1.2 Data, Sampling, and Variation in Data and Sampling
3 min read•june 25, 2024
Data types and sampling methods are crucial in business statistics. represents non-numerical attributes, while consists of measurable values. Understanding these distinctions helps in choosing appropriate analysis techniques.
Random sampling ensures unbiased representation of a . Simple random, stratified, cluster, and are common methods. Each has advantages for different research scenarios, helping businesses make informed decisions based on reliable data.
Types of Data and Sampling Methods
Qualitative vs quantitative data
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- represents non-numerical attributes, characteristics, or categories (colors, marital status, product reviews)
- consists of numerical values that can be measured or counted
- involves countable values, often integers (number of employees, defective products)
- includes measurable values that can take on any value within a range (height of students, time to complete a task)
Types of random sampling
- ensures each element in the has an equal chance of being selected, resulting in an unbiased and
- Can be conducted with or without replacement
- divides the population into homogeneous subgroups (strata) based on a specific characteristic, then applies simple random sampling within each stratum to ensure representation of all subgroups
- involves dividing the population into naturally occurring groups (clusters), randomly selecting a of clusters, and including all elements within the selected clusters in the sample
- Systematic sampling selects elements from the population at a fixed interval, with the starting point chosen randomly and the interval determined by dividing population size by desired sample size
Sources of Variation in Data and Sampling
Sources of data variation
- arise from differences between sample statistics and population parameters due to chance
- Can be reduced by increasing sample size
- Types include (non-) and (inherent in sampling)
- occur during data collection, processing, or analysis and are not related to the sampling process
- result from inaccuracies in data collection instruments or methods (poorly worded survey questions, faulty measuring devices)
- occur when some elements in the sample do not respond, potentially leading to biased results if non-respondents differ from respondents
- happen when the does not accurately represent the population (outdated telephone directories, incomplete email lists)
- are mistakes made during data entry, coding, or analysis (typos, incorrect data entry, programming errors)
Population, Sample, and Statistical Concepts
- Population refers to the entire group of individuals or objects about which information is desired
- Sample is a subset of the population selected for study
- A is a numerical characteristic of the population, while a is a numerical characteristic of the sample
- Variability refers to the extent to which data points differ from each other
- A sampling frame is the list of all elements in the population from which the sample is drawn
- A representative sample accurately reflects the characteristics of the population it was drawn from
Key Terms to Review (38)
Cluster Sampling: Cluster sampling is a probability sampling technique where the entire population is divided into groups or clusters, and a random sample of these clusters is selected to represent the whole population. This method is often used when the population is geographically dispersed or when a complete list of all individual members is not available.
Continuous: Continuous data are quantitative data that can take on any value within a given range. These values are often measured and can include fractions or decimals.
Continuous Quantitative Data: Continuous quantitative data refers to numerical data that can take on any value within a given range, rather than being restricted to a set of discrete values. This type of data is measured on a continuous scale and can have an infinite number of possible values between any two points.
Convenience sampling: Convenience sampling is a non-probability sampling technique where subjects are selected because of their convenient accessibility and proximity to the researcher. It is often used when quick, easy, and inexpensive data collection is needed.
Coverage Errors: Coverage errors refer to the discrepancy between the target population and the population that is actually represented in a sample. These errors occur when the sampling frame, which is the list or source from which the sample is drawn, does not accurately reflect the true target population, leading to biased or incomplete data.
Discrete: Discrete data consists of distinct, separate values, typically countable and finite. These values often represent whole numbers.
Discrete Quantitative Data: Discrete quantitative data refers to numerical data that can only take on specific, distinct values within a defined range. Unlike continuous quantitative data, discrete data represents countable, non-overlapping quantities that are typically integers or whole numbers.
Measurement Errors: Measurement errors refer to the discrepancies between the true value of a measurement and the observed or recorded value. These errors can arise from various sources and can have significant implications for data analysis and decision-making in the context of data, sampling, and variation in data and sampling.
Non-Response Errors: Non-response errors are errors that occur in a survey or study when selected participants fail to respond or provide complete information. These errors can significantly impact the accuracy and representativeness of the data collected, affecting the overall quality of the research findings.
Nonsampling Errors: Nonsampling errors are errors that occur in the data collection and analysis process, independent of the sampling method used. These errors can arise from a variety of sources, including human mistakes, equipment malfunctions, or biases in the data collection and processing, and can have a significant impact on the accuracy and reliability of the data.
Parameter: A parameter is a characteristic or value that defines the conditions or limits of a system, process, or function. It serves as a variable that can be adjusted or measured to influence the behavior or outcome of something being studied or analyzed.
Population: A population is the entire set of individuals or items that a statistical analysis is focused on. It encompasses all elements from which data can be collected.
