LEVELS OR SCALES OF MEASUREMENT

1. LEVELS OR SCALES OF MEASUREMENT
Level/Scale Characteristics Example
1. Nominal Nominal variables (also called categorical
variables) can be placed into
categories. They don’t have a numeric
value and so cannot be added, subtracted,
divided or multiplied. They also have no
order
No. reflected at the back
shirts of the athletes
2. Ordinal The ordinal scale contains things that you
can place in order.
Ranks
3. Interval An interval scale has ordered numbers with
meaningful divisions.
Temperature is on the
interval scale: a difference
of 10 degrees between 90
and 100 means the same as
10 degrees between 150
and 160
4. Ratio Has all thecharacteristics of the interval
scale except that it has an absolute zero
point
Height, weight
*a zero weight means no
weight at all

2. SHAPES, DISTRIBUTIONS AND DISPERSION OF
DATA
1. SYMMETRICALLY SHAPED TEST SCORE
DISTRIBUTION
A. Normal Distribution or Bell Shaped Curve
Frequencies
Test Scores

3. SHAPES, DISTRIBUTIONS AND DISPERSION OF
DATA
1. SYMMETRICALLY SHAPED TEST SCORE
DISTRIBUTION
A. Rectangular Distribution
Test Scores
Frequencies

4. SHAPES, DISTRIBUTIONS AND DISPERSION OF
DATA
1. SYMMETRICALLY SHAPED TEST
SCORE DISTRIBUTION
A. U-shaped Curve
Test Scores
Frequencies

5. SHAPES, DISTRIBUTIONS AND DISPERSION OF
DATA
2. SKEWED DISTRIBUTIONS OF TEST SCORES
A. Positively Skewed Distribution
B. Negatively Skewed Distribution
Scores
No.
of
Students
Scores

6. What is Variability in Statistics?
Variability (also called spread
or dispersion) refers to how spread out a
set of data is. Variability gives you a way to
describe how much data sets vary and
allows you to use statistics to compare
your data to other sets of data.

7. The four main ways to describe
variability in a data set are:
• RANGE
• INTERQUARTILE RANGE
• VARIANCE
• STANDARD DEVIATION

8. MEASURES OF VARIABILITY
A. Range
B. Standard deviation
C. Quartile Deviation or Semi-
interquartile Range

9. DESCRIPTIVE STATISTICS
• The first step in data analysis is to describe or
summarize the data using descriptive
statistics.

10. What is Variability in Statistics?
Variability (also called spread
or dispersion) refers to how spread out a
set of data is. Variability gives you a way to
describe how much data sets vary and
allows you to use statistics to compare
your data to other sets of data.

11. I. MEASURES OF CENTRAL TENDENCY
-numerical values which describe the average or
typical performance of a given groups in terms
of certain attributes.
-basis in determining whether the group is
performing better or poorer than the other
groups.

12. Descriptive Satistics When to use and
characteristics
a. Mean Arithmetic average, use when
the distribution is
normal/symmetrical or bell
shaped. Most reliable/stable
b. Median Point in a distribution above
and below which are 50% of
the scores/ cases; medpoint of
a distribution; use when the
distribution is skewed
c. Mode Most frequent/ common score
in a distribution

13. II. MEASURES OF VARIABILITY
- Indicate or describe how spread the scores are.
The larger the measures of variability the
more spread the scores are and the group is
said to be heterogeneous; the smaller the
measure of variability the less spread the
scores are, the group is said to be
homogenous.

14. MEASURES OF VARIABILITY
A. Range-difference between the highest and lowest
score; counterpart of the mode