Calculating Sample Size

Sample Size Calculation Guide for Probability Sampling

Key Parameters:

Population Size (N):
– Total individuals in your target group
– Only needed when population ≤ 100,000
– Example: 500 customers in a loyalty survey

Confidence Level:
– 90% (1.645), 95% (1.96), or 99% (2.576)
– Probability your results match the population

Margin of Error:
– ± Percentage for your results
– Common values: 3% (0.03) to 7% (0.07)

Estimated Proportion:
– Use 0.5 for maximum variability
– Example: 0.2 for 20% expected response rate

Calculation Formula:

Initial Sample Size:
n₀ = (Z² × p × (1-p)) ÷ e²

Adjusted Sample Size:
n = n₀ × N ÷ (n₀ + N – 1)

Example:

For 10,000 employees, 95% confidence,
5% margin, and p=0.5:
n₀ = (1.96² × 0.5 × 0.5) ÷ 0.05² = 385
n = 385 × 10,000 ÷ (385 + 9,999) ≈ 366

General Considerations for Non-Probability Sampling:

• No Statistical Formulas: There aren’t strict formulas to calculate a ‘minimum’ sample size in the same way as with probability sampling. The determination is often subjective and based on experience, judgment, and the specific goals of the study.
• Focus on Saturation (for Qualitative Research): In qualitative research (e.g., using convenience, purposive, or snowball sampling to conduct interviews or focus groups), a key concept is saturation. This means continuing to collect data until new information no longer emerges and you’re hearing the same themes and perspectives repeatedly.
• Goal-Oriented Approach: Think about the specific goals of your study. What kind of data do you need to collect? What specific subgroups do you need to include in your sample? The sample size should be sufficient to address these objectives.
• Available Resources: Practical considerations like budget, time, and access to participants play a significant role in determining the feasible sample size.

Strategies for Estimating Sample Size for Common Non-Probability Sampling Methods:

1. Convenience Sampling:

Description: Selecting participants who are easily accessible and available.

Sample Size Estimation:

Consider the scope of your study: A very broad scope requires a larger sample than a narrowly defined one.

Balance feasibility with representativeness (within your accessible population): Try to get as diverse a sample as possible within the convenient group. If you’re surveying students in a class, make sure you include students from different backgrounds, majors, etc.

Pilot testing: Conduct a small pilot study to get a sense of the variability in responses and refine your data collection methods. This can help you determine if you need a larger sample.

Example: A researcher wants to survey students about their opinions on a new campus policy. They survey students in their own classes. Sample size will depend on how many classes they teach and how many students are in those classes. They might aim for a certain percentage of the total student population in their classes.

• Purposive (Judgmental) Sampling:

Description: Selecting participants based on specific characteristics or expertise relevant to the research question.

Sample Size Estimation:

Identify key subgroups: Determine the specific subgroups or types of individuals you need to include to get a comprehensive understanding of the topic.

Ensure adequate representation of each subgroup: Aim for a sufficient number of participants within each subgroup to capture the diversity of perspectives.

Expert input: Consult with experts in the field to determine the appropriate sample size for each subgroup.

Example: A researcher wants to understand the experiences of CEOs in the tech industry. They purposively select CEOs from companies of different sizes, sectors, and geographical locations to ensure a diverse range of perspectives. The sample size will be determined by the number of relevant subgroups and the desired depth of information from each.

• Quota Sampling:

Description: Selecting participants to match the proportions of certain characteristics in the population (e.g., age, gender, ethnicity).

Sample Size Estimation:

Determine the population proportions: Obtain data on the proportions of the characteristics of interest in the population (e.g., from census data).

Set quotas for each subgroup: Determine the desired sample size for each subgroup based on the population proportions.

Ensure feasibility: Consider the availability of participants within each subgroup and adjust the quotas accordingly.

Example: A researcher wants to survey residents of a city, ensuring that the sample matches the city’s population in terms of age and gender. They set quotas for each age/gender group based on census data and then recruit participants until each quota is met.

• Snowball Sampling:

Description: Participants recruit other participants from their networks. This is useful for reaching hard-to-reach populations.

Sample Size Estimation:

Start with a small initial sample: Begin by recruiting a few participants who meet the study criteria.

Continue until saturation is reached: Keep recruiting participants through referrals until new information no longer emerges.

Monitor the network: Keep track of how participants are connected to ensure that the sample doesn’t become too homogenous (i.e., everyone is connected to everyone else).

Example: A researcher wants to study the experiences of undocumented immigrants. They start by interviewing a few immigrants and then ask them to refer other potential participants in their community. The sample size will depend on how quickly new information emerges and how extensive the network of referrals is.

Key Considerations for All Non-Probability Methods:

• Transparency: Clearly describe your sampling method, the rationale behind it, and any limitations in your research report. This is crucial for readers to assess the credibility of your findings.
• Justification: Explain why a non-probability sampling method was chosen over a probability method. Common reasons include the inaccessibility of the target population, the exploratory nature of the research, or limited resources.
• Triangulation: Use multiple data sources or methods to validate your findings. For example, supplement interviews with observations or document analysis.
• Reflexivity: Be aware of your own biases and how they might influence your sampling decisions and data interpretation.

In summary: While there are no hard and fast formulas for calculating sample size in non-probability sampling, you can use a combination of strategic thinking, pilot testing, and monitoring data saturation to arrive at an appropriate sample size. Be sure to clearly describe your method and acknowledge the limitations of your approach.