Psych Assessment Norms and Statistics for Testing

1. NORMS AND BASIC
STATISTICS FOR
TESTING
Psychological
Testing and
Assessment

2. WHY WE
NEED
STATISTICS
First, statistics are used for
purposes of description.
Second, we can use statistics to make
inferences, which are logical
deductions about events that cannot
be observed directly.

3. WHY WE NEED STATISTICS
• Data gathering and analysis might be considered analogous to criminal investigation and
prosecution (Cox, 2006; Regenwetter, 2006; Tukey)
• First comes the detective work of gathering and displaying clues, or what the statistician John
Tukey calls exploratory data analysis.
• Then comes a period of confirmatory data analysis, when the clues are evaluated against rigid
statistical rules.
• Descriptive statistics are methods used to provide a concise description of a collection of
quantitative information.
• Inferential statistics are methods used to make inferences from observations of a small
group of people known as a sample to a larger group of individuals known as a population.

4. SCALES OF
MEASUREMEN
T

5. PROPERTIES
OF SCALES
Magnitude- It is the property
of “moreness”.
Equal Intervals- If the difference
between two points at any place on
the scale has the same meaning as
the difference between two other
points that differ by the same
number of scale units.
Absolute 0- It is obtained
when nothing of the property
being measured exists.

7. NOMINAL:
-Eye Color (e.g. Blue, Brown, Green)
-Nationality (e.g. German, Filipino, Lebanese)
-Personality Type (e.g. Introvert, Extrovert)
-Employment Status (e.g. Unemployed, Part-time, Retired)
-Type of Smartphone Owned (e.g. Iphone, Samsung,
Google Pixel)

8. ORDINAL
-Academic Grades (A, B, C…)
-Satisfaction (Extremely Satisfied, Quite Satisfied,
Slightly Dissatisfied, Extremely Dissatisfied)
-Level Of Education Completed (High School,
Bachelor’s Degree, Master’s Degree)
-Seniority Level At Work (Junior, Mid-level, Senior)

9. INTERVAL
-Temperature In Degrees Fahrenheit or Celsius (But not
Kelvin)
-IQ Score
-Income Categorized as Ranges (P30-39k, P40-49k,
P50-59k, and so on)

10. RATIO
-Weight in grams
-Number of employees at a company
-Speed in miles per hour
-Length in centimeters
-Age in years
-Income in dollars

11. FREQUENCY DISTRIBUTIONS
• The frequency distribution displays scores on a variable or a measure to reflect how
frequently each value was obtained.

14. PERCENTILE RANKS
• Percentile ranks replace simple ranks when we want to adjust for the
number of scores in a group.
• A percentile rank answers the question, “What percent of the scores fall
below a particular score (Xi)?”

15. PERCENTILES
• Percentiles are the specific scores or points within a distribution.
• Percentiles divide the total frequency for a set of observations into
hundredths.
• Instead of indicating what percentage of scores fall below a particular score,
as percentile ranks do, percentiles indicate the particular score, below which
a defined percentage of scores falls.

16. PERCENTILE RANK VS PERCENTILE
Percentile Rank: This is a percentage indicating how a particular value (like a test score) compares to the rest of the
scores in a distribution. For example, a percentile rank of 80 means that 80% of the scores in the distribution are
lower than that specific score.
Percentile: This is a value itself that divides a dataset into 100 equal parts. The nth percentile represents the value
below which n% of the data points fall. For example, the 75th percentile is the value that separates the bottom 75%
of the data from the top 25%.
Example: Imagine a class of 100 students took a test.
• If Sarah scores at the 80th percentile, it means that 80% of the students scored below her. Her percentile rank is
80.
• If the 75th percentile score was 85, it means that 75% of the students scored 85 or less. 85 is the value at the 75th
percentile.

17. DESCRIBING
DATA

18. MEASURES OF CENTRAL TENDENCY
1. MEAN
The arithmetic average score in a distribution is called the mean.
To calculate the mean, we total the scores and divide the sum by
the number of cases, or N. The capital Greek letter sigma (S)
means summation.

19. MEASURES OF CENTRAL TENDENCY
2. MEDIAN
The median, defined as the middle score in a distribution, is determined by ordering the scores in
a list by magnitude, in either ascending or descending order.
To calculate the median, first arrange the data set in ascending order. If the number of data points
is odd, the median is the middle value. If the number of data points is even, the median is the
average of the two middle values.
Example: Data set: 2, 5, 1, 8, 4
Arrange in ascending order: 1, 2, 4, 5, 8
The median is the middle value, which is 4.

20. MEASURES OF CENTRAL TENDENCY
3. MODE
The most frequently occurring score in a distribution of scores is the mode.
As an example, determine the mode for the following scores obtained by another TRW job
applicant, Bruce. The scores reflect the number of words Bruce word-processed in seven 1-
minute trials:
43 34 45 51 42 31 51

21. MEASURES OF VARIABILITY
Variability is an indication of how scores in a distribution are scattered or dispersed.
1. The range of a distribution is equal to the difference between the highest and the lowest
scores.
2. A distribution of test scores can be divided into four parts are quartiles.
3. The interquartile range is a measure of variability equal to the difference between Q3
and Q1.

24. SKEWNESS
• Skewness is an indication of how the measurements in a distribution are distributed.
1. A distribution has a positive skew when relatively few of the scores fall at the high end of
the distribution.
2. A distribution has a negative skew when relatively few of the scores fall at the low end of
the distribution.

26. DESCRIBING DISTRIBUTIONS
STANDARD DEVIATION
The standard deviation is an approximation of the average deviation around the mean.

27. NORMS
• Norms refer to the performances by defined
groups on particular tests.
• Age-Related Norms- Certain tests have different
normative groups for particular age groups.
• A norm-referenced test compares each person
with a norm.
• A criterion-referenced test describes the
specific types of skills, tasks, or knowledge that
the test taker can demonstrate such as
mathematical skills