Independent and dependent variables

The student chose four widths (the factor she changed) and measured the height of the wet front (the response).

• Correct: Independent: width of the strip. Dependent: height the water climbed in 10 minutes.: Correct: she set the width and measured the height.
• Independent: height the water climbed. Dependent: width of the strip the student cut.: This reverses them; the height is what she measured, not what she set.
• Independent: the type of filter paper. Dependent: the time the strips were left in water.: Paper type and time were kept the same for every strip; they are controlled variables.
• Independent: the 10-minute time limit. Dependent: the width and the height of each wet strip.: The time was fixed for all strips, and the width was chosen, not measured.

Controlled variables are kept the same for every strip: the same filter paper, the same 10 minutes and the same 1 cm dipped in.

• Correct: Type of paper: Controlled: every strip was cut from the same filter paper.
• Width of the strip: Not controlled: width is the independent variable, the factor deliberately changed.
• Correct: Time before measuring: Controlled: every strip was measured after 10 minutes.
• Height of the wet front: Not controlled: height is the dependent variable, the measured result.
• Mean height for each width: Not controlled: the mean height is calculated from the dependent variable after the run.

The means (6.1, 6.2, 6.0, 6.1 cm) differ by less than the spread within each width (strips of the same width differ by up to 0.5 cm). There is no trend with width.

• Correct: Over this range, strip width had no clear effect on how high water climbed in 10 minutes.: Correct: the differences between means are smaller than the differences among repeats of the same width.
• Wider strips pulled water higher, because a wider strip has more paper for water to stick to.: The means do not rise with width: 4.0 cm strips averaged the same as 0.5 cm strips.
• Narrower strips pulled water higher, because their mean height at 0.5 cm was the largest value.: The 0.5 cm mean (6.1 cm) is not the largest, and a 0.1 cm difference is far smaller than the variation among repeats.
• The investigation failed, because a well-designed experiment shows a difference between groups.: A result showing no effect is a real finding when the design is sound; experiments test, they do not have to show a change.

Moving air carries water vapor away from the surface and speeds evaporation. Because the fan was only in the 40 °C cabinet, the 40 °C group differed in two ways, so the extra loss cannot be credited to temperature alone. Air movement should have been a controlled variable.

• Correct: Only the 40 °C cabinet had a fan, so moving air was a second difference between the groups.: Correct: two factors changed together, so their effects cannot be separated.
• Three dishes per temperature is too few repeats for any comparison of the means to be made.: Three repeats is few, but the 40 °C dishes (6.9-7.5 g) do not overlap the others; the bigger problem is the second difference.
• The dishes were weighed at the start, which could have disturbed the water before the experiment.: Every dish was weighed the same way, so weighing is the same in every group and cannot explain a difference.
• Mass of water lost is a dependent variable, so it is not possible to control it during the experiment.: The dependent variable is measured, not controlled, but that is how every experiment works, not a weakness.

An if-then prediction starts with the independent variable (temperature), states the expected change in the dependent variable (mass lost) and gives a reason (more molecules can break free of their hydrogen bonds).

• Correct: If the water temperature is higher, then more water will evaporate in 24 hours, because more molecules have enough energy to break their hydrogen bonds and escape.: Correct: IV in the "if", DV in the "then", reason after "because".
• If water evaporates, then the temperature of the cabinet will rise, because evaporation releases heat into the surrounding air and warms the inside of each cabinet.: This reverses the variables, and evaporation removes heat from what is left behind rather than releasing it.
• If the dishes are identical, then the experiment will be fair, because identical dishes hold the same mass of water.: This describes a controlled variable, not a prediction about the dependent variable.
• If more water is lost, then the temperature was higher, because hot water evaporates.: This runs backward, from result to cause, and the reason simply repeats the claim.

A control group gets the baseline condition (no warming) while everything else matches the experimental groups: same dishes, same mass, same cabinet type and the same time.

• Correct: Three identical dishes of 50.0 g water left at room temperature in a cabinet that is switched off, with no fan: Correct: baseline temperature, everything else identical, with repeats.
• Three dishes of 50.0 g water at 50 °C, to extend the range of temperatures that were tested: A 50 °C group is another experimental group, not a no-warming baseline.
• One dish of 50.0 g water sealed with a lid in the 40 °C cabinet, to show what happens when no water can escape the dish: A sealed dish changes a different factor (open versus closed) and is a single dish, so it is not the baseline for open dishes.
• Three dishes holding 100.0 g of water at 20 °C, so that more water is available to evaporate: Changing the mass of water adds a second difference instead of providing a baseline.