Understanding Measurement: Scaling, Numbers & Scoring Flashcards
Measurement Definition
- '’the assignment of numerals to objects or event according to rules’’
- psychological measurement can be seen as the process by which: “numbers are assigned to represent the quantity of psychological attributes”
Understanding Numbers
- numbers can represent attributes in different ways (i.e., quantity vs identity)
- the value of “0” has different meanings on different measures
Properties of Numbers
- there are 3 important properties that numbers vary in: different amounts of information about potential differences in attributes; differ in the way that zero can be understood
1. Identify
2. Order
3. Quantity
- Identity
➢ Simplest measurements are those that identify categories of people
❖ Ability to reflect “sameness versus difference”
➢ Ask teachers to indicate whether students have behavioural problems:
❖ 1 = No
❖ 2 = Yes
➢ In this case, numbers are simply labels of categories
❖ Represent quality; not quantity (e.g., not the severity of a behavioural problem)
Rules for Identity:
1. Numbers must establish identical categories
❖ People within one group should be the same as each other (on the criteria)
2. Groups Mutually Exclusive
❖ Groups must be different to one another and one person cannot be in both groups
3. Groups Are Exhaustive (i.e., everyone in the sample should fit a group)
❖ If a person does not fit into either group, then a third group is required
- Order
➢ Some numbers identify people and indicate the order between people
❖ This conveys more information about the relative amount of an attribute people possess
➢ Numbers indicate the rank order of people relative to an attribute
❖ 1 = The least amount
❖ 2 = A moderate amount
❖ 3 = The highest amount
➢ These numbers are essentially still labels (i.e., identify groups)
➢ But give more information by indicating the hierarchy of the groups (i.e., their order)
❖ 1 = Low Performing student
❖ 2 = Moderate Performing Student
❖ 3 – High Performing Student
➢ Still limited in their use
❖ Do not quantify the degree of difference between the groups
- Quantity
➢ Numbers with the property of quantity provide…
❖ … information about the magnitude of differences people have in an attribute
➢ These numbers reflect real numbers (i.e., no longer labels)
❖ A number of 1 defines the basic unit on any particular scale
➢ Real numbers are also referred to continuous numbers
❖ Numbers can go up or down in a continuous manner
❖ Sometimes referred to “scaler” or “quantitative” values
➢ Continuous numbers allow us to quantity of an attribute
❖ Based on some unit of measurement (i.e., degrees of temperature)
Example – Thermometer
➢ Reflects temperature in degrees (above or below 0)
❖ Unit of measurement = degrees
➢ Represent the quantity of temperature:
❖ 50°C is not only warmer than 40°C - it is 10°C warmer
Understanding the Value of Zero (0)
- zero can mean different things in different contexts
1. absolute zero - 0 reflects an attribute has no existence
2. arbitrary zero (‘relative zero’) - a hypothetical indicator to quantify an attribute
-does not reflect absence/ non-existence of an attribute - e.g. a temperature of 0 degrees does not mean there is no temperature
Arbitrary Zero in Psychology
➢ Psychology regularly evaluates attributes using relative/ hypothetical zero
❖ Not indicating that people have absolutely no intelligence, self-esteem, social skills etc…
❖ Everyone has these attributes but just to different degrees
➢ Some psychological tests produce a score of 0 for individuals
❖ This is an arbitrary value to indicate low levels of an attribute
➢ Important to consider what the test is actually measuring and how it is scored
❖ This will determine how we interpret a test score
➢ This can sometimes be challenging however …
Example: If a child takes a spelling test of 10 words…. and gets 0 correct
❖ Technically, their score has an absolute score of 0 (i.e., they got no correct answers)
❖ But it would be incorrect to assume that the child as no spelling ability
❖ Therefore, we may choose to interpret 0 as an “arbitrary value”
Interpreting Zero
Determining how we interpret zero is fundamental to:
1. how we analyse scores
2. how we interpret scores
1. The analysis we can conduct are influenced by what zero represents:
❖ Absolute 0: enables multiplication or division (as zero is a “real” value)
❖ Arbitrary 0: may need to restrict analysis to addition/ subtraction
2. Important to consider what as test actually tells us:
❖ Absolute 0: Should mean that an individual has none of the attribute
❖ Arbitrary 0: Will indicate low levels of an attribute
…but not that the attribute does not exist
Units of Measurement
➢ Understanding the units of measurement is important
❖ For time and height, we have predetermined/ standard units of measurement
❖ For self-esteem, how do we exactly determine how to measure it?
