Sampling and Data Collection Methods
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Questions and Answers

Why might it be impractical to collect data from an entire population in some cases?

It's not always possible to access every individual, and sometimes exhaustive treatment isn't feasible, especially with theoretically infinite worlds.

What is sampling, in the context of data collection?

Sampling is a method of selecting a finite number of cases to make measurements, inferences, and decisions about a larger population.

What are the main objectives when selecting and using a sample?

To select a sample representative of the population, design appropriate measurement methods, conduct correct analysis, and present results correctly to the audience.

Why are surveys sometimes regarded with skepticism?

<p>There are many poorly conducted surveys, which can lead to mistrust in the validity of surveys in general.</p> Signup and view all the answers

Why can estimates based on samples sometimes be more accurate than those based on a census?

<p>Censuses often involve large administrative organizations, which can introduce many errors due to complexity and time pressure. Samples can be more accurate when resources are dedicated for training the sampling personnel and to improving data quality.</p> Signup and view all the answers

What historical problems led to interest in population censuses and projections?

<p>Military, political, economical, and insurance-related issues prompted the use of population censuses and projections.</p> Signup and view all the answers

How is a representative sample selected?

<p>The text states a sample should be selected to be as representative as possible, but doesn't explain how.</p> Signup and view all the answers

Provide an example of a census that occurred before the year 1700?

<p>The emperor Yao took a census of the population in China in the year 2238 B.C.</p> Signup and view all the answers

What is the approximate number of possible samples when selecting a sample of 200 from a population of 300,000 without replacement, considering order as important?

<p>2.49 × 10^1095</p> Signup and view all the answers

If order is not important, how many possible samples are there when selecting 200 items from a population of 300,000 without replacement?

<p>3.15 × 10^720</p> Signup and view all the answers

How many different samples can be created when sampling with replacement, selecting 200 items from a population of 300,000?

<p>2.66 × 10^1095</p> Signup and view all the answers

What does statistical theory provide regarding the domain of all possible samples in sampling?

<p>It gives us an appreciation of the size of our major domain of interest being that of all possible samples.</p> Signup and view all the answers

Name two things that probabilities allow us to decide when applying statistical theory to sampling?

<p>The appropriate sampling design to use and quantifying accuracy in measurement.</p> Signup and view all the answers

What is the term used to describe the process of selecting a sample of units from a finite population?

<p>sampling design</p> Signup and view all the answers

In a sampling design, what does P(Si) represent?

<p>the probability that a particular sample Si has of being selected</p> Signup and view all the answers

If S is the set of all possible samples, what is the range of values that P can take?

<p>[0,1]</p> Signup and view all the answers

What is the key difference between a population and a sample?

<p>A population includes all individuals, while a sample is a subset of the population.</p> Signup and view all the answers

What is the error that occurs when a sample does not accurately represent the desired target population?

<p>Misspecifying the target population.</p> Signup and view all the answers

In the context of sampling, what is a 'statistic'?

<p>A statistic is a formula used to compute estimates from sample data.</p> Signup and view all the answers

What are the formulas used to compute estimates called?

<p>They are called statistics.</p> Signup and view all the answers

What type of bias occurs when only volunteers participate in a survey?

<p>Selection bias.</p> Signup and view all the answers

What type of error occurs when a person does not always tell the truth in a survey?

<p>Measurement bias.</p> Signup and view all the answers

What is the purpose of sampling?

<p>The purpose of sampling is to obtain information about a population.</p> Signup and view all the answers

What does $\frac{n(n-1)}{N(N-1)}$ represent in the given text?

<p>It represents the probability that two individuals from a population of size $N$ are included in a sample of size $n$.</p> Signup and view all the answers

Name two ways an interviewer can introduce measurement bias during a survey.

<p>Misreading questions or leading the respondent to answer in a specific way.</p> Signup and view all the answers

Why might question wording and order cause measurement bias?

<p>They can influence how respondents answer, leading to inaccurate data.</p> Signup and view all the answers

What is $X$ and $S^2$ when used as estimators?

<p>$X$ is the sample mean and $S^2$ is the sample variance.</p> Signup and view all the answers

What is the main consequence of only gathering observations on a part of the population?

<p>It introduces uncertainty associated with the sample being selected.</p> Signup and view all the answers

When the sampling is not done, what would happen to the 'population characteristic of interest'?

<p>It would be known exactly.</p> Signup and view all the answers

In simple random sampling without replacement, if order is not important, what is the probability of selecting a specific element, such as element A, when there are samples AB and AC?

<p>2/3</p> Signup and view all the answers

What is the general inclusion probability (Ï€i) for an individual from a population of size N being included in a sample of size n under simple random sampling?

<p>n/N</p> Signup and view all the answers

In simple random sampling with replacement, what is the probability of a specific element appearing in any one position of a sample?

<p>1/N</p> Signup and view all the answers

If there are 50 elements in a population and a sample of 10 elements is picked with replacement, what is probability that element 'x' is part of the sample?

