Sampling Design and Sample Size

Sampling Design

• The objective of sampling is to select individuals for a study, so accurate population information can be derived.
• Sampling is selecting study units from a population.
• A population can be too large to collect data from all its members.
• Statistical inference is not needed if the entire population is examined.
• A representative sample is a subgroup of the population included in the research.
• A representative sample has all the key characteristics of the population.

Population and Sample

• Sample size determination identifies the number of samples needed from a population.
• This ensures the sample is large enough to yield an accurate estimate of the population parameter.
• It also makes sure it is manageable and cost-effective for analysis.
• Confidence Level denotes the level of unpredictability with a specific statistic.
• Margin of Error indicates the degree of error in results from random sampling surveys.

Sample Size Determination Example

• Estimating the average word count of news articles on a major journalism website requires a 95% confidence level and a 5% margin of error.
• Conducting sampling 100 times means that in 95 instances, the true average word count falls within a certain range.
• With a computed sample averaging 1,200 words and a margin of error of ±5%, the true average article length would likely be between 1,140 and 1,260 words.
• This range is the confidence interval, meaning that repeating the sampling 95% of the time, the average article length would be in this range.

Steps in Data Gathering

• Set the objectives for collecting data to establish the margin of error and confidence level.
• Identify required funds for data collection.
• Determine necessary data based on the set objectives.
• Determine the study design, such as observational or experimental.
• Determine the data gathering method and define comprehensive data collection points.
• Identify sampling techniques and methods that provide a good representation of the population.
• Design data gathering forms and collect data.

Two Types of Samples

• Probability samples use an objective chance mechanism, involving randomization.
• They require a sampling frame, which is a complete list of the population elements.
• The probabilities of selection are known.
• Probability Samples are known as random samples and used to draw valid generalizations about the universe/population.
• Non-probability samples are haphazard, purposive, or taken from volunteers.
• The probabilities of selection are unknown
• Non-probability Samples should not be used for statistical inference.

Basic Sampling Techniques of Probability Sampling

• Simple random sampling is the most basic method.
• Simple random sampling assigns equal probabilities of selection to each possible sample.
• Systematic random sampling selects every kth individual from the population.
• The first individual corresponds to a random number between 1 and k.
• Stratified random sampling separates the population into non-overlapping groups called strata.
• Then, a simple random sample is obtained from each stratum.
• Individuals within each stratum are homogeneous or similar.
• Cluster sampling takes the sample from naturally occurring groups in the population.
• Clusters are constructed so that the sampling units are heterogeneous within the cluster but homogeneous among clusters.

Sampling Methods: Best Use Cases

• Simple Random Sampling (SRS) is best for small, homogeneous populations with unbiased selection, but is not ideal for large populations where subgroup analysis is needed.
• Stratified Sampling works well when subgroups exist and must be represented but it is not ideal when the population is homogenous.
• Systematic Sampling is good for large, ordered populations like production lines but not ideal when patterns in data create bias.
• Cluster Sampling is useful when studying large, dispersed populations but not when clusters are too different internally.
• Multi-Stage Sampling is employed for complex, large-scale surveys requiring cost efficiency but not where precision is more important.

Examples of Sampling Techniques

• Communication styles across age groups: dividing the population into age groups and sampling equally from each ensures representation.
• Community radio listenership: randomly selecting cities (clusters) and surveying households within them is more feasible than sampling across an entire country.
• Media consumption habits of university students: obtaining a list of 10,000 students and randomly selecting 500 ensures each student has an equal chance of being chosen.
• Podcast feedback: selecting every 50th subscriber from a list of 5,000 after a random start uses a systematic approach.

Non-Probability Sampling Techniques

• Accidental Sampling has no selection system; the sample includes whoever the researcher or interviewer encounters by chance.
• Quota Sampling involves a specified number of people of certain types included in the sample.
• The researcher knows population categories and draws samples from each.
• Each categorical sample's size is proportional to the population that belongs to that category.

Non-Probability Sampling Advanced Techniques

• Convenience Sampling is a quick process to get immediate reactions from people.
• This can be done with telephone interviews to get the immediate reactions from a group about a certain issue.
• Purposive Sampling relies on researcher-defined criteria.
• Individuals are interviewed if they satisfy these criteria.
• This helps to determine the target population for a study.
• Judgment sampling selects a sample based on an expert's judgment.

