Two Kinds of Groups, Two Different Jobs
In Randomized Block Design, you learned that researchers form groups of similar experimental units and then randomly assign treatments separately within each group. In Stratified Random Sampling, the population is divided into groups, and a random sample is selected from every group. The groups may look similar in the two methods, but the purpose of the groups—and what chance determines—are different.
The key question is: What is the study doing with the groups? In an experiment, blocks help organize the assignment of treatments. In a sample, strata help organize the selection of people or other individuals from a population. Identifying whether the study is assigning treatments or selecting a sample is the first step to naming the method correctly.
For example, suppose students are grouped by their prior reading scores. If researchers randomly assign a reading program to students within each score group, those groups are blocks. If a school randomly selects students from every score group to estimate the opinions of all students, those groups are strata. The characteristic used to form the groups could be the same; the study’s action with those groups determines the name.
Blocking Versus Stratifying: A Side-by-Side Comparison
| Question | Blocking in an experiment | Stratifying in a sample |
|---|---|---|
| What is divided into groups? | Experimental units, such as people, plants, or objects in the experiment | The population from which the sample will be selected |
| What are the groups called? | Blocks | Strata |
| What happens within every group? | Treatments are randomly assigned to experimental units | Individuals are selected at random for the sample |
| What is the grouping meant to help with? | Organizing a treatment comparison so each treatment is represented among units with similar values of a relevant variable | Ensuring that every stratum is represented in the sample; stratification can reduce sampling variability when individuals within strata are similar on the variable of interest |
| Where does chance act? | In the assignment of treatments within each block | In the selection of individuals within each stratum |
| What is the main question? | How should treatments be assigned to the experimental units? | How should individuals be selected from the population? |
In a randomized block design, the researcher uses information about experimental units to form blocks before applying treatments. Then chance determines which units in each block receive each treatment. As explained in Why Random Assignment Is the Key to Causation, random assignment helps make treatment groups comparable on average.
In stratified random sampling, the researcher divides the population into strata and randomly selects individuals from every stratum. The sample may include different numbers from different strata. As in the earlier tutorial on Stratified Random Sampling, the selection plan specifies how the random samples are taken within the strata. Stratification is about selecting the sample, not assigning treatments.
These methods also connect to different questions of inference. Random selection can support generalizing findings to the population from which the sample was selected. Random assignment can support a cause-and-effect conclusion about treatments. As discussed in Scope of Inference: Four Combinations, selection and assignment are separate features; having one does not automatically mean a study has the other.
Worked Example: Comparing Two Study Strategies
Worked Example: Reading Scores as Blocks
A fictional school wants to compare two study strategies for a unit test. The response is each student’s test score, measured in points. Before the study, the school groups 30 participating students into three blocks based on a reading assessment: 8 students with lower scores, 12 with middle-range scores, and 10 with higher scores. Within each block, the school will randomly assign students to Strategy A or Strategy B.
Classify the design: These groups are blocks, not strata. The students are experimental units, and the study uses the groups to organize treatment assignment. The school is not taking a sample from each group to estimate an opinion or describe a population characteristic; it is assigning strategies to the participating students.
Plan the assignment: Within the lower-score block of 8 students, randomly assign 4 to Strategy A and 4 to Strategy B. Within the middle-range block of 12 students, randomly assign 6 to each strategy. Within the higher-score block of 10 students, randomly assign 5 to each strategy. The school could use a chance process separately within each block to determine who receives Strategy A; the other students in that block receive Strategy B.
Check the design: Both strategies appear in all three blocks, and chance determines assignments within each block. The blocks do not all have the same size, so the number assigned to each strategy is not the same in every block. Here the total is 15 students per strategy: \(4+6+5=15\).
Conclude: This is a randomized block design because students are grouped by a variable measured before treatment and are randomly assigned to strategies within each group. Reading score is the block variable; study strategy is the treatment factor; and test score is the response. Blocking organizes the comparison by prior reading level, but it does not tell the school which strategy will produce higher scores.
The assignment counts in this example follow from the stated sizes of the blocks. If the school had only said that there were 30 students in three reading-level blocks, without giving the size of each block, it could not claim that each block contained 10 students or specify equal assignments of 5 per strategy in every block. It could instead state a plan to assign the treatments as evenly as possible within each block, provided the exact allocation is determined from the actual block sizes.
Worked Example: Selecting a Sample From Every Department
Worked Example: Departments as Strata
A fictional company wants to estimate the proportion of its employees who favor a proposed change to work schedules. The company has 240 employees: 120 in production, 72 in sales, and 48 in administration. It divides the employees by department, then uses a random process to select 20 employees from each department for a survey.
Classify the design: The departments are strata because they are groups in the population used to organize random selection. The company randomly selects employees within every department. It does not assign treatments to the employees, so this is not a randomized block design.
