Definition. If observations (including responses to test items) measure a given amount of a given quantity, then their variation depends on the variation of the quantity amount, in such a way that it is possible to deduce from them that the quantity amount has increased or decreased.
Remark 1. If one admits that the variability of observations depends on other factors and if one ignores the extent to which these factors determine the observed variation, one can deduce from the observations neither an increase nor a decrease of the quantity amount, because one cannot exclude that this variation results from undesired perturbations when the quantity amount did not change. This is the fatal flaw of the psychometric approach to psychological measurement.
Remark 2. The development of measurement instruments consists, among other things, in limiting within known boundaries the effect of the disturbing factors on the indicators that are used to deduce the variations of the quantity amount to be measured.
Remark 3. The development of measurement instruments requires the experimental manipulability of the quantity amount. For example, to study the disturbing variations of a response device, one has to be sure that the quantity amount does not vary (or varies negligibly) while one observes the behavior of the response device. To study the sensitivity of the response device to the variations of the quantity amount, one has to be able to increase or decrease more and more finely the quantity amount to be measured.
Remark 4. There is nothing like this in the realm of psychometric scoring techniques: one does not know how to manipulate the amount of intelligence nor the amount of anxiety for example, like one manipulates the temperature amount of water in the cooking pot by increasing the flow of gas. But this statement deserves contradiction… Who would like to refute this argument?
Remark 5. In psychology, tests or questionnaires are called measurement instruments. This linguistic custom is misleading because if one measured some quantity amounts with tests or questionnaires, the reason would be that the respondent were the measurement instrument, as she, not the test, produces the responses. Consequently, psychologists who are scientifically responsible for their practices should stop naming tests and questionnaires “measurement instruments”. If they do not stop, they contribute to propaganda that hawks the false idea that tests enable one to measure psychological quantities. Such propaganda demonstrates to informed audience that either they have no clear idea of what measurement is, or that they do not reject its deceptive character despite the evidence.
Remark 6. The definition above does not suffice to define metric measurement usually performed by measurement instruments. The definition is suitable for qualitative indicators, which enable ordinal measurement of the quantity amount to be measured. For example, if qualitative variations fulfill the definition, in such a way that one can deduce that the quantity amount increased, one ignores the amount of the increase: one knows only that it is strictly positive. Ordinal measurement allows one to speak the language of “more or less”, not the language of “how much”. As metric measurement supposes ordinal measurement, metric measurement is fasified if ordinal measurement is falsified.
Remark 7. As far as one describes in a given language how quantities like intelligence or anxiety manifest themselves, this language is not of the “more or less” sort. Most of observed variations do not match the “more than” nor the “less than” relationships. The scientific error of psychologists who believe in quantities like anxiety or intelligence lies in their refusal to admit that the phenomena (observables) they are studying are primarily qualitative. Instead of respecting their qualitative form, they disguise them as numbers (or scores), “counting their chickens before they are hatched”: they behave as if one could speak scientifically of anyone’s intelligence or anxiety in terms of more or less, with no problem of authenticity. But does the evidence, as exhibited in our descriptives frames, teach us that the language of “more or less” is suitable to genuinely speak of anyone’s intelligence or anxiety manifestation?
Conclusion. Either intelligence (or anxiety, or any psychological quantity) can be measured with test responses, in which case an ordering should emerge from the observations, or one cannot measure intelligence (or anxiety, or any psychological quantity) with test responses.