What Is Varied, and What Is Measured?
In Experimental Units, Factors, and Treatments, you learned to identify what receives an assigned condition, what feature is deliberately varied, and which condition each unit receives. This tutorial connects those ideas to the variables in an experiment. The feature researchers deliberately vary is the explanatory variable. The measured outcome is the response variable.
For example, if a researcher assigns seedlings to different amounts of light and later measures their height, the amount of light is the explanatory variable. The height is the response variable. Asking these two questions—“What condition is assigned?” and “What is measured as an outcome?”—helps keep the experiment’s variables distinct.
A factor names the general feature under study; its levels name the particular settings or categories. In the seedling example, “amount of light” is the factor, while “full sunlight” and “partial shade” are its levels. The seedlings’ height, measured in centimeters after a stated period, is the response variable.
The response does not have to be a number. Researchers might record whether each seedling survives (yes or no), a category, or measure its height, a numerical variable. In either case, the response variable is what the researchers record as an outcome. A particular recorded value—such as a height of 12.4 centimeters—is one observation of that variable, not a different variable.
A Reliable Identification Routine
The factor, levels, and response are easiest to identify when you work from the study description rather than from isolated words. First find the condition that researchers assign or control. Then name the factor and list the specific levels. Finally, locate what researchers measure for each experimental unit and describe how it is recorded.
Ask what feature researchers assign or control. Name it as the explanatory variable, or factor.
Write the specific conditions or categories of the factor. If there is more than one factor, list the levels for each factor separately.
Name the response variable and include its units, categories, measurement method, or timing when the description provides them.
The factor is assigned or controlled; the response is recorded as an outcome. Do not label a measured outcome as a treatment.
For a clear description, state the role and the context: “The factor is the fertilizer condition, with levels of no fertilizer and fertilizer. The response is plant height in centimeters, measured four weeks after planting.” This is more informative than simply listing “fertilizer” and “height,” because it distinguishes the levels and explains how the response is measured.
Not every variable mentioned in a study is one of its experimental factors or its response. Researchers may record background information, such as a participant’s age, or keep a condition the same for everyone. Those details may help describe the study, but they are not necessarily deliberately varied explanatory variables. Identify the study’s question and assignment before deciding what role each variable plays.
Worked Example: A Categorical Response
Worked Example: Testing Two Seed Treatments
A fictional greenhouse team assigns 80 seeds to one of two soaking conditions before planting: plain water or a mild nutrient solution. Fourteen days after planting, the team records whether each seed has produced a sprout.
Identify the explanatory variable: The explanatory variable, or factor, is the seed-soaking condition. It is the feature the team deliberately assigns to the seeds.
Identify the levels: The two levels are soaking in plain water and soaking in the mild nutrient solution. These are the specific conditions of the factor. In this one-factor experiment, they are also the two treatment conditions.
Identify the response: The response variable is whether a seed has produced a sprout by day 14. Its possible recorded categories are “yes” and “no,” so this response is categorical rather than numerical.
Keep the variable separate from its values: “Whether the seed has sprouted by day 14” names the response variable. For one particular seed, “yes” is its recorded response value. The number of seeds that sprout could be summarized later, but it is not the factor being assigned.
Conclusion: The factor is seed-soaking condition, with levels of plain water and nutrient solution. The response is sprouting status 14 days after planting. A complete identification names both the outcome and when it is assessed.
Specify What the Response Measures
A response label can be too vague to identify what researchers actually recorded. “Plant growth,” “health,” or “performance” may describe a broad idea, but a measurement plan needs a specific variable. As in the earlier tutorial Deciding Which Variables to Measure, define what is recorded for each unit and use suitable units or categories.
For example, “plant growth” could mean height, number of leaves, or change in height over a stated period. These are not interchangeable responses. Likewise, “sleep quality” could be a rating on a defined scale, the number of times a participant wakes, or hours slept. Naming the measurement prevents readers from having to guess what the researchers mean.
When a study records more than one outcome, it has more than one response variable. Researchers might measure both a plant’s height and its number of leaves. Those two outcomes should be named separately, even though the same factor is used to compare conditions. The response variables need not have the same type or units.
Worked Example: A Numerical Response
Worked Example: Comparing Two Cooling Settings
A fictional engineering class tests two fan settings on 30 identical model devices. The class randomly assigns 15 devices to the low setting and 15 to the high setting. After each device runs for 20 minutes, students record its surface temperature in degrees Celsius.
Identify the explanatory variable: The factor is fan setting. It is deliberately varied by assigning each device to one of the two settings.
Identify the levels: The levels are low fan setting and high fan setting. They are specific assigned conditions, not measurements taken from the devices.
Identify the response: The response variable is the device’s surface temperature, measured in degrees Celsius after 20 minutes of operation. Temperature is numerical.