Describe what chance does: The company uses a separate random selection to choose 20 of the 120 production employees, 20 of the 72 sales employees, and 20 of the 48 administration employees. The resulting sample has \(20+20+20=60\) employees, with members from all three departments.
Interpret the plan: The plan ensures that every department is represented in the sample. It does not select the same proportion of employees from each department: the sample includes 20 of 120 production employees, 20 of 72 sales employees, and 20 of 48 administration employees. The company should describe the sampling plan accurately when it reports how the sample was obtained. To estimate the company-wide proportion, weight each department’s sample proportion by its share of the workforce: \(\frac{120}{240}\hat p_{\text{production}}+\frac{72}{240}\hat p_{\text{sales}}+\frac{48}{240}\hat p_{\text{administration}}\).
Conclude: This is stratified random sampling. The company divides the population into strata and selects individuals at random within each stratum. The aim is to obtain information from every department, not to compare assigned work-schedule treatments.
Notice that equal sample counts across strata do not make the plan an experiment. Nor does using the same kind of grouping characteristic—such as department—in itself determine the design. The method is stratified sampling because chance is used to select employees from the groups.
Worked Example: One Study Can Use Both Methods
Worked Example: Sample by Age, Then Assign Treatments Within Age Blocks
A fictional research team wants to compare two reminder messages for encouraging adults to attend a free health-screening appointment. The team’s target population is adults registered with a local clinic. It divides the clinic’s roster into two age strata: ages 18–44 and ages 45 or older. It randomly selects 40 adults from each stratum to take part in the study. Among the 80 selected adults, the team then forms two age blocks and randomly assigns 20 adults in each block to Message A and 20 to Message B. The response is whether each person attends the appointment.
Classify the sampling step: The age groups are strata when the team randomly selects 40 adults from each group. This is stratified random sampling because the groups organize selection from the clinic’s population.
Classify the assignment step: After the sample is selected, the same age groups serve as blocks when the team randomly assigns messages within each group. They are blocks at this stage because the groups organize treatment assignment among the experimental units.
Check the counts: The sample contains 40 adults in each age group. Within each age block, 20 are assigned to Message A and 20 to Message B. In total, 40 adults receive each message: \(20+20=40\). Each message is represented in both age groups.
Conclude: The study uses both stratified random sampling and a randomized block design, but at different stages. Stratified sampling selects participants from the population; blocking organizes the random assignment of messages to the selected participants. The stratified random sample can support generalizing to the population covered by the clinic roster; if the age strata differ in size, population-wide estimates should weight each age group’s sample result by that group’s share of the roster. Random assignment supports a cause-and-effect comparison of the messages for the participants in the experiment.
A study does not have to choose between the two methods if it includes both stages. Describe each stage separately: first explain how participants or units were selected, then explain how treatments were assigned. This prevents the word “random” from obscuring two different uses of chance.
Common Mistakes and AP Exam Tips
- Calling every group a block. Groups used to select a sample are strata. Reserve “blocks” for groups used to organize treatment assignment in an experiment.
- Calling every group a stratum. If participants are already in a study and treatments are randomized within groups, those groups are blocks for the assignment procedure.
- Using the characteristic alone to name the method. Age, department, or prior score can be used in either method. Identify what happens within the groups: selection or assignment.
- Confusing random selection with random assignment. Random selection chooses individuals from a population; random assignment allocates experimental units to treatments. State which one the study uses.
- Assuming that every group has the same size. A description of three blocks or strata does not imply equal counts. Use stated group sizes when describing the number selected or assigned.
- Claiming that either method guarantees a particular result. Stratified sampling does not guarantee that a sample statistic equals the population value, and blocking does not guarantee that treatments will have different outcomes or eliminate all variation.
- Claiming generalizability from blocking alone. Blocking organizes an experiment; it does not make the experimental units a random sample. Consider random selection and random assignment separately, as in Generalizing Results to a Population.
For a full-credit comparison, name what is being grouped, state whether chance selects individuals or assigns treatments, and explain the purpose of the grouping. If a study uses both methods, identify the sampling step and the assignment step separately.
Check Your Understanding
Classify each grouping as blocks, strata, or both, and explain where chance is used.
- A researcher randomly selects adults from each of three age groups to estimate the proportion who use a public transit app. Are the age groups blocks or strata? Why?
- An experiment groups plants by initial height and randomly assigns a fertilizer within each group. What are the groups called, and what is the treatment?
- A survey has 200 people divided into four neighborhood strata, but the description does not give each stratum’s size. Can you conclude that 50 people were selected from each? Explain.
- A study randomly selects participants from two job categories and then randomly assigns each participant to one of two training programs within job category. Identify where stratified sampling occurs and where blocking occurs.
- In one or two sentences, explain why random assignment within blocks does not by itself support generalizing results to a broader population.