7.3 Determining Sample Size and Dealing with Non-response

Determining sample size is crucial for accurate research. It depends on confidence levels, margins of error, and population size. Researchers use formulas to calculate ideal sample sizes, considering factors like population variability, costs, and time constraints.

Non-response in surveys can lead to reduced sample sizes and biased results. To combat this, researchers use strategies like offering incentives, sending reminders, and using mixed-mode surveys. These methods help increase response rates and maintain sample representativeness.

Sample Size Determination

Sample size calculation methods

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• Sample size depends on level of confidence (95%, 99%), higher confidence requires larger samples
• Margin of error (±3%, ±5%), smaller margins require larger samples
• Population size (1,000, 10,000, 100,000), larger populations require larger samples but effect diminishes as size increases
• Formula for calculating sample size for a proportion: $n = \frac{Z^2 * p * (1-p)}{e^2}$
  • $n$ = sample size
  • $Z$ = Z-score for desired confidence level
  • $p$ = estimated proportion with characteristic of interest
  • $e$ = desired margin of error
• Adjust sample size for finite populations using finite population correction factor: $n_{adjusted} = \frac{n}{1 + \frac{n-1}{N}}$
  • $N$ = population size

Factors in sample size determination

• Variability of population, more heterogeneous populations require larger samples to capture diversity
  • Homogeneous populations require smaller samples
• Cost constraints, larger samples more expensive due to recruitment costs, incentives, data collection and processing
  • Budget limitations may necessitate smaller samples
• Time constraints, tight deadlines may limit feasible sample size
  • Larger samples require more time for recruitment, data collection, analysis
• Researchers must balance desired precision, cost and time constraints
  • Trade-offs may be necessary to ensure study is feasible and delivers meaningful results

Dealing with Non-response

Non-response causes and consequences

• Causes include refusal to participate, inability to reach respondents, incomplete or invalid responses
• Consequences:
  • Reduced sample size decreases statistical power, increases margin of error
  • Non-response bias occurs when non-respondents differ systematically from respondents
    • Leads to biased estimates and inaccurate conclusions
  • Impaired sample representativeness, non-response distorts sample's representation of target population
    • Limits generalizability of findings
• Non-response can lead to over or under-representation of certain subgroups
  • Skews sample composition, affecting accuracy of population estimates

Strategies for increasing response rates

• Incentives like monetary rewards (cash, gift cards) or non-monetary rewards (personalized feedback, prize draw entry)
  • Motivate participation and increase response rates
• Reminders via follow-up emails, calls or messages encourage non-respondents to participate
  • Multiple reminders sent at predetermined intervals help convert initial non-respondents
• Mixed-mode surveys combine different modes (online, phone, mail) to reach respondents
  • Allows respondents to choose preferred participation mode
  • Increases likelihood of reaching diverse sample and improving response rates
• Personalization by addressing respondents by name, tailoring survey content to interests or characteristics
  • Increases engagement and motivation to participate
• Timing and duration, launching surveys at optimal times (avoiding holidays, busy periods)
  • Providing sufficient time for respondents to complete survey
  • Balancing need for timely data with desire for higher response rates