1. Scientific Practice
Measurements

2. 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

3. 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)

4. 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

5. 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

6. Ratio Scales An interval scale that has an absolute reference point
the Kelvin temperature scale
0 K is 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

7. 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

8. 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

9. 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

10. 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