependent variable, so it is never held constant.

Trap Calling the result a controlled variable

A controlled variable is set to the same value before the trials begin: 200 mL of water, 25 °C, 20 starting fronds. The frond count at the end is a result, even when two beakers happen to finish with the same number. If a question asks for a controlled variable, ask: could the students have chosen this value ahead of time? If not, it is the dependent variable.

Also watch the study the question names. Nitrate was controlled in Study 1 and varied in Study 2, so the right label depends on which study you are asked about.