The Nature of Measurement • Measurement is a process of assigning numerals to observations according to some established set of rules • Numbers in measurement eliminate ambiguity in classification and promote uniformity in practice • Measurements can be qualitative or quantitative depending the how the number system is applied
Quantitative • Main Entry: quan·ti·ta·tive1: of, relating to, or expressible in terms of quantityFrom www.webster.com • Something you can count • More objective than qualitative analysis • Usually easier to display
Qualitative • Main Entry: qual·i·ta·tive: of, relating to, or involving quality or kind • From www.webster.com • Usually more subjective than quantitative analysis • More “open-ended”
In the physical Sciences • Measurements in the physical sciences tend to be quantitative. • The role of measurement is to enable us to classify attributes or properties of “objects” so that we can fruitfully apply mathematical concepts, theories and techniques in reasoning about them. • In other words, the answer to why we do measurements in the physical sciences is that if we do it properly we will be able to establish mathematical models with equations and prediction capabilities which are the goal of the inquiry.
Direct Measurements • Measuring the length and width of a table • Principle of direct comparison – use an established “standard” to measure a given property of an object
Indirect Measurement • Measurements on a scale outside of human capacity – the distance from earth to the sun , or the size of an atom
Resolution - the smallest measurable amount • Accuracy - the fractional error in making a measurement; difference between the measured value and the “actual” value
Results of the Measuring Process • A measurement can be looked upon as a relationship between some property / attribute of a physical system and of quantities that define it - the length and width of a desk! • The measured quantity can always be expressed in different numerical scales and related to each other in precise mathematical ways.
Errors of Observation • Given a well-described experimental procedure to measure certain properties of a “system”, there will be scatter in the results obtained through repeated application of the procedure. • This is experimental error – different measured values of the same property using identical measurement process.
Error occurs even when the rules of the measurement process is strictly observed. • They are due to inherent looseness in the these rules: • Random, accidental, not controllable, …….. ( incompleteness ) • Systematic, repeatable, instrument caused, ……( inaccuracy)