Three Groups to Name Clearly
In Mixed Practice: Planning a Statistical Study, we practiced matching a study question to a population, variables, and a data-collection plan. This tutorial makes one part of that plan precise: identifying the population, the sampling frame, and the sample. The terms are related, but they do not mean the same thing.
Suppose a school wants to learn how many hours its Grade 9 students spend on homework in a typical week. The school needs to be clear about which students its question is about, which list it will use to find students, and which students will actually be selected. If these groups are confused, a conclusion may describe a different group from the one the question intended.
The population is defined by the study question, including any boundaries such as school, grade, and date. The frame is a practical source for locating members of that population. Ideally, the frame includes every population member and no one outside the population. In practice, a frame can be incomplete or contain ineligible entries, so the frame and population may not match.
A sample is not the same as the entire frame. If a school has a list of 40 students and selects 8 of them, the list is the frame and the 8 selected students are the sample. The population might be those 40 students, or it might be a larger or differently defined group. You have to use the study description to tell.
A useful way to keep the terms straight is to ask three questions in order: Who do we want to learn about? What list or source will we use to find them? Who was selected? These questions correspond to the population, sampling frame, and sample.
Worked Example: A Roster of 40 Grade 9 Students
Worked Example: Homework Time at Northview High
Northview High wants to estimate weekly homework time for all Grade 9 students currently enrolled on October 9. Its Grade 9 roster, checked on October 9, contains 40 students. The school selects students with IDs R03, R08, R14, R19, R24, R29, R33, and R38 for a survey. Identify the population, sampling frame, and sample.
| R01 | R02 | R03 | R04 | R05 | R06 | R07 | R08 | R09 | R10 |
|---|---|---|---|---|---|---|---|---|---|
| R11 | R12 | R13 | R14 | R15 | R16 | R17 | R18 | R19 | R20 |
| R21 | R22 | R23 | R24 | R25 | R26 | R27 | R28 | R29 | R30 |
| R31 | R32 | R33 | R34 | R35 | R36 | R37 | R38 | R39 | R40 |
Population: All Grade 9 students enrolled at Northview High on October 9. The date and grade make the intended group specific. Since the roster was checked on that same date and is stated to contain all 40 such students, the population has 40 members.
Sampling frame: The school’s October 9 Grade 9 roster, shown above. It has 40 entries, one for each student in the stated population.
Sample: The 8 selected students: R03, R08, R14, R19, R24, R29, R33, and R38. The selected sample has 8 members. The other 32 roster entries are not part of this sample.
This example has a perfect match between the population and frame: every population member appears once on the roster, and no one outside the population appears. That does not make the population and frame interchangeable concepts. One is the group of interest; the other is the list used to locate that group. The distinction matters as soon as those sets differ.
Also notice that the IDs are labels, not measurements of homework time. The study would record a homework-time response for each selected student. As in Deciding Which Variables to Measure, the variable still needs a clear definition, such as the number of hours spent on homework during the previous seven days.
When the Frame and Population Do Not Match
A sampling frame can miss some population members, include people who are not eligible, or do both. An eligible person missing from the frame is an omission. An ineligible person listed on the frame is an extra entry. These differences matter because a person cannot be selected from a list that does not include them, and an ineligible entry might be selected instead of a population member.
To identify a mismatch accurately, use one consistent reference date. Decide who belongs to the population on that date, then check who is included on the frame for that same date. Avoid inferring someone’s eligibility from a later or earlier roster without knowing when their status changed.
Worked Example: An Out-of-Date Grade 10 Roster
Worked Example: Who Is on the October 9 List?
A school plans to estimate weekly library visits among all students currently in Grade 10 on October 9. Its roster contains 40 entries. The school checks each entry against October 9 enrollment records and finds that 2 listed students transferred out of Grade 10 before October 9. It also confirms that 4 students were enrolled in Grade 10 by October 9 but were missing from the roster. Identify the population and frame, and count the eligible students represented on the list.
Population: All students enrolled in Grade 10 at the school on October 9. This is the target group specified by the question. The 2 students who transferred out before October 9 are not members of this population. The 4 students enrolled by October 9 are members.
Sampling frame: The 40-entry roster used to select students. It is the frame even though its entries do not match the population exactly.
Eligible population members on the frame: Of the 40 entries, 2 are ineligible on October 9. Therefore, 38 listed students are members of the October 9 population. Four additional population members are not listed. The frame has 40 entries, but it contains only 38 of the population members.
Population size: There are 38 eligible listed students plus 4 eligible students omitted from the roster, so the population has 42 members.
These counts are consistent in two directions: the population has \(42\) members, of whom \(38\) appear on the roster and \(4\) do not; the roster has \(40\) entries, of whom \(38\) are eligible and \(2\) are not. The roster is therefore not a complete and exact list of the population.
If the school selects from this roster, the 4 omitted students cannot be selected from it, while either of the 2 ineligible entries could be selected. The term sample refers to the individuals actually selected from the frame; it does not change the population definition. The mismatch is a reason to examine the frame before treating a selected group as representing the intended population.
