STAT 443 Survey Methods

Course Information

• Course title: STAT 443: THEORY SAMPLING
• Lecturer: Winnie M. Onsongo (PhD)
• Department: Department of Statistics and Actuarial Science
• University: University of Ghana
• Email: [email protected]
• Date: November 5, 2024

Prerequisites

• Introduction to statistics and probability
• Basic algebra
• Research methodology

Assessment and Grading

• Assignments + Interim Assessment (30%)
• Exam (70%)
• Homework submitted on time, late submissions not accepted
• Duplicate solutions not graded

Course Objectives

• Discuss theoretical and practical considerations of survey data
• Discuss strategies for conducting preliminary analysis of large-scale, complex surveys
• Develop data handling skills to prepare data for analysis

Introduction

• Sample survey methods is a branch of statistics dealing with collecting and analyzing data from finite populations
• This study covers suitable statistical principles and methods for collecting and analyzing data from finite populations
• Society relies on data from surveys to describe the world and reflect the population it claims to represent
• Quantitative data is essential to support arguments and discussions

Introduction Continued

• Figures are essential to present data and understand situations clearly.
• Those presenting statistical data have responsibility to present it fairly and objectively, including proper data sourcing, scope and methodology.

Sample Surveys and Opinion Polls

• Finite populations have individuals with measures of interest
• Exact characteristic values can be determined by studying each individual
• Limited resources often require estimating characteristics by studying a smaller group (sample)
• Data collected on individuals are often quantitative and factual, describing social or economic characteristics
• Data is considered independent observations from a population following a probability model.
• Surveys collected on humans can include views and preferences (opinion polls)
• Sample surveys can aid market research for product qualities

Definitions

• Finite population: A collection of units like households, people, cities or countries
• Census: A complete count of all units in the population
• Population: A collection of all sampling units in a region at a specific time or period
• Sampling unit: An element or group on which observations are made (e.g., income of an individual in a household)
• Representative sample: A sample reflecting all salient features of the population
• Sampling frame: A list of all units in the population to be surveyed (e.g., university students with registration numbers)
• Static/exhaustive list: A single list of all sample units existing before the study
• Dynamic list: A list generated during the study of sample units. (e.g., patients visiting a doctor)

Why Sample?

• Sampling allows a representative picture of a population without studying the entire population
• There are several reasons for using statistical sampling rather than complete enumeration
• Reduced cost: Expenditures are minimized when studying a portion of the population
• Faster data collection and processing
• Higher accuracy due to in-depth training for the personnel
• Broader scope and flexibility in data collection

Types of Surveys

• Demographic surveys (e.g., household surveys, family size, etc.)
• Educational surveys (e.g., school attendance, graduation rates)
• Economic surveys (e.g., industrial production, consumer spending, etc.)
• Public polls and surveys (e.g., public opinion on specific issues)
• Marketing surveys (e.g., consumer preferences, product needs, and impact on the market)

Principal Steps in a Survey

• Define clear, understood survey objectives
• Determine population for sampling (e.g., educational survey using students from basic school to senior high-school)
• Identify necessary data related to survey objectives. Avoid unnecessary questions
• Specify required degree of precision in data collection
• Choose suitable measurement instrument and method (e.g., interview, questionnaires). Develop recording forms
• Develop a comprehensive sampling frame
• Select sample based on the sampling plan; determining cost and time of various sampling plans
• Conduct a pre-test to address any problems before large-scale field work (e.g., test questionnaires and field methods)
• Organize fieldwork adequately(e.g., handle non-response, address missing observations, training)
• Summarize and analyze data (appropriate tools based on survey objectives, method of estimation, tolerable error limits)

Methods of Data Collection

• Physical observations (e.g., personal contact; observing individuals, recording data)
• Personal Interview (e.g., preparing standardized questionnaires for an interview)
• Mail inquiry (e.g., well-made questionnaires mailed to respondents, self-addressed envelopes with postage)
• Web-based inquiry (e.g., surveys on web pages; links sent via email)
• Registration (e.g., data recorded at specified locations- births and deaths, family details)
• Transcription from existing records (e.g., collection from existing data)

How to Sample

• Goal: Create a fair representation of the population with high accuracy estimates
• Various sampling methods exist (e.g., accessibility, haphazard)
• Accessibility/haphazard sampling: Choosing the easiest to access observations (potential lack of representativeness)
• Judgment sampling/purposive sampling: Surveyor intentionally picks individuals with good accessibility and representativeness

Quota Sampling

• Highly structured method, defining how many individuals are needed in each quota
• Main criticism of haphazard and judgmental sampling: lack of a clear basis for representativeness (no set guiding principles)

Central Concept of Probability Sampling

• Population characteristics (e.g. total, mean, proportion falling into a category)
• Estimating population characteristics from a sample of 'n' units

Probability Sampling

• Specifying sample size 'n'
• Identifying all potential samples of 'n' units drawn from the population
• Defining probabilities for each sample
• Using probabilistic methods to select the sample (e.g., Simple Random Sampling)

Probability Sampling Methods

• Simple random sampling: Basic method, used for other probability sampling schemes
• Systematic sampling: Enhancing precision and ensuring subgroup sampling
• Stratification: Performing to enhance population-level estimates and facilitate estimates for sub-groups

Selection Probability

• Probability of including a unit in the sample
• Selection probability may not to be known initially; it is sufficient to know or estimate this during the analysis
• External factors can affect this sampling

Notations

• Table showing population and sample quantities (e.g., size, unit index, value, average, total)

Sampling from a Finite Population

• Sampling mechanism: Assigning selection probabilities to population members
• Two ways to obtain a sample
  • Without replacement: Units not put back in the population
  • With replacement: Units placed back in the population

Characteristics of the Population

• Population average
• Population variance
• Population total

China Town

• Example, Population (e.g the number of households, properties, businesses)
• Variables of interest (e.g., number of buildings, dwellings).
• Listing of various dwellings/units/elements in China Town (data)
• Population totals (e.g. total number of blocks)
• Population averages (e.g. average dwellings)
• Population variances (e.g. Variance in number of dwelling/blocks)
• Ratio (e.g. ratio of no. of dwelling to no. of blocks)
• Proportion

Proportion

• Proportion can be calculated as the average of a variable
• Defined for lots (e.g., determining whether a lot is occupied or empty)

Population Quantities

• Population covariance
• Population correlation

Sampling Mechanisms

• Assigning probabilities to all samples possible from a population for a given sample size

Sampling with Equal Probabilities

• Mechanism to determine probabilities based on samples from a population
• Two versions: -Without replacement (units only picked once) -With replacement (Units can be picked repeatedly)

Sample Quantities

• Sample Fraction (Sample Size/Population Size)
• Differentiating between population quantity
• Sample quantity
• Estimate

Some Observations

• When is an estimator good?,
• Expectation, Variance, Bias, Mean Square error

Thank You

Test your knowledge on the key concepts and prerequisites of the STAT 443 course, focusing on survey methods. This quiz covers objectives, grading criteria, and essential steps in conducting surveys, providing a comprehensive review for students. Ideal for those looking to reinforce their understanding of this important module.