9814

Expanded Magnitude Estimation Method

This Demonstration presents an expanded version of the magnitude estimation method used to assess the perceived intensity of physical and chemical stimuli by humans or their preference for a product. It is based on the individual subject or panelist's assessment, not as a single number or equivalent length, but as lower and upper limits of a range. This is followed by Monte Carlo simulations to produce the mean response and its standard deviation. These can also be computed directly from the entered ranges' limits. If the entered minimum equals the entered maximum in all the evaluations, this reduces to the traditional method.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Snapshot 1: twelve relatively high ratings having a relatively small spread
Snapshot 2: eight relatively low ratings having a relatively large spread
Snapshot 3: ten ratings entered as in the traditional method (all the minima are equal to their corresponding maxima)
This Demonstration simulates an expanded version of the magnitude estimation method, where the sensory evaluations are entered as lower and upper limits of a range rather than single numbers or equivalent lengths. The calculation of the mean and standard deviation of the entered evaluations is done in two ways for mutual verification:
1. By Monte Carlo simulation, generating and averaging of numerous combinations of values chosen randomly from within the respective intervals. The mean and standard deviation of this generated data are considered as those that correspond to the specified ranges.
2. Analytically, using the formulas and , where is the number of evaluations. The term is the variance of a continuous uniform distribution with a domain from to .
The number of Monte Carlo random trials , the seed value, and the and are entered with sliders. The evaluations are activated by clicking a checkbox, as is the use of the entered seed's value. In order to produce new random trials with exactly the same parameter settings, first click the "clear" button and then the "generate" button.
The output includes the mean and standard deviation values calculated by the above two methods, the histogram of the values generated by the Monte Carlo simulations, and a plot of the normal distribution that has the same mean and standard deviation as the generated data.
When all the are equal to their corresponding , this is equivalent to the traditional magnitude estimation method. The histogram in this case consists of a single bin, and the standard deviation value is to be printed in red.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+