Scientific Practice Measurements

What is Measurement? Assigning comparative labels to things to help explain their relationships… sounds a bit abstract… …but things/relationships is all there is… …and that’s all that science is about! so measurement is rather central to science Measurements are typically, but not exclusively, numerical not all types of measurement are equivalent four different levels of measurement nominal, ordinal, interval and ratio

Nominal Scales The ‘lowest’ level of measurement nominal implies ‘names’ Just labels to stick things into categories and separate them No implicit order eg yes/no shirt numbers of footballers 1 – goalie, 10 – striker (but not ‘10x better’!) can serve to separate and provide some info if refer to #10, it’s likely to be about a striker not a goalie blue, yellow, red, green etc no implicit order (though underlying spectrum has)

Ordinal Scales The measurements can be ‘ordered’ (ranked) the order of finishers in a race (first, second, etc) but time between each can vary dramatically equal gaps not implied the Likert scale (1  5) agree strongly, agree, neutral, disagree, disagree strongly again, the ‘gaps’ between each are not equal agree - neutral doesn’t ‘equal’ neutral - disagree

Interval Scales The ‘gaps’ (intervals) between units of measurement are equal the Centigrade scale the temp difference between 20 and 30 C is the same as between 10 and 20 C though they might not ‘feel’ that way! there is no absolute reference point 0 C is arbitrary water’s freezing point used to define the baseline Much more common in science

Ratio Scales An interval scale that has an absolute reference point the Kelvin temperature scale 0 K is -273.16 C the reference point is absolute absolute zero (0 K) is, well, absolute! for our everday lives, time is a ratio scale zero time is absolute like interval scales, ratio scales common in science These measurement scales are important as they determine the types of data-handling/statistics that can be performed

Summaries of Data Scientists seldom take single measurements need repeated measurements to… minimise error permit extrapolation to the general case eg my eyes are blue 32 out of 100 subjects studied had blue eyes 32% of the general population have blue eyes Data is plural (datum is singular) Could just report all measurements… contains unadulterated ‘info’ about what you did but doesn’t carry a ‘message’ about the findings can’t see the wood for the trees

Summaries of Data Here is a set of ordered data… Mode Median Mean 17, 18, 18, 18, 19, 19, 20 21, 21 Mode the most common value(s) of a list of data (18) Median the central value in the ordered data (19) Mean sum of values/sample size (171 / 9 = 19) Range (or maybe Maximum and Minimum) highest minus lowest (21 – 17 = 4) starts to indicate variability, but biased by extremes

Indicating Variability This is an important aspect of measurement 17, 18, 18, 18, 19, 19, 20 21, 21 and 18, 19, 19, 19, 19, 19, 19, 19, 20 and 19, 19, 19, 19, 19, 19, 19, 19, 19 all have the same mean Need a way to summarise data both in terms of ‘central tendency’ and ‘spread’ mean and standard deviation median and quartiles Will cover measures of variation in detail elsewhere

Summary Measurements are labels assigned to things to explain relationships Four levels… Nominal – names; no inherent order Ordinal – ordered; ‘gaps’ not equal Interval – ordered; ‘gaps’ are equal Ratio – ordered; equal gaps; absolute ref point Summaries of data needed to ease interpretation – eg mode, mean, median, range Need indicators of ‘spread’ as well as ‘centre’ eg range, max, min, standard deviation