Business Statistics: Measurement, Data Collection, and Measurement Scales

Statistics, Data, and Statistical Thinking

Types of Data and Variables

In business statistics, understanding the nature of data and variables is foundational. Data can be classified based on how it is collected and its intended use in analysis.

• Variable: An attribute of the population or process under study that can assume more than one value. Units under study are called variables.

• Primary Data: Data collected by the researcher or analyst specifically for use in a particular study.

• Secondary Data: Data originally collected for another purpose but used in the current study.

Examples of Data Sources

Data sources can be classified as primary or secondary, with examples illustrating their use in business statistics.

• Primary Data Examples:

  • Data obtained from a sample of consumers asked to evaluate a product.

  • Data obtained from annual inventory.

• Secondary Data Examples:

  • Data contained in the Statistical Abstract of the United States.

  • Data contained in surveys conducted by other organizations.

Primary and Secondary Sources

It is important to distinguish between primary and secondary sources of data, as this affects the reliability and relevance of the data for statistical analysis.

• Primary Source: The original collector or publisher of the data (e.g., Gallup Poll report).

• Secondary Source: A source that obtained the data from the primary source (e.g., a textbook summarizing the work of others).

• Caveat: If possible, always use the primary source of secondary data to ensure accuracy.

Advantages and Disadvantages of Data Sources

Both primary and secondary data sources have their own advantages and disadvantages, which must be considered when designing a study.

Advantages	Disadvantages
Control over data production process (sampling, measurement, data processing, etc.) Data likely to be appropriate and adequate for answering the question of interest Low cost Can obtain data quickly Little statistical expertise required to obtain data	May be expensive May require much time to produce the data Statistical expertise required to produce data No control over the data production process Data likely to be inappropriate and/or inadequate for answering the question of interest

Measurement and the Measurement Process

Definition and Components of Measurement

Measurement is the process by which numbers are assigned to phenomena occurring in the real world. The goal is to translate characteristics and properties of real-world phenomena into a form that can be analyzed.

• Empirical Events: Observable characteristics of an object, individual, or organization.

• Numbers: Numerals or symbols used to identify or designate empirical events.

• Mapping Rules: Statements that dictate the assignment of numbers to empirical events.

Steps in the Measurement Process

The measurement process involves several key steps to ensure that the data collected is valid and reliable.

1. Identify the variable of interest and develop a conceptual definition for the variable.

2. Develop an operational definition for the variable.

3. Develop or obtain a measurement instrument.

4. Evaluate the measurement instrument according to validity, reliability, and practicality.

Conceptual vs. Operational Definitions

Conceptual definitions relate the concept being defined to one or more other concepts, often resembling a dictionary definition. Operational definitions specify the procedures for assigning numbers to the concept being measured, including what is to be observed, under what conditions, and with what instruments.

• Example (Conceptual): "Round" defined as spherical, globular, or ball-shaped.

• Example (Operational): A golf ball is round if it can be passed through a particular circular testing device four times in a row.

Evaluating Measurement Procedures

Accuracy in Measurement

Accuracy in measurement has two aspects: unbiasedness and reliability. An unbiased measurement process does not systematically overstate or understate the true value of the variable. Reliability (or precision) means that repeated measurements on the same unit give approximately the same result.

• Unbiased: Measurements are centered around the true value.

• Reliable: Measurements are consistent across repeated trials.

Concepts Used in Evaluation of Measurement Instruments

Measurement instruments are evaluated based on several criteria:

• Validity: The extent to which an instrument measures what it claims to measure.

• Reliability: The extent to which an instrument produces consistent results over time.

• Practicality: The extent to which an instrument is economical, convenient, and interpretable.

• Sensitivity: The extent to which an instrument discriminates along the dimension of concern.

• Influentiality: The extent to which the information provided is influential.

Errors in Data

Sources of Measurement Error

Measurement errors can arise from various sources, affecting the quality and reliability of data.

• Measurement Instrument: May not adequately represent the property or characteristic of interest.

• Measurer: May not apply the measurement instrument correctly or may record measurements improperly.

• Respondent: May misinterpret questions or provide inaccurate answers due to various factors (e.g., fatigue, embarrassment).

• Definitional Error: A discrepancy between the data needed to make a decision and the data collected.

Methods for Describing Sets of Data: Measurement Scales

Types of Measurement Scales

The scale of measurement determines the kind of information a number reflects and what statistical operations are permissible.

• Nominal Scale: Numbers are used only to classify items into categories. Arithmetic is not meaningful.

• Ordinal Scale: Numbers indicate order but not the magnitude of difference between items. Arithmetic is not meaningful, but ranking is.

• Interval Scale: Numbers indicate both order and equal intervals between measurements, but there is no true zero point. Addition and subtraction are meaningful.

• Ratio Scale: Numbers indicate order, equal intervals, and a true zero point. All arithmetic operations are meaningful.

Examples and Applications

Examples help clarify the differences between measurement scales:

• Nominal: Defective = 1, Nondefective = 0

• Ordinal: Ranking of sensory inspectors (e.g., 1 = Bob, 2 = Sue, 3 = Steve, 4 = John)

• Interval: Temperature in Fahrenheit (e.g., 80°F is not twice as hot as 40°F)

• Ratio: Weight, height, income (e.g., $100 is twice as much as $50)

Design of Experiments and Data Collection Techniques

Experimental vs. Observational Studies

Data collection in business statistics can be performed through experimental or observational studies, each with distinct characteristics.

• Experimental Study: The analyst manipulates or changes certain independent variables to obtain information about their influence on dependent variables.

• Observational Study: The analyst measures the variable of interest for the units under study without disturbing them.

Advantages and Disadvantages of Study Types

Observational Study	Experimental Study
Typically less expensive than experiments Possible to produce large data sets Applicable to a wider variety of questions Better for describing and learning about populations Can study specific variable manipulations Provides better evidence of causation	Conclusions from experiments tend to be more credible due to controlled conditions May be expensive Usually produces small data sets Applicability constrained by ability to manipulate variables May not generalize across people, settings, and time

Data Collection Techniques

Common techniques for collecting data include interrogation (personal interview, self-enumeration) and observation.

• Personal Interview: Analyst obtains data by asking individuals involved in the phenomenon.

• Self-Enumeration: Individuals respond to questionnaires without analyst present.

• Observation: Analyst or machine observes the phenomenon and records data.

Summary Table: Measurement Scales

Scale	Information Provided	Examples	Permissible Operations
Nominal	Classification only	Defective/Nondefective	Counting, mode
Ordinal	Order/ranking	Ranking inspectors	Median, percentiles
Interval	Order, equal intervals	Temperature (°F)	Addition, subtraction
Ratio	Order, equal intervals, true zero	Weight, income	All arithmetic operations