How do you establish a Scale Construct in Measurement ?

A scale must have a defined construct. e.g. a thermometer

1. any measurement must have a unit, e.g 'C, 'F.
2. a unit must be defined; 0'C is when water turns into ice at mean sea level. This called for a standard. It is the property of water; i.e. the property of the measured object.
3. a scale of an instrument must be of equal interval.
4. an instrument must be known for purpose; e.g clinical thermometer.
5. You must know how to use the instrument i.e. a nurse would shake it before taking your temperature
6. an instrument must be initiated to zero; i.e. 0'C hence calibrated.
7. a reliable instrument is not bias; a nurse use the thermometer repeatedly irrespective of man or women of all size.
8. a scale shall be able to predict an outcome; nobody has ever been to the sun but we can predict the temperature of the sun.

Using the correct instrument for purpose; i.e. mass spectrogrammeter we can predict the temperature of the sun. Similarly, nobody has ever been into some one's mind and measure their intelligent, a person's ability to think but we can infer by measurement just like we measure the sun's surface temperature provided we use the correct instrument and know how to use it correctly.

In education, the instrument is the exam paper, assignment, evaluation by observation of a student's performance for a given task. But how do you calibrate an exam paper ? What is the unit of measurement ?

Rasch Measurement Model offers us an intelligible explanation.