The reference date prevents a common logic error. The example explicitly says the 2 transfers happened before October 9 and the 4 omitted students were enrolled by October 9. Without those facts, their October 9 eligibility could not be determined merely from the roster’s size.
Selected Students and Respondents Are Not Always the Same Group
A study may select a sample and then find that some selected people do not provide data. Keep the selection step separate from the response step. The selected individuals remain the sample the study set out to contact; the people who actually answer are the respondents. A difference between those groups may affect what the collected data represent, but it does not turn the frame into the sample.
Worked Example: A Sample of 10, With 8 Responses
Worked Example: The Grade 11 Reading Survey
A school wants to describe minutes spent reading for pleasure in a typical week among all Grade 11 students enrolled on October 9. Its current Grade 11 roster has 40 students. The school selects 10 students from that roster and sends each the same survey. Eight selected students return it. Identify the population, frame, sample, and respondents.
Population: All Grade 11 students enrolled at the school on October 9. The question is about this complete group, not only the students who return the survey.
Sampling frame: The October 9 Grade 11 roster of 40 students. The scenario gives no indication of missing or ineligible entries, so for this example we treat the roster as an accurate list of the population.
Sample: The 10 students selected from the roster. The sample size is 10, whether or not all selected students respond.
Respondents: The 8 selected students who return the survey. Two of the 10 selected students do not return it. Thus the respondent count is 8, while the sample selected for the survey is still 10.
The 8 responses provide data about 8 people, but the study’s selected sample consists of 10 people. If a report says “we surveyed a sample of 8,” it may be describing the number of responses imprecisely. A clearer statement is: “Ten students were selected, and eight responded.”
The population has 40 members in this example, the frame lists all 40, and 10 are selected. The 8 respondents are a subset of those 10 selected students. Keeping each count attached to its correct group helps explain how the data were collected without silently shrinking the population to the people who answered.
A Reliable Identification Routine
When a study description includes a group and a list, use this sequence. It applies the distinctions from Defining the Population of Interest and Census Versus Sample without assuming that the list itself defines the study’s goal.
Name the people or observational units, location, and relevant date or time period that define who the study aims to learn about.
Identify the roster, database, or other source from which individuals will be selected. That source is the sampling frame.
List or count the individuals chosen from the frame. That selected group is the sample.
At the same reference date, look for population members missing from the frame and frame entries outside the population. If data collection has begun, separately count respondents.
This routine does not decide whether the sample is representative; it only identifies the groups and checks the list against the intended population. As discussed in Sources of Variability in Collected Data, results can vary across samples. The next tutorial, Why Random Selection Matters, will explain why the method used to select a sample is important. For now, do not treat the mere existence of a list or a selected group as proof that it represents the population well.
Common Mistakes and Full-Credit Communication
- Calling the roster the population automatically. A roster is the frame when it is the source used to select people. The population comes from the study question and may be larger, smaller, or differently bounded.
- Calling everyone on the frame the sample. If only a subset is selected, that subset—not the full list—is the sample. In the 40-student example, the roster is the frame and the 8 selected students are the sample.
- Defining a population without a boundary. “Grade 10 students” may be unclear if the school, enrollment status, or date matters. Say, for example, “all Grade 10 students enrolled at the school on October 9.”
- Ignoring extra or missing entries. A frame can contain ineligible people and omit eligible ones. State which mismatch occurs and, when possible, count each group explicitly.
- Confusing selected students with respondents. A student who was selected but did not answer is still part of the selected sample. Report both counts when they differ.
- Using dates loosely. Do not decide who belongs to a population on one date using status information from another date unless the timing is stated. Full-credit reasoning uses the same clearly stated reference date for the population and frame comparison.
A precise response can be short while still showing the distinctions: “The population is all Grade 9 students enrolled at Northview High on October 9. The sampling frame is the October 9 Grade 9 roster of 40 students. The sample is the 8 students selected from that roster: R03, R08, R14, R19, R24, R29, R33, and R38.” If the list has a mismatch, add the number and identity of omitted or ineligible members rather than claiming that the frame and population are identical.
Check Your Understanding
For each situation, identify the population, sampling frame, and sample. State any mismatch or difference between selected people and respondents.
- A school wants to learn about current Grade 8 students. Its current roster lists 36 students, and 9 are selected. What are the population, frame, and sample?
- A survey concerns all students enrolled at a school on May 1. A May 1 roster lists 50 students, including 3 who transferred out before May 1, and omits 2 who enrolled by May 1. How many population members are represented on the list, and how many are in the population?
- A club has a current list of 24 members. Six are selected for a survey, but only 5 return it. Which number is the sample size, and which number is the respondent count?
- A study asks about students in one school district, but the only available frame is one high school’s Grade 11 roster. Explain why the frame is not the same as the population.
- Why should a description of population membership and frame accuracy use a consistent reference date?