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Chapter 1

PSYC 2P25 Chapter Notes - Chapter 1: Standard Score, Standard Deviation, Trait Theory

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Michael Ashton

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Chapter 1: Basic Concepts in Psychological Measurement
Some Simple Statistical Ideas
Levels of Measurement
There is not usually a meaningful “zero” level of a psychological trait
In psychology, we are not able to describe ratios between people’s levels of a variable or a
person’s absolute amount of a variable
Ways of measuring
o Ranking people
o Observation
Standard Scores
Measure the differences between scores
o Differences in numbers used for measuring variables might cause difficulties when we
want to compare someone’s scores across two or more traits
o So we need some way to relate scores on one scale to scores on another scale, so that
we can compare levels of one characteristics with levels of another, or to compare
scores on the same characteristic as measured by different scales
Scores are converted into standard scores
o The first step in calculating a standard score is to take an individual’s score on a given
scale, and then subtract the mean score for the person’s that have been measured. This
difference tells us whether the person is above average or below average.
o The second step is to divide this difference (between the person’s score and overall
average) by the standard deviation, a number that indicates how much variability there
is among a variable
o The result of the two steps is to give a universal or standard way of expressing people’s
scores on a given characteristic, regardless of the original distribution of scores on that
Standard scores have two special properties
o The average score on a standard-score scale is exactly one. That way after we have
calculated the scores, we can meaningfully compare a person’s scores across different
Correlation Coefficients
After we have calculated the scores, we can easily figure out the extent to which the two
variables “go together,” or correlate
Correlation coefficient = r
o It can have values ranging anywhere from a maximum of +1 to a minimum of -1
o +1 perfect positive; -1 perfect negative
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o Between +.20 and -.20 is a weak correlation
o Between +.20 and +.50/-.20 and -.50 is a moderate correlation
o Above +.50 or below -.50 is an extreme correlation
The binomial effect size display (BESD) is a table that helps to give us an intuitive understanding
of the meaning of a correlation of a give size
o Contains two rows and two columns
o One row represents the set of people who have a “high” or above-average level of one
variable, and the other row represents the “low” or below-average
o One column represents the set of people who have a “high” or above-average level of a
second variable, and the other column represents the “low” or below-average of that
second variable
Assessing Quality of Measurement: Reliability and Validity
The extent to which it agrees with other measurements of the same variable. When there is a
good agreement between measurements, this tells us that they are assessing some real
characteristic, rather than meaningless numbers.
There are several ways that reliability can be assessed
Internal-Consistency Reliability
o When evaluating the quality of a psychological measurement, we need to consider the
error that results from differences among the “items” or parts of the measurement,
such as the various questions on a test or scale
o To the extent that an item measures some specific variable of its own, rather than the
characteristic that we are trying to assess, we say that the item has “error” variance. If a
test or scale overall has a large proportion of error variance, then it cannot be
measuring any single, common characteristic reliably.
o The reliability of a score that is found by averaging responses to several items basically
depends on two things:
The number of items
If we are averaging out people’s responses to items that have
something in common, that common element will become stronger and
strong when we add more and more items, so by averaging out across a
larger number of items, we get a more reliable score.
The correlations between items
If we are averaging out people’s responses to items that have
something in common, that common element will be stronger to the
extent that the items are correlated with each other, because those
correlations tell us how much each individual item is measuring the
common characteristic.
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