Distinguish the variable from a recorded value: “Surface temperature after 20 minutes” is the response variable. If a particular device has a recorded temperature of 34.2°C, that number is an observed value of the response. It is not another factor level.
Conclusion: The explanatory factor is fan setting, with low and high as its levels. The response is surface temperature in degrees Celsius after 20 minutes. The units and timing make the response precise.
When an Experiment Has More Than One Factor
Some experiments deliberately vary more than one feature. Name each factor separately and list its levels before describing the response. As in the earlier tutorial on experimental units, factors can be combined to form treatments. But the response remains the outcome or outcomes measured on the units; it is not one of those combinations.
Suppose researchers vary both the type of packaging and the storage temperature for a food sample. Packaging type and storage temperature are two explanatory variables. If each packaging condition is used at each temperature, each experimental unit receives a combination of levels. The response might be the number of days until visible spoilage. That measured outcome is distinct from both factors.
A useful table makes these roles visible. Keep one row for each factor and another for the response, instead of placing every study detail in one list.
| Role in the experiment | Example description |
|---|---|
| Explanatory variable (factor) | Packaging type |
| Levels of that factor | Paper wrap; reusable container |
| Second explanatory variable (factor) | Storage temperature |
| Levels of the second factor | Cool storage; room-temperature storage |
| Response variable | Days until visible spoilage |
Worked Example: Two Factors and Two Responses
Worked Example: Testing Seedling Conditions
A fictional garden program grows 48 seedlings. Each seedling is assigned one of two light conditions—bright indirect light or partial shade—and one of two watering schedules—watering every day or every other day. After four weeks, the program records each seedling’s height in centimeters and whether it is alive.
Identify the explanatory variables: There are two factors: light condition and watering schedule. Both are deliberately varied by the program.
List the levels of each factor: Light condition has the levels bright indirect light and partial shade. Watering schedule has the levels every day and every other day. Keeping these lists separate makes clear which feature each set of levels belongs to.
Describe the treatment combinations: Each treatment combines one light level with one watering level. The four combinations are bright indirect light with daily watering, bright indirect light with watering every other day, partial shade with daily watering, and partial shade with watering every other day.
Identify the responses: There are two response variables. The first is seedling height after four weeks, measured in centimeters. The second is survival after four weeks, recorded as alive or not alive. Height is numerical; survival status is categorical.
Conclusion: The explanatory factors are light condition and watering schedule, each with two stated levels. The responses are height in centimeters and survival status, both assessed after four weeks. The four treatment combinations are assigned conditions; neither measured outcome is a treatment.
Common Mistakes and AP Exam Tips
- Calling the response the factor. A quiz score, temperature, or sprouting status is generally an outcome if it is recorded after conditions are assigned. Name the assigned feature as the factor and the measured outcome as the response.
- Giving only a broad factor name. “Light” may identify the factor, but a complete answer also lists its levels, such as bright indirect light and partial shade.
- Listing levels without saying which factor they belong to. In a study with two factors, label each set of levels. Otherwise, readers may not know whether “daily” refers to watering, exposure, or something else.
- Using a vague response label. “Growth” does not say exactly what was recorded. “Seedling height in centimeters after four weeks” is specific and interpretable.
- Confusing a variable with one observed value. “Surface temperature in degrees Celsius” is a response variable; a recorded value such as 34.2°C is one observation of it.
- Assuming every recorded variable is a response. Background details may be collected without being outcomes of interest. Explain which variable is measured as the experimental outcome rather than merely appearing in the study description.
- Suggesting the labels alone prove causation. Identifying a factor and response clarifies the study’s roles; it does not by itself establish what conclusions the design supports. As discussed in Experiments and Why They Can Show Cause, the design matters too.
For full credit, use complete, contextual statements: “The factor is fan setting, with low and high as its levels. The response is each device’s surface temperature in degrees Celsius after 20 minutes.” If there are two factors or multiple outcomes, name every one and keep each role clear.
Check Your Understanding
For each scenario, identify the explanatory variable or variables, their levels, and the response variable or variables. Include measurement details when provided.
- A fictional bakery assigns loaves to two proofing times, 40 minutes or 60 minutes, then measures loaf height in centimeters after baking. Identify the factor, levels, and response.
- A researcher assigns houseplants to either a standard fertilizer or no fertilizer. After six weeks, the researcher records whether each plant has flowers. Is the response numerical or categorical? Identify the factor and its levels.
- A fictional sports program assigns athletes to either a short warm-up or a longer warm-up and records the time each athlete takes to complete a course, in seconds. Identify the explanatory variable and response precisely.
- A classroom experiment varies both screen brightness (low or high) and text size (small or large). Students then rate reading comfort on a scale from 1 to 5. Identify the factors, their levels, and the response.
- A study assigns rechargeable batteries to two charging modes and records both the number of hours each battery operates and whether it becomes unusually warm. How many response variables are recorded, and what are they?