Population: In the context of statistics and probability, a population refers to the complete set of all individuals, objects, or measurements of interest that a researcher wishes to study or make inferences about. It is the entire group or collection that is the focus of the statistical analysis.
Processing Errors: Processing errors refer to mistakes or inaccuracies that occur during the data processing stage, which involves collecting, organizing, and analyzing data. These errors can arise from various sources and have significant implications for the quality and reliability of the data being analyzed.
Qualitative data: Qualitative data are non-numerical observations that describe qualities or characteristics. These data often come from surveys, interviews, or open-ended questions.
Qualitative Data: Qualitative data refers to non-numerical information that cannot be quantified or measured numerically. It is descriptive in nature and provides insights into the qualities, characteristics, and meanings of a phenomenon rather than its numerical measurements.
Quantitative continuous data: Quantitative continuous data are numerical values that can take any value within a given range, including fractions and decimals. These data points are typically measured rather than counted.
Quantitative data: Quantitative data is numerical information that can be measured and analyzed statistically. It often includes counts, measurements, and projections.
Quantitative Data: Quantitative data refers to numerical information that can be measured, counted, or expressed using numbers. It is data that can be quantified, analyzed, and used to make informed decisions.
Quantitative discrete data: Quantitative discrete data consists of numerical values that represent countable quantities. These values can only take on specific, distinct integers and not fractions or decimals.
Random Sampling Error: Random sampling error is the difference between a sample statistic and the corresponding population parameter that arises due to the natural variability of drawing a random sample from a population. It is an unavoidable source of error that occurs when making inferences about a population based on a sample.
Representative sample: A representative sample is a subset of a population that accurately reflects the members of the entire population. It ensures that all relevant characteristics are proportionately included in the sample.
Representative Sample: A representative sample is a subset of a population that accurately reflects the characteristics of the entire population. It is a crucial concept in statistics and data analysis, as it allows researchers to make inferences about the larger population based on the information gathered from the sample.
Sample: A sample is a subset of a larger population that is selected and studied to gain insights about the entire population. It is a fundamental concept in statistics and probability, as it allows researchers to make inferences about the characteristics of a population without having to study the entire population.
Samples: A sample is a subset of a population used to represent the entire group. Samples are used in statistics to draw conclusions about populations without examining every individual.
Sampling bias: Sampling bias occurs when a sample is not representative of the population from which it was drawn, leading to skewed or invalid results. It can arise from improper sampling techniques or systematic exclusions.
Sampling errors: Sampling errors occur when a sample does not accurately represent the population from which it was drawn. These errors can lead to incorrect conclusions about the population.
Sampling Errors: Sampling errors refer to the differences between the statistics calculated from a sample and the true population parameters. They arise due to the natural variation that occurs when a subset of a population is selected for analysis, rather than the entire population.
Sampling Frame: The sampling frame is the list or set of all the elements or units in the population from which a sample is to be drawn. It serves as the foundation for selecting a representative sample for statistical analysis.
Selection Bias: Selection bias is a type of systematic error that occurs when the sample selected for a study or experiment is not representative of the population of interest. This can lead to inaccurate or biased results, as the data collected may not accurately reflect the true characteristics of the population.
Simple Random Sampling: Simple random sampling is a type of probability sampling where each element in the population has an equal chance of being selected as part of the sample. It is a fundamental technique used to obtain a representative sample from a larger population, allowing for unbiased statistical inferences to be made about the population characteristics.
Statistic: A statistic is a numerical value or summary measure calculated from a sample of data. It is used to describe and analyze the characteristics of a population when the entire population cannot be observed or measured directly.
Stratified sample: A stratified sample is a sampling method in which the population is divided into distinct subgroups, or strata, that share similar characteristics. A random sample is then taken from each stratum to ensure representation from all groups.
Stratified Sampling: Stratified sampling is a probability sampling technique where the population is divided into distinct subgroups or strata, and samples are randomly selected from each stratum in proportion to the stratum's size. This method ensures that the sample is representative of the overall population, allowing for more precise estimates and inferences.
Systematic sample: A systematic sample is a type of probability sampling where every nth element from a list is selected after a random starting point. It ensures that the sample is spread evenly over the population.
Systematic Sampling: Systematic sampling is a type of probability sampling method where elements are selected from a population at regular intervals. This technique is used to ensure a representative sample is drawn from the target population by following a predetermined pattern of selection.
Variability: Variability refers to the degree of dispersion or spread in a set of data, indicating the extent to which individual data points differ from the central tendency or average value. It is a fundamental concept in the analysis of data, as it provides insights into the consistency and predictability of a dataset.
Variation: Variation refers to the differences or changes in data points within a dataset. It is a crucial concept for understanding the spread and distribution of data.