<p>10/50 or 1/5</p> Signup and view all the answers

When sampling with replacement, what is the probability that a specific element appears in position 1 AND also in position 2 of a sample?

<p>1/N * 1/N or 1/N²</p> Signup and view all the answers

For simple random sampling without replacement, how is the probability of selecting a particular element calculated in terms of factorials and permutations, considering the order of selection?

<p>P(N-1, n-1) / P(N, n) = n/N. We can write permutators in terms of factorials: ( (N - 1)! / (N-1 - (n-1))!) / (N! / (N-n)!) = n/N</p> Signup and view all the answers

What does πi represent in the context of sampling and inclusion probabilities?

<p>The inclusion probability of the i-th element</p> Signup and view all the answers

Under simple random sampling, is the inclusion probability of an element affected by whether the sampling is done with or without replacement, or whether the order matters?

<p>No</p> Signup and view all the answers

What actions are taken regarding data immediately after it is collected and handed to data entry personnel?

<p>The data is coded and entered into the system.</p> Signup and view all the answers

What type of data manipulation may occur prior to data analysis?

<p>Data cleaning, respondent clarification, and data imputation.</p> Signup and view all the answers

What does the first set of statistical calculations, completed after data cleaning involves?

<p>Summary statistics, point estimates, and precision calculations.</p> Signup and view all the answers

Besides summary statistics, what are two other types of analysis that may be performed on survey data?

<p>Comparison between subgroups, correlation, and regression analysis.</p> Signup and view all the answers

What critical information should be included in all survey reports?

<p>A general declaration of the conditions under which the survey was carried out.</p> Signup and view all the answers

Flashcards

Probability of selecting an element (without replacement, order not important)

In sampling without replacement where order is not important, the probability of selecting any specific element is the number of favorable combinations divided by the total possible combinations.

Probability of selecting a specific element (without replacement, order important)

In sampling without replacement, the probability of selecting one particular element in the sample can be found by taking the product of the probabilities of selecting all the remaining elements.

Inclusion Probability (Simple Random Sampling)

The probability that an element in a population of size 'N' is included in a sample of size 'n' under simple random sampling is always the same, regardless of whether it's with or without replacement, or whether order is important or not.

Element Position (Simple Random Sampling with Replacement)

Each element in a sample has an equal chance of appearing in any specific position within the sample.

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Probability of Element Position (Simple Random Sampling with Replacement)

In simple random sampling with replacement, the probability of a given element being selected at any position within the sample is the same for all positions.

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Sampling

The process of selecting a representative subset of a population for study.

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Finite Population

A population where every individual can be studied.

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Infinite Theoretical Population

A population with an unlimited number of individuals, making it impossible to study everyone.

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Representativeness

The ability of a sample to accurately represent the characteristics of the entire population.

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Census

Collecting data from every member of a population.

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Sample Data

A collection of data from a sample that often provides more accurate estimates than a census due to reduced errors from administrative complexity.

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Non-respondents

The act of neglecting to include all of the members of a population in a survey, sample, or census.

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Sample Surveys vs. Censuses

Surveys based on samples are often considered more accurate than those based on a census because they allow for more attention to data quality and reduce errors from large administrative processes.

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Sample Selection

The careful selection of individuals for a sample is crucial for achieving accurate and representative results.

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Measuring Methods

The process of planning and executing data collection methods to ensure efficiency and accuracy.

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Data Analysis

Analyzing data collected from a sample to extract meaningful insights and draw conclusions.

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Result Presentation

Presenting the findings from a study in a clear, concise, and visually appealing manner to reach the intended audience.

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Sampling without Replacement, Order Matters

The number of ways to choose a sample of a specific size from a population, where the order of selection matters.

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Sampling without Replacement, Order Doesn't Matter

The number of ways to choose a sample of a specific size from a population, where the order of selection does not matter.

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Sampling with Replacement

The number of ways to choose a sample of a specific size from a population, where you can select the same item multiple times.

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Sample Space

The set of all possible samples that can be drawn from a population under a specific sampling design.

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Sampling Design

A procedure used to select a sample of units from a population, where each sample is assigned a probability of being chosen.

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Selection Probability

The probability that a specific sample will be selected under a given sampling design. Essentially, how likely is this particular sample to be chosen?

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Statistical Theory

The study of how to collect, analyze, and interpret data from samples, allowing us to make inferences about the population from which the samples were drawn.

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Sampling Theory

The application of statistical theory to the process of sampling, helping us to select and analyze samples in a way that ensures they accurately represent the population.

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Combination

The probability of selecting a specific combination of 'n' objects out of 'N' total objects, where order doesn't matter.

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Simple Random Sampling

A statistical method where each individual in a population has an equal chance of being selected for a sample.

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Estimator

A value calculated from a sample that estimates a population characteristic.

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Statistic

A specific formula used to calculate an estimator.

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Sample Mean (XÌ„)

The average of all values in a sample.

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Sample Variance (S²)

A measure of how spread out the data is in a sample.

