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Gallup World At its website (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?

Step by step solution

01

Identify Survey Design

Gallup's survey design involves conducting face-to-face interviews with approximately 1,000 randomly selected adults in each of the 21 sub-Saharan African countries. This approach suggests a 'stratified sampling' design, where countries serve as strata to ensure coverage across different geographical regions.

02

Analyze Population Impact

Gallup sampled a fixed number of 1,000 adults per country regardless of the population size. In larger countries like Nigeria, 1,000 people represent a smaller fraction of the total population compared to smaller countries like Togo. As a result, the same sample size may lead to less precise estimates in countries with larger populations because the sample constitutes a smaller proportion of the overall population.

03

Evaluate Precision of Estimates

Precision in statistics refers to the variability of the estimate. A smaller sample relative to a population size increases the standard error, leading to less precise estimates. Therefore, in larger countries such as Nigeria, the standard error is likely higher than in smaller countries like Togo, affecting the accuracy of the survey results.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stratified Sampling

Stratified sampling is a method used in survey design to ensure that different segments or "strata" of a population are represented in the sample. In the case of the Gallup World Poll conducted in sub-Saharan Africa, the countries themselves act as the strata. This means that Gallup is looking to capture a comprehensive picture of various regional differences across the continent.
By sampling 1,000 adults in each country, Gallup ensures that each country's unique cultural, social, and economic contexts are considered. It also allows for more precise comparisons between countries. For instance:

• Each country, regardless of size, has equal weight in the survey.
• Ensures that larger countries do not dominate the results simply because of their size.
• Encourages representation of minority segments within countries by emphasizing structure over sheer size.

Stratified sampling enhances the quality and reliability of survey data by making sure that every regional unit is covered, providing a more equitable and balanced view of the situation across all surveyed areas.

Precision of Estimates

The precision of estimates in statistics refers to how much variation, or uncertainty, there is around the survey's results. This can often be measured by the standard error, which describes the expected variation if the survey were repeated multiple times. In the Gallup World Poll, each country has a fixed sample size of 1,000 adults.
However, the precision of these estimates varies between countries because 1,000 people represent different proportions of the population in each country. For example:

• In Nigeria, with a population of about 130 million, 1,000 people is a small fraction, leading to potentially greater standard error and less precision.
• In smaller countries like Togo, with a population of approximately 5.4 million, 1,000 people form a large fraction, resulting in more precise estimates.

Therefore, while the number of respondents per country is the same, the reliability of conclusions drawn from the data needs to account for these differences in population size. More nuanced interpretations and tailored strategies might be necessary for larger populations to maintain precision.

Population Impact

The impact of a survey method on a population is a key consideration when designing research to inform policy or understanding. The choice of sampling 1,000 adults per country in the Gallup World Poll has notable population impacts that need to be considered. This standard sample size attempts to balance equality and equity across nations.
Even though this method fosters balanced representation:

• It may also face limitations in reflecting the actual opinions and conditions in more populous countries, given the smaller proportion of people sampled.
• In countries with high regional diversity, results may mask underlying local variations due to sampling limitations.

Despite this, by maintaining a consistent sample size, Gallup aims to facilitate straightforward cross-country comparisons. Researchers and policymakers must consider the unique population contexts of each nation to accurately interpret the impact and relevance of the survey findings. Adjusting assumptions or employing additional stratified methods may be needed to integrate these insights effectively into decision-making processes.