NURS 2031H Chapter Notes - Chapter 7: Observational Error, Central Tendency, Likert Scale
26 Jun 2018
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Chapter 7
MEASUREMENT
1. THE PROCESS OF MEASUREMENT
Simplest level of measurement is giving a numerical value to a phenomenon
Hypothetical constructs: measure attributes that are not directly observable,
consists of behaviors, attitudes, process and other attributes that tend to occur
together
oCannot observe depression, but can observe manifestations of depression
oThis is the most common measurement technique in health
oProblems arise with this because “it all depends” is very present
Many varying conceptualizations may exist for a phenomenon and this creates many
existing scales to measure the same construct
oUsers of scales must be clear (because of stated above) about their own
definitions of constructs and selection of an instrument must be congruent
with their definition
Definitions of constructs: how it is conceptualized, what they believe
should/should not be included, how construct can be
operationalized)
Instrument: what you use to measure with
2. VARIABLES
Types of variables: used to consider differences in variables
Categorical variables: must satisfy two conditions
oMutually exclusive – person cannot be placed into two or more categories
oCollectively exhaustive – all possible options must be covered
Discrete variables: the answer is constrained to be a whole number and cannot be
any value in between
Obsessive variables – continuous variables
A categorical variable is exclusive and exhaustive; numerical values assigned have
no quantitative (mathematical) meaning; values assigned as labels only
(nominal/ordinal levels of measurement)
A discrete variable consists of separate, indivisible categories – no values can exist
between two neighboring categories (can’t take on any values between whole
numbers)
Note: Many textbooks do not differentiate between categorical and discrete
variables, but the distinction here is important in that discrete variables
A continuous variable is divisible into an infinite number of fractional parts – there
are an infinite number of possible values that fall between any two observed values
Levels of variables: different ways of describing variables
Nomial, ordinal, interval and ratio – differentiated by 3 attributes:
oRules for assigning numbers to different values of the variable
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oMathematical properties of the resulting scales
oTypes of statistics that can be used with them
Nomial (similar to categorical variables)
oMust be mutually exclusive and collectively exhausted
oNumbers can be assigned but they are simply numbers
We can change the numerical assignment without gaining or losing
any information
Assign a hospital with #1 and the other #2 but the actual #s don’t
mean anything.
oAre limited
All that can be done is determine which category has the most
members
Some cases can have two categories that are just about equal
(bimodal distributions)
If sample size is small model value can change as new people are
added to the sample
Ordinal
oMust be mutually exclusive and collectively exhaustive
oCategories must be in rank order
oDistances between successive values are not consistent
oMust use median to describe central tendency, and range or interquartile
range for dispersion
oStatistics that can be used are limited to non-parametric ones based on
ranks
oNot all ordinal scales are constructed equally
Interval and ratio scales
oInterval restrictions: be mutually exclusive, collectively exhaustive, and
values have to be equally spaced
oRatio scale restrictions: be mutually exclusive, collectively exhaustive, values
have to be equally spaced, and needs to have a meaningful zero
oDifference between interval and ratio scale:
Interval: Celsius and Fahrenheit use different temperatures to define
zero degrees
It is an arbitrary value and not a meaningful value
Ratio scale: Kelvin scale begins at absolute zero
oDifference lies the mathematical operations that can be done for each
oFor both differences are meaningful:
Intervals are equal, adding and subtracting values are meaningful
oRatios between values are only meaningful for ratio scales
oMeasure of central tendency is the mean and measure of dispersion is the
standard deviation
3. CONSTRUCTING SCALES
Psychometric theory
Scale development is based on classical psychometric theory which assumes that
the score obtained on a scale consists of two parts: the unobserved true score plus
some degree of error.
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find more resources at oneclass.com
So in other words, we never see the true score because there is always a degree of
error associated with it.
Assumptions:
oThe error is unrelated to the true score (the amount of error is the same
throughout the entire range of the scale’s possible scores)
oExpected value of the error for each of the items on the scale is zero (the
errors will cancel each other out)
oNB: The longer the scales, the more the errors will cancel each other out –
longer scales are better than shorter ones.
Classical test theory (CTT): assumes that the score that’s obtained on a scale actually
consists of two parts –
oThe true (unobserved) score
oSome error
CTT is so prevalent due to underlying assumptions are considered “weak” = apply in
most situations
To understand assumptions need to understand basic premise of scale construction
oThe score we have observes (Xo) is made of two parts
The true score (Xt)
Some error (E)
Xo = Xt + E
oMeans we never see true score this is due to there always being some error
associated with it
Assumed the error has a mean of zero
Sometimes add to true score, sometimes makes it smaller
If added up errors for large numbers of items the average value
would be zero
oTrue score = score person would obtain if scale has infinite number of
items/if respondent completed it an infinite number of times
So error terms of individual item/administration cancel each other
out
oA true score does not mean an honest score – person could consistently lie
about something
True is just referring to the score being free from error
Assumptions of CTT
oError is unrelated to the true score (amount of error is same throughout
entire range of scales possible scores)
oExpected value of error for each item is zero and the errors will cancel each
other out as all items are added up to get the total score
The above suggests longer scales are freer from random error than
shorter scales because there is more chance for errors to cancel out
Devising the items:
Most of what is measured in health are hypothetical constructs
oHas direct implication for what items do/do not appear on scale
What the scale should encompass arises from one’s theory or
conceptualization of the construct
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Simplest level of measurement is giving a numerical value to a phenomenon. Definitions of constructs: how it is conceptualized, what they believe should/should not be included, how construct can be operationalized) Instrument: what you use to measure with: variables. Types of variables: used to consider differences in variables. Categorical variables: must satisfy two conditions: mutually exclusive person cannot be placed into two or more categories, collectively exhaustive all possible options must be covered. Discrete variables: the answer is constrained to be a whole number and cannot be any value in between. A categorical variable is exclusive and exhaustive; numerical values assigned have no quantitative (mathematical) meaning; values assigned as labels only (nominal/ordinal levels of measurement) A discrete variable consists of separate, indivisible categories no values can exist between two neighboring categories (can"t take on any values between whole numbers) Note: many textbooks do not differentiate between categorical and discrete variables, but the distinction here is important in that discrete variables.
