Notes on Bias and Simple Random Sampling (SRS)

Bias types to avoid

  • Interviewer bias: phrasing or tone can tilt the respondent's answer.
  • Volunteer bias: volunteers are often more extreme; not representative of the whole group.
  • Remedy: avoid relying on volunteers; use sampling techniques that include a broader, representative group.

Simple Random Sampling (SRS)

  • Abbreviation: SRS (common in papers).
  • Goal: every member of the population has an equal chance of selection.

Sampling frame

  • Definition: list of all potential participants.
  • Example: list of all students from the registrar.
  • After obtaining the list, assign numbers 1 through N to the frame.

Random numbers and randomness

  • Random number table (historical) vs. technology-based methods (Excel, TI-84, Google Sheets, random.org).
  • True random vs pseudorandom:
    • True random: no underlying rule; every number is equally likely.
    • Pseudorandom: generated by algorithms; not truly random.
  • Probability in true random sampling: P(i)=1NP(i) = \frac{1}{N} for all i in the sampling frame.
  • How to read a random-number table: read left-to-right; decide digits per number based on N (e.g., two digits if N ≤ 99).

Procedure: from numbers to sample

  • Use the random numbers to pick individuals from the sampling frame by their assigned numbers.
  • Map each selected number to the corresponding participant in the frame.

Example: Governors from 50 states

  • Population: 50 governors, numbered 01–50.
  • Desired sample: 10 governors.
  • Read two digits at a time from the random-number source; each two-digit number selects a governor.
  • This yields a simple random sample with no deliberate bias in selection.