BASIC STATISTICAL
CONCEPTS IN
PSYCH ASSESSMENT
LILIBETH L. MANIGO, RGC
Assistant Professor I
Department of Psychology
▪ Researchers usually don’t know how to interpret someone’s raw
score: Usually, we won’t know whether, in nature, a score should be
considered high or low, good, bad, or what. Instead, the best we can
do is compare a score to the other scores in the distribution,
describing the score’s relative standing.
▪ Relative standing reflects the systematic evaluation of a score
relative to the sample or population in which the score occurs. The
way to calculate the relative standing of a score is to transform it into
a z-score.
▪ With z-scores we can easily determine the underlying raw score’s
location in a distribution, its relative and simple frequency, and its
percentile. All of this helps us to know whether the individual’s raw
score was relatively good, bad, or in-between.
▪ First, they were somewhat subjective and imprecise.
▪ Second, to get them we had to look at all scores in the
distribution.
▪ However, recall that the point of statistics is to accurately
summarize our data so that we don’t need to look at every
score.
▪ The way to obtain the above information, but more
precisely and without looking at every score, is to compute
each man’s z-score.
▪ A z- score describes a score in terms of how much it is above or
below the average.
▪ A z-score is the distance a raw score is from the mean when
measured in standard deviations.
▪ A z-score always has two components:
(1) either a positive or negative sign which indicates whether the
raw score is above or below the mean, and
(2) the absolute value of the z-score which indicates how far the
score lies from the mean when measured in standard deviations.
▪ Like any raw score, a z-score is a location on the distribution.
▪ However, the important part is that a z-score also simultaneously
communicates its distance from the mean. By knowing where a
score is relative to the mean, we know the score’s relative
standing within the distribution.
▪ A z-distribution is the distribution produced by transforming
all raw scores in the data into z-scores.
▪ A “+” indicates that the z-score (and raw score) is above and
graphed to the right of the mean. Positive z-scores become
increasingly larger as we proceed farther to the right. Larger
positive z-scores (and their corresponding raw scores) occur
less frequently.
▪ Conversely, a “-” indicates that the z-score (and raw score) is
below and graphed to the left of the mean. Negative z-scores
become increasingly larger as we proceed farther to the left.
Larger negative z-scores (and their corresponding raw scores)
occur less frequently.
▪ However, as shown, most of the z-scores are between -3 and +3.
▪ A third important use of z-scores is for computing the
relative frequency of raw scores.
▪ Relative frequency is the proportion of time that a score
occurs, and that relative frequency can be computed using
the proportion of the total area under the curve.
▪ We can use the z-distribution to determine relative
frequency because, as we’ve seen, when raw scores
produce the same z-score they are at the same location on
their distributions.