Introspectionist and behaviorist interpretations of ratio scales of perceptual magnitudes.

Saaty’s 1977 article is his first comprehensive publication of the ideas behind AHP. He reveals his creativity in a new method for ratio measurement that includes pairwise ratio matrices, derived ratio scales from those matrices, and checks on the consistency of data. His ingenuity in using ratio measures is revealed by the use of hierarchical structures to display priorities and then a rescaling of them in a manner that allows synthesis for a composite ratio result. Face validity is provided by many supporting examples and mathematical validity is provided by the solution to many theorems. https://doi.org/10.13033/ijahp.v9i3.532

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A New Multichannel Fourier Transform Spectrometer

International Astronomical Union Colloquium ◽

10.1017/s0252921100048314 ◽

1999 ◽

Vol 170 ◽

pp. 36-40

Author(s):

Tyler E. Nordgren ◽

Arsen R. Hajian

Keyword(s):

Fourier Transform ◽

Extrasolar Planets ◽

Signal To Noise Ratio ◽

Fourier Transform Spectrometer ◽

Test Bed ◽

Signal To Noise ◽

Stellar Spectra ◽

Band Emission ◽

Noise Ratio ◽

Ratio Scales

AbstractStellar spectra have been obtained using a multichannel Fourier Transform Spectrometer (FTS) which incorporates components of the Navy Prototype Optical Interferometer. It is well known that a FTS can provide superior wavelength stability as compared to traditional spectrometers. Unfortunately the FTS traditionally suffers from exceptionally poor sensitivity, which until now has limited its uses to sources with high fluxes and/or those with narrow band emission (e.g. the Sun, nebulae, and laboratory samples). We present stellar observations using a new FTS design which overcomes this sensitivity limitation by using a conventional multichannel spectrometer in conjunction with the FTS system. The signal-to-noise ratio of spectra from our test-bed observations are consistent with the theoretical prediction and show that for N channels the sensitivity scales like N, while the signal-to-noise ratio scales like . With this type of an instrument on a 3-m telescope and 9 000 channels we expect to be able to detect and measure such exciting astrophysical phenomenon as gravitational redshifts from single, main sequence stars and extrasolar planets of terrestrial mass.

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The Magnitude and Direction of Collider Bias for Binary Variables

Epidemiologic Methods ◽

10.1515/em-2017-0013 ◽

2019 ◽

Vol 8 (1) ◽

Cited By ~ 2

Author(s):

Trang Quynh Nguyen ◽

Allan Dafoe ◽

Elizabeth L. Ogburn

Keyword(s):

Linear Regression ◽

Selection Bias ◽

Odds Ratio ◽

Risk Difference ◽

Binary Variables ◽

Spurious Association ◽

Ratio Scales ◽

Regression Adjustment ◽

Collider Bias

AbstractSuppose we are interested in the effect of variableXon variableY. IfXandYboth influence, or are associated with variables that influence, a common outcome, called acollider, then conditioning on the collider (or on a variable influenced by the collider – its “child”) induces a spurious association betweenXandY, which is known as collider bias. Characterizing the magnitude and direction of collider bias is crucial for understanding the implications of selection bias and for adjudicating decisions about whether to control for variables that are known to be associated with both exposure and outcome but could be either confounders or colliders. Considering a class of situations where all variables are binary, and whereXandYeither are, or are respectively influenced by, two marginally independent causes of a collider, we derive collider bias that results from (i) conditioning on specific levels of the collider or its child (on the covariance, risk difference, and in two cases odds ratio, scales), or (ii) linear regression adjustment for, the collider or its child. We also derive simple conditions that determine the sign of such bias.

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A Rejoinder to Forman on AHP, with Emphasis on the Requirements of Composite Ratio Scales

Decision Sciences ◽

10.1111/j.1540-5915.1992.tb00403.x ◽

1992 ◽

Vol 23 (2) ◽

pp. 509-517 ◽

Cited By ~ 19

Author(s):

Bertram Schoner ◽

William C. Wedley ◽

Eng Ung Choo

Keyword(s):

Ratio Scales

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Ratio scales of sugar sweetness

Perception & Psychophysics ◽

10.3758/bf03210175 ◽

1970 ◽

Vol 7 (5) ◽

pp. 315-320 ◽

Cited By ~ 144

Author(s):

Howard R. Moskowitz

Keyword(s):

Ratio Scales

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Meßniveau und Analyseverfahren – Das Problem „strittiger Intervallskalen”

Zeitschrift für Soziologie ◽

10.1515/zfsoz-1978-0301 ◽

1978 ◽

Vol 7 (3) ◽

Cited By ~ 8

Author(s):

Klaus R. Allerbeck

Keyword(s):

Social Research ◽

Correlation Coefficients ◽

Theory Building ◽

Interval Scale ◽

Social Survey ◽

Ordinal Measure ◽

Interval Scales ◽

Ratio Scales ◽

Measure Of Association ◽

General Adoption

AbstractMany variables used in social research are measured „by fiat”. The „undermeasurement controversy” focusses on the question whether such variables may be treated as interval scales in the process of data analysis. To resolve this issue, the original prescriptions by STEVENS (1946) are critically examined. From a philosophy of science perspective, the problem of the undermeasurement controversy needs redefinition. The traditional issue „Should ordinal scales be treated as interval” is shown to be strictly nonsensical.A strict comparison of statements about relationships between variables assumed to be „measured” at the ordinal or interval level is not possible. In particular, linearity of relationships is a meaningful concept only if interval scales are assumed. However, statements about 1. existence, 2. direction and 3. comparative strength of relationships are possible at both ordinal and interval levels of measurement. Thus, a meaningful question is whether treatment of an assumed interval scale as merely ordinal yields different or identical statements.It is empirically demonstrated that for typical social survey data of an attitudinal nature, the use of an ordinal measure of association and the use of product-moment correlation coefficients lead to virtually identical statements (to the extent to which their comparison is meaningful).The generalizibility of the result is discussed. An argument for the parametric strategy is made. The coding of variables measured by fiat is discussed. Progress of theory-building in sociology requires that theories state more than just the direction of relationships. Thus ratio scales are needed. It is pointed out that metric concepts are both a condition and consequence of development in theory as well as empirical research. A general adoption of a conservative ordinal strategy would effectively prevent such empirical and theoretical progress.

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