Usefulness of Non-Probability Sampling

• Non-Probability Sampling is useful when few are willing to be interviewed, if there are extreme difficulties in locating or identifying subjects.
• Non-Probability Sampling is also useful when probability sampling is too expensive, or when population elements cannot be enumerated.

Sources of Errors in Sampling

• Non-sampling error results from the survey process.
• Non-sampling error includes any errors that are not attributed to sample-to-sample variability.
• Sampling error arises from taking one sample instead of examining the whole population.
• Sampling error also happens when using sampling to estimate information about a population.

Sources of Data

• Primary sources are authoritative first-hand accounts of an event or time period.
• Primary sources include original thinking, reports on discoveries or events, or the sharing of new information.
• These sources are often created when the events occurred, while others can be created later on.
• Secondary sources offer analysis, interpretation, or restatement of primary sources.
• Secondary Sources can be considered persuasive
• Secondary sources involve generalization, synthesis, interpretation, commentary, or evaluation to convince the reader.

Primary Data Collection

• Primary data can be collected through five methods: direct personal interviews, indirect/questionnaire methods, focus groups, experiments, and observation.
• Direct personal interviews involve direct contact, where gathering information comes from questioning the interviewee.
• Indirect/Questionnaire Method involves sourcing and accessing existing data originally collected for the purpose of the study.
• A focus group is a group interview with around 6-12 people sharing similar characteristics or interests guided by facilitator.
• An experiment is a data collection method involving direct human intervention on conditions that affect a variable's values.
• Observation is collecting data on a phenomenon, recording observations as it actually happens.

Indirect/Questionnaire Method: Types of Questions

• Open-ended questions allow free responses recorded in the respondent's own words, without providing possible answers.
• For example: asking a respondent to describe what a birth attendant did when labor started.
• Closed questions offer a list of options or answers for respondents to choose what fits better.
• Closed questions are useful when the array of possible responses is known.
• For example: Did you eat any of the following foods yesterday? (Fish or meat: Yes/No; Eggs: Yes/No).

Open-Ended vs. Closed-Ended Questionnaires

Key Design Principles of a Good Questionnaire

• Keep the questionnaire short and concise.
• Determine if questions will be open-ended or closed-ended.
• Include important questions relevant to the study.
• Write questions properly.
• Order the questions in the right way.
• Avoid prompting participants with questions that could alter the reliability.
• Write an introductory letter or something similar.
• Give special instructions.
• Translate questions.
• Always test data before the survey.
• The primary element of writing a survey is to determine the objective.

Elvis Presley Example

• Two surveys were taken in late 1993/early 1994 about Elvis Presley
• One survey asked participants to express how they feel and to consider the possibilities of Elvis still being alive.
• The other survey asked them to express how they feel regarding a television show about Elvis Presley's death and to consider the possibility of him being alive or not.

Elvis Presley Example Outcomes

• Two surveys were taken in late 1993/early 1994 about Elvis Presley
• One survey asked participants to express how they feel and to consider the possibilities of Elvis still being alive.
• The other survey asked them to express how they feel regarding a television show about Elvis Presley's death and to consider the possibility of him being alive or not.
• 8% of respondents in one of the surveys to the first question stated that they thought Elvis might still be alive
• 16% of respondents to the second question stated that they thought he could be alive.

Example Health Surveys

• In 1995, two health surveys were conducted.
• One survey asked to report the respondent's weight and followed by asking "Are you trying to lose weight?" was asked immediately after.
• The second survey asked the same questions, but with a larger gap between them.

Weight Loss Survey Results

• In 1995, two health surveys were conducted.
• One survey asked respondents to report weight and immediately posed weight loss question.
• Second survey included "Are you trying to lose weight?" mid-survey, with weight query at its end.
• 28.8% of men and 48.0% of women in the first survey said they are trying to lose weight.
• In the second survey, The men who reported wanting to lose weight was 26.5% and the women was 40.9%.

Secondary Data Collection

• Secondary data can be collected by:
• Reports published in newspapers and periodicals.
• Financial data that has been issued in annual reports.
• Information and records Maintained by institutions.
• Internal reports of the government departments
• Information from official publications

Key Points for Secondary Data

• Verify the validity and reliability of data by checking the collection method employed.
• Using inappropiate data for research is inadvisable.