Question

How would you go about selecting a representative sample for a survey of all students in your school if the objective of the survey were to answer the following questions:

1. Do students with many brothers and sisters do better or worse in studies compared to those with only one brother or sister (or none)?
2. What is the most popular break-time activity for students in the primary school (Classes I-V), middle school (Classes VI-VIII), secondary school (Classes IX-X) and senior secondary school (Classes XI-XII)?
3. Is a student’s favourite subject likely to be the subject taught by the favourite teacher? Is there any difference between boys and girls in this regard?

(Note: Make different sample designs for each of these questions).

Answer 1

Based on the prompt in activity, designing these surveys requires moving from abstract sociological theory to applied quantitative methodology. To avoid the “unrepresentative sample” bias discussed in the previous activity, each research question demands a distinct sampling strategy.

Here is a methodological breakdown for selecting a representative sample for each specific objective:

1. Sibling Count and Academic Performance:
   • The Objective: To compare students with many brothers and sisters against those with only one or none.
   • Sample Design: Stratified Random Sampling (by Sibling Count). A simple random sample of the whole school might accidentally capture too few students from large families. Instead, you would use school admission records to divide the entire student population into two distinct strata: “0-1 siblings” and “2+ siblings.” You would then randomly select an equal number of students from each stratum to ensure you have a statistically significant sample size to compare their academic results.
2. Break-Time Activities Across School Levels:
   • The Objective: To identify the most popular break-time activity across Primary (Classes I-V), Middle (Classes VI-VIII), Secondary (Classes IX-X), and Senior Secondary (Classes XI-XII).
   • Sample Design: Stratified Sampling with Proportionate Allocation. The school population is already naturally divided into these distinct academic blocks (similar to standard educational board structures). Because the primary section often has a much larger total enrollment than the senior secondary section, you must sample proportionately. If Primary students make up 40% of the school, they should make up 40% of your total sample. You would randomly select students from within each of these four strata to ensure every age group's unique peer-group behavior is accurately captured.
3. Teacher Influence and Gender Differences:
   • The Objective: To determine if a favourite subject is tied to a favourite teacher, and if this differs between boys and girls.
   • Sample Design: Cluster Sampling followed by Stratification. Since students experience teachers collectively within a classroom setting, it is most efficient to use classrooms as your primary sampling unit. You would randomly select intact sections (clusters) from various grades. Once the surveys are administered within those selected classrooms, you would systematically stratify the data by gender during the analysis phase to isolate whether boys and girls relate differently to institutional authority figures.