Chapter 5: Standardizing Distributions Flashcards
Why do we use standardized/rescaled scores?
Unlike physical variables (e.g., age, height, weight) that
have natural metrics that are easy to understand (e.g., years, inches, pounds), many psychological, educational, and social science variables (e.g., depression, IQ, academic performance) do not have inherent metrics.
To facilitate interpretation, researchers often use
standard scores with “universal” metrics.
What is the Minnesota Multiphasic Personality Inventory (MMPI)?
A widely used test of adult personality and psychopathology
It has 567 items that use a true or false response format
Clinical scales include depression, hysteria, psychopathic deviance, masculinity-femininity, paranoia, etc.
What is the NEO PI-R?
The Revised NEO Personality Inventory (NEO
PI-R)
A personality inventory that examines a
person’s Big Five personality traits
What are the Big Five personality traits?
- Openness to experience
- Conscientiousness
- Extraversion
- Agreeableness
- Neuroticism
What is a Standardized Metric?
Personality inventories (including the MMPI and
NEO PI-R) are rescaled to have a mean of 50
and standard deviation of 10
Z-score scales are another example of a standardized metric
What is a z-score scale?
The z-score scale is a common standardized
metric that sets the mean to 0 and the standard
deviation to 1
What does a z-score express?
A z-score expresses an individual’s distance to
the center of the data relative to the average
distance
It’s the location of a score in a distribution
expressed in standard deviation units from the
mean
What is the z-score formula?
Z = score (x) - population mean (μ) ➗ population standard deviation (σ) = distance ➗ average distance
The deviation score in the numerator captures
the distance/deviation of a score from the
center
Dividing by the standard deviation standardizes an
individual’s distance relative to the average
distance
IF we don’t know the population mean and
population standard deviation we can use the sample mean and sample standard deviation instead…
z = score (x) − sample mean (x̄) ➗ sample standard deviation (s) - this is the formula we’ll use most frequently
If z = -1 this tells us that the score is one standard
deviation below the mean
If z = 0.5 this tells us that the score is 0.5 standard deviation above the mean
- Z-scores are assumed to come from a normal distribution, with a mean of 0 and a standard deviation of 1, however, the variables being standardized may not necessarily be normally distributed themselves.
- When standardizing variables, we don’t necessarily change the shape of the distribution, since the original shape contains important information.
- Z-scores are useful both for comparing individuals and for comparing groups.
What is Standardized Mean Difference/Cohen’s d effect size?
It is usually difficult to assess the magnitude of an
experimental effect or group difference on the raw
metric of the data
A common approach is to express the mean
difference as a z-score
This application of z-scores is called a standardized
mean difference or Cohen’s d effect size
Dividing the mean difference by the standard
deviation expresses the group difference in the
z-score metric
It is the difference between two group means expressed in z -core or standard deviation units
Represented by ( d = ….)
Dividing the sample mean difference (X̄1 - X̄2) by the average sample standard deviation expresses the group difference in the z-score metric
n1 = # of participants in group one, etc.
S/2/1 sample variance for group one, etc. (sample variance squared)
This is for comparing groups
Know the “Standardized Mean Difference/Cohen’s d Effect Size Guidelines:”
It’s negligible if = less than |.20|
It’s small if = |.20 to .50|
It’s moderate if = |.50 to .80|
It’s large if = greater than |.80|
Use absolute value | | to remove positive and negative signs
| = absolute value
To apply Cohen’s effect size benchmarks, what
is the level of effect size for 0.318?
A. Negligible
B. Small
C. Medium
D. Large
B. Small
