Question

At its Web site (www.gallupworldpoll .com) the Gallup World Poll describes their methods. After one report they explained: Results are based on face-to-face interviews with randomly selected national samples of approximately 1,000 adults, aged 15 and older, who live permanently in each of the 21 sub-Saharan African nations surveyed. Those countries include Angola (areas where land mines might be expected were excluded), Benin, Botswana, Burkina Faso, Cameroon, Ethiopia, Ghana, Kenya, Madagascar (areas where interviewers had to walk more than 20 kilometers from a road were excluded), Mali, Mozambique, Niger, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda (the area of activity of the Lord's Resistance Army was excluded from the survey), Zambia, and Zimbabwe..... In all countries except Angola, Madagascar, and Uganda, the sample is representative of the entire population. a) Gallup is interested in sub-Saharan Africa. What kind of survey design are they using? b) Some of the countries surveyed have large populations. (Nigeria is estimated to have about 130 million people.) Some are quite small. (Togo's population is estimated at \(5.4\) million.) Nonetheless, Gallup sampled 1000 adults in each country. How does this affect the precision of its estimates for these countries?

Short answer

Gallup uses stratified sampling, and a uniform sample size affects precision—more precise in smaller countries, less in larger ones.

Step-by-step solution

Understanding the Survey Design

Gallup is conducting a survey in 21 sub-Saharan African countries using face-to-face interviews. This is a stratified sampling approach because they are surveying separate national samples within each country. Each country represents a stratum, and within each stratum, a simple random sample of approximately 1,000 adults is drawn.

Estimating Precision in Large Populations

In countries with large populations, such as Nigeria, selecting a fixed sample size of 1,000 adults means the sample represents a smaller proportion of the total population. Although 1,000 is a statistically valid number for most surveys, the precision or confidence in the results may be slightly lower compared to smaller countries unless the sample size is increased.

Estimating Precision in Small Populations

For smaller countries like Togo, a sample size of 1,000 adults constitutes a larger proportion of the total population. Thus, the estimates from this survey are likely to be more precise because a larger fraction of the population is typically needed to capture the diversity present within the total population.

Analyzing the Consistent Sample Size

By keeping the sample size constant across different countries, Gallup ensures comparability of results. However, this uniformity may lead to varying levels of precision. Smaller countries may benefit from increased precision, while larger countries may experience slight variations.

Key concepts

Stratified Sampling

Stratified sampling is a method in survey design that helps organize larger populations into smaller groups, known as strata. In the Gallup World Poll, each country within sub-Saharan Africa acts as its own stratum. This approach ensures that specific characteristics within each nation are reflected in the survey data.

By dividing the survey into strata based on countries, Gallup can draw random samples that represent each segment effectively. This method minimizes bias and ensures a diverse set of opinions and experiences are captured. For instance, in this poll, approximately 1,000 adults from each country were sampled, allowing separate analyses for each nation while maintaining an overall picture of the region. Here are some benefits of stratified sampling:

• Improves accuracy and reduces sampling error by ensuring all segments of the population are represented.
• Facilitates comparability across strata, allowing for in-depth analysis where needed.
• Ensures cost-effectiveness by focusing survey resources on distinct groups that matter in the analysis.

Precision of Estimates

When conducting surveys, the precision of estimates refers to how closely the survey results reflect the true characteristics of the entire population. In the Gallup survey, the sample size remains constant at 1,000 adults per country. This has implications for the precision of estimates in countries with varying population sizes.

In large populations, such as that of Nigeria, the sample size of 1,000 represents a smaller proportion of the population. This might slightly reduce the precision, as smaller samples in large populations may not fully capture their diversity. Conversely, in smaller populations like Togo, the same sample size constitutes a larger proportion, possibly increasing the precision of the estimates due to the greater representation of diverse experiences.

Benefits of improved precision include:

• Increased confidence in decision-making based on survey results.
• More reliable insights that closely mirror the true population dynamics.
• Enhanced ability to detect and analyze trends and differences within and across strata.

Sample Size

Sample size plays a critical role in survey design and influences the reliability of the survey findings. A sample size of 1,000 across each sub-Saharan African country represents a standardized approach, balancing the need for representativeness with practical constraints such as budget and logistics.

Larger sample sizes generally lead to more precise and reliable estimates, yet they require more resources. For Gallup, maintaining the same sample size provides consistency, simplifies data collection, and supports comparisons across countries. However, it's important to understand that this may affect the precision depending on each country's unique population size.

Key considerations regarding sample size include:

• Trade-offs between sample precision and survey costs.
• Potential need for larger samples in more diverse or populous strata.
• Impact of sample size on the ability to generalize findings to the entire population.

Sub-Saharan Africa

Sub-Saharan Africa is a diverse region with distinct cultural, geographic, and demographic characteristics across its nations. When conducting surveys across such a varied landscape, it's crucial to account for these differences to ensure accurate and relevant data is collected.

The Gallup World Poll focuses on 21 countries in this region, each presenting its own unique challenges and opportunities for data collection. Factors such as remote locations, security issues, and varying population sizes influence survey design. These considerations are vital for capturing comprehensive insights that are reflective of the region's vast diversity.

Essential considerations when surveying in Sub-Saharan Africa include:

• Adapting survey methodologies to accommodate different languages and cultural norms.
• Navigating logistical challenges from geography and infrastructure.
• Ensuring representation from various local contexts to provide a holistic view of the region.