➢ Fundamentally, units of measurement can be two types:
❖ Arbitrary Units
o Random & inconsistent (subjective)
❖ Standard Units
o Quantifiable, commonly accepted, & consistent
Arbitrary Units
➢ ‘Relative’ units that could be used/ compared to measure an attribute:
❖ Length determined by the number of hands or feet
❖ Height determined by number of double decker busses
❖ Mass compared to the number of elephants
➢ Disadvantages of Arbitrary Units:
❖ They can create confusion as there is no uniformity in measurement
o The units may vary from one person to another (e.g., different size hands)
❖ The units may vary each time you measure the same thing
o Results vary simply due to difference in the measurement units
Arbitrary Measurement Units
➢ Three ways a measurement unit can be arbitrary:
1. Unit size
❖ If the unit size is inconsistent or may vary every measurement
o e.g., the hand size of different people may vary
2. Units of measurement are not tied to an object
❖ Arbitrary units can be used to measure many objects/ things
❖ Not specific to an attribute
o e.g., Hand-length could be used to measure a piece of wood, a car, and a garden
3. Units can be used to measure different features/ dimensions of an object
❖ Could hypothetically measure width and weight in the same unit
o e.g., A boat is 3 ‘elephants’ long and weighs 15 ‘elephants’
Standard Units
➢ All measurement units are fundamentally arbitrary
❖ Based on some standard which is usually not a precise or stable
➢ However, there are standard units of measurement that exist
❖ Designed to provide reliable and reproducible units
Examples
❖ Length (e.g., metres and centimetres)
❖ Weight (e.g. kilograms, grams)
❖ Time (e.g., hours, seconds, milliseconds)
➢ Standard units can still be somewhat arbitrary
❖ e.g., Time can be used to measure various things
o i.e., Reaction time or length it takes someone to complete an experiment
➢ Standard units help:
❖ Maintain uniformity in measurement
❖ Establish consistent units that are aimed to assess a specific attribute
❖ Common consensus on what these mean
Psychology: Units of Measurement
➢ Psychological attributes = harder to determine units of measurement
❖ What units of measurement reflect intelligence (or self-esteem)?
➢ Typically use standardised scales with a series of response options
❖ Questions are phrased to tap into the main aspects of the construct to be measured
❖ Respondents answer in relation to the concept
➢ Most psychological units of measurements ARE still arbitrary
❖ But normally only in relation to the unit size
o e.g., difficult know the real difference between “agree” and “strongly agree”
➢ Psychological tests are typically tied to specific attributes & dimensions
❖ Use specific response scales and scoring systems
➢ Standard units of measurement can be used to measure psychological attributes
❖ e.g., reaction time used to assess cognitive abilities
Counting (Units)
➢ A fundamental facet of measurement is counting
❖ Counting involves adding answers together to create an overall scores (additivity)
➢ A key assumption is that the unit size of measurement does not change
❖ i.e., remains constant/ identical
➢ A unit increase at one point should be identical to a unit increase at another point
❖ Measurement units are consistent for every measurement done
➢ It is why consistent units of measurements are important
❖ May get different scores if you used different units of measurement
❖ Reliability can be questioned
Measurement and Psychological Units
➢ Measurement Unit
❖ The scoring metric/ number on each test item/ question of a test
o i.e., what an individual scores for each question on a test
➢ Psychological Unit
❖ Reflects the “true” level of a psychological attribute
Levels of Measurement
➢ Measurement involves assigning numbers to reflect real psychological differences
❖ i.e., in a specific psychological attribute
➢ Scaling is how numbers are linked to behavioural observations to create a measure
➢ Four levels of measurement – differentiated by:
❖ Specific rules based on the properties of numbers
❖ Understanding of zero
❑ Nominal Scales
❑ Ordinal Scales
❑ Interval Scales
❑ Ratio Scales
Nominal & Ordinal Scales (Categorical Data = Identify Groups)
- Nominal Scales
➢ Identify groups/categories that have no meaningful order (e.g., sex/ gender)
