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Measurement Scale

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Measurement Scale - Continuous


The continuous measurement scale is used to provide a means for measuring a continuous quantity which can be subdivided into finer-and-finer increments.


Types of Data

Continuous Data Example

Continuous Data

Reference: Juran’s Quality Control Handbook


A. Characteristic’s entity to be evaluated

B. Data sheet showing 20 samples (#1 to #20), each with a size of 5 parts

C. Sample number (#9)

D. Single value (part #4 out of sample #9) - continuous or variable data

Measurement Scale - Discrete


To provide a means for measuring count data using integer or whole numbers. Usually used to enumerate as a means to establish density for opportunities for defects.


Discrete Data

Reference: Juran’s Quality Control Handbook


A. Data sheet

B. Typical Attribute or Discrete data

C. Event you’re interested in

D. Outcomes that result from that Event - Attribute or Discrete data

Measurement Scale - Interval


To provide a means for establishing a precise relationship between data where the measurement member is some function of the magnitude, but there is no absolute zero.


Interval Data

space block

Reference: Statistics Probability, Inference and Decision


A. The measurement scale - interval: degree Celsius

B. The measurement scale - interval: degree Fahrenheit

Note that if we consider 10ºC (50ºF) compared to 20ºC (68ºF), we could not say that in Fahrenheit the temperature is twice as much. Also, it would be wrong to imply that the second temperature is twice the first. In Celsius, only the second measurement is twice the first.

C. The surface variation being measured.

D. The scale: millimeters

E. “Remote” absolute zero.

Measurement Scale - Logarithm


To display non-linear data in a format that spans several orders of magnitude. To provide a presentation technique that can be read with a degree of precision for a wide range of values.


Logarithm Data

Reference: Business Statistics


A. Linear vertical scale «Y».

B. Linear horizontal scale «X».

C. Curve representing the function: Y=f(X).

D. Difficulty to detect any variation of y for different Xs.

E. Logarithms vertical scale.

F. New line representation of the function: log Y=b+mX (if linear).

G. PPM vs Sigma (values from less than one, to over 100,000 can be read from this scale).

Major Considerations

If the non linearity of the data is such that useful information cannot be obtained, then taking the logarithm is appropriate. The use of log base 10 is most often used, but any other base can be selected if desired.

Application Cookbook

1. Enter data in excel spreadsheet.

2. Select log 10, log x, ln, as req'd.

3. Plot data.

Logarithm Data Example

Measurement Scale - Nominal


To classify data into classes, each given a distinguishing symbol or name with no relationship between the various categories in terms of relative size.


Nominal Data

Reference: Statistics Probability, Inference and Decision


A. Workers wearing glasses = category of workers

B. Certified inspectors = classification

C. Missing approval signature = type of defect

D. Different type of defects on left wing upper surface = poor quality categories, whole numbers / integers only, Go / No Go, Pass / Fail, Yes / No

Measurement Scale - Ordinal


The ordinal measurement scale is used to rank data as a means to establish relative importance with no information about the distance between categories. To yield more knowledge about relative size, importance or relationship of a category of items.


Ordinal Data

Reference: Statistics Probability, Inference and Decision


A. Ordinal scale.

B. Ranked typical answers - in ascending or descending order.

C. Relative height order - category = people (not including brooms).
Whole numbers / integers only.

Measurement Scale - Ratio


The ratio measurement scale is used to provide a means for establishing a precise relationship between data where the measurement is some direct function of the magnitude with equal distance between categories and the presence of an absolute zero.


Ratio Data

Reference: Statistics Probability, Inference and Decision


A. Data plot of the characteristic: position = f(time)

B. Measurement scale – ratio: position (with zero)

C. Measurement scale – ratio: Time (with zero)

Measurement Scale - Likert Scale


The Likert measurement scale can be used to evaluate customer satisfaction using an ordinal scale with a range of ratings or degrees of satisfaction arranged in order. To determine what you are doing right, as well as wrong.


Likert Scale

Reference: Customer Satisfaction Assessment Guide


A. Ordinal scale arranged in ascending or descending order.

B. A series of questions to be rated by the customer.

C. Simple set of instructions.

D. An attempt to collect names/addresses so that follow up can be conducted in the future.

Major Considerations

Keep the survey very simple. Make it easy for the customer to tell you he is not happy. The goal is to gather data to best know how to satisfy the customer.

Application Cookbook

1. Designing the Survey Questionnaire:

Design Considerations:

  • Length (not too long);
  • Types of questions (statements of fact or measures of performance and importance);
  • Open-ended questions/probes (respondents will be able to volunteer issues and provide explanations);
  • Appearance (simple, not busy).

Type of Question Formats:

  • Closed-ended (yes/no);
  • Rating scales (even or add numbers? Both can be useful);
  • Open ended (free response).

2. Other Considerations:

Focus on one theme; Its usually best to include a midpoint in rating scales (e.g. 3/5/7 categories);

Try to solicit your customers feelings with regard to your competitors;

Identify specific target control groups:

  • At least 10% of total customer base;
  • Stratify various customer segments;
  • Give prior notice before delivering survey;
  • Personalize the survey and cover letter;
  • Address confidentiality;
  • Offer an incentive or token of appreciation for completion;
  • Follow up with a collection strategy;
  • Develop action plans based on results;
  • Communicate results to customers;
  • Follow up with repeat surveys to monitor changes with time.

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