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Population Mean (μ)

The true average value of a characteristic in the entire population.

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Population Variance (σ²)

The true spread of data across the entire population.

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Measurement Bias

A type of bias that occurs when the data collected is inaccurate, often due to issues with the survey questions or how they are asked.

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Truthfulness in Surveys

People may not always be truthful when answering survey questions.

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Misinterpretation of Survey Questions

Survey questions can be misinterpreted by respondents, leading to inaccurate data.

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Forgetting in Surveys

Respondents may forget details, leading to inaccurate answers in a survey.

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Social Desirability Bias

Respondents may try to impress the interviewer by giving socially desirable answers, ignoring their true feelings or actions.

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Data Preparation

The process of preparing collected data for analysis, which includes cleaning, verifying, and handling missing values.

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Data Imputation

Substituting plausible values for missing data points using various statistical techniques.

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Summary Statistics

Calculating descriptive statistics, such as means, standard deviations, and proportions, to summarize key variables in the data.

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In-depth Analysis

Analyzing relationships between variables in the data to determine correlations and potential causal connections.

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Report Generation

Creating reports tailored to different audiences, starting from general overviews to more statistically detailed insights.

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Study Notes

Chapter 1: The Sampling Problem

  • Five problems related to sampling are presented: calculating average weekly expenditure of a Maltese family in October, determining average velocity of oxygen molecules in a container, calculating the proportion of Maltese adults using computers, estimating potato yield in Mgarr during autumn, and estimating the number of Maltese children with asthma.
  • Solving these problems is more complex than initially appears, needing detailed descriptions of the situations of interest.

1.2 From Distrust to Wide Use

  • Interest in population censuses and projections dates back to biblical times, driven by military, political, economic, and insurance needs.
  • Historical examples include censuses in ancient China (2238 BC), Charlemagne's inquiries about church properties (762), and the Domesday Book (1086).
  • The distrust in sampling by politicians and administrators lasted until the 1940s/50s. Sampling gained acceptance due to theoretical backing, improved methodologies, and software availability.
  • Sampling reduces measurement to a controlled number of cases improving accuracy.

1.3 Role of Statistical Theory in Sampling

  • The fundamental problem of sampling is selecting 'n' elements from a population of 'N' elements. 
    • This can be considered in different contexts: without replacement order important, without replacement order not important, and with replacement.
  • Specific mathematical formulas dictate the number of possible samples when selecting samples of size n from a population of N.

1.4 Selection Probabilities

  • A sampling design assigns probabilities to each sample, indicating the likelihood of selecting particular samples.
  • Simple Random Sampling (SRS) is the simplest design assigning equal probability to each sample.
  • The probability of selection of each element in a sample is denoted as Ï€i.
  • Formulas for calculating the probabilities of selecting specific samples are presented, differentiating between scenarios with and without replacement, considering order as important or not.
  • Examples are provided working with a population composed of three elements.

1.7 Selection Bias

  • Selection bias is a sampling error where certain sections of the target population are not included in the sampled population (under-coverage).
  • Specific sources of selection bias include deliberate selection to confirm prior opinions, mis-specification of the target population, substitution of units in the sample with substitute units that are more readily available or accessible, non-response from sampled units, or the use of a volunteer sample.

1.8 Measurement Bias

  • Measurement bias represents inaccuracy in the information obtained.
    • Reasons include individuals not always telling the truth, not understanding questions, forgetting, trying to impress the interviewer, not misinterpreting questions, or biased questions.
  • Better designed questionnaires can help to reduce inaccurate answers.

1.9 Questionnaire Design

  • Guidelines for designing effective questionnaires include: define research objectives, using simple and straightforward questions, tying questions to focus of interest, avoiding questions that would elicit specific answers, deciding between open and closed questions, considering questioning ordering effects, and testing questions before application.

1.10 The Sample Survey

  • Steps to conducting a sample survey including identifying objectives, defining target population, evaluating resources, determining data needs, defining measurement methods, choosing methodologies for data collection (e.g., telephone, email, in-person), sample size determination, constructing sampling frame, interviewer selection, pretesting, data collection and analysis, and final report.

1.11 Other Points Regarding Surveys

  • Surveys can vary in scope and execution, necessitating careful consideration when interpreting results.
  • Not all surveys are for summarizing statistics as they can be used for decision-making, hypothesis testing and for developing a greater understanding in numerous areas of investigation.

Additional Notes

  • The document includes specific examples of sampling methods and describes important theoretical concepts.
  • It highlights factors that can affect the quality of data collection and explains terms like sample, sampling frame, observation unit, target population, and sampling unit.
  • The text references the need for statistical theory in formulating appropriate sampling methodologies and selecting/applying best practices for the design of surveys.

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Description

This quiz explores key concepts in sampling and data collection, including the practicality of collecting data from entire populations. Understand the objectives of using samples, the skepticism surrounding surveys, and the historical context of population censuses. Test your knowledge with questions that challenge your understanding of statistical theory and sampling methods.

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