❖ Numbers only meet the property of identity (i.e., individuals sharing common attribute)
❖ Assigned a numerical label that has no hierarchy (e.g., 1 = Male; 2 = Female)
❖ Nominal data often presented as frequencies/ percentages - Ordinal Scales
➢ Identify groups/ categories but labelled in a meaningful order (e.g., education level)
❖ Numbers meet the properties of identity and order
❖ Assigned a numerical label with a hierarchal order
o (i.e., 1 = secondary school; 2 = undergraduate; 3 = postgraduate)
❖ Ranks people according to the amount of attribute they possess
o No attempt to determine how much each person possess the attribute
o The distance between the numbers may vary
❖ Ordinal data typically described as frequencies and percentages
Interval & Ratio Scales (Continuous Numbers)
- Interval Scales
➢ Produce continuous numbers which do NOT HAVE a “true” zero (i.e., arbitrary zero)
❖ Unit of measurement is constant
➢ Example: Temperature would be measured on an interval scale
❖ Temperature can be minus (-15°C), zero (0°C), or positive (30°C)
❖ 0°C does not represent absence of temperature
❖ An increase temperature from 40°C to 42°C is the same as 80°C to 82°C
❖ Not appropriate to say 80°C is “twice as warm” as 40°C (as zero is arbitrary)
➢ Example: Most psychological questionnaire scales produce interval data
❖ A self-esteem scale ranging from 0 (“Strongly Disagree”) – 4 (“Strongly Agree”)
❖ A score of 0 does not mean no self-esteem (just low levels) - Ratio Scales
➢ Ratio data produces continuous data which HAS a “true” zero (i.e., absolute zero)
❖ Numerical measurement which is ordered and tells us the exact value between units
❖ Unit of measurement is constant
❖ Zero indicates an absence of the feature being measured
➢ Higher level of measurement:
❖ Provides more information and allows for sophisticated inferences
➢ Example: Distance
❖ 0 metres travelled means an individual has travelled no distance
❖ Appropriate to infer that travelling 20 metres is twice as far as 10 metres (as 0 is absolute)
➢ Example: Height
❖ A person who is 180 cm’s in height is twice as tall as a person who is 90 cm’s tall
➢ Very few psychological measures actually produce ratio-level data
Numbers For Statistical Analysis
➢ Any test will provide us with numbers to analyse….
❖ HOWEVER, this does not we should use them or that it will be meaningful
➢ If we tried to calculate a mean score based on nominal/ ordinal data (i.e., groups)
❖ We would get some odd results
❖ Numerical statistics wouldn’t make much sense here
➢ Example: Nominal Groups Based On Hair Colour
o 1 = Black Hair
o 2 = Blonde Hair
o 3 = Brown Hair
o 4 = Grey Hair
➢ If we calculated average hair colour here, we could get an average value of 2.45
❖ This would be difficult to understand
o Average hair colour is a mixture of blonde/ brown???
➢ Nominal numbers is mainly used to identify groups (not the quantity of differences)
Nominal / Ordinal Data Still Useful
➢ Nominal/ Ordinal data still useful for allowing us to explore group differences:
1. Descriptive information for each group:
❖ How many people are in each group? Is one group much larger than another?
❖ Do the groups differ in composition (i.e., are there more females in one group)?
2. Comparing different groups:
❖ T-tests (two groups) and ANOVA (more than two groups) analyses
o These analysis explore whether different groups vary in an attribute
❖ The nominal/ ordinal data is used to group individuals
❖ These groups are then compared in their scores from an interval or ratio scale
o i.e., Do the groups differ on a continuous number
Nominal Scales: Binary Variables
➢ The only exception is when a nominal numbers include only two groups
➢ If we categorised individuals based on their scores from a depression scale
❖ Could create a dichotomous variable that is assigned binary codes
❑ 0 = Not depressed
❑ 1 = Depressed
➢ This can reflect interval data
❖ 0 does not mean absolutely no depression
❖ But Group 1 reflects higher levels than Group 0
➢ This binary number could then be used like a continuous number
❖ To see if the two groups are correlated with scores on another attribute (i.e., sadness)
❖ We would know the depressed group are higher in sadness
o As the value of 1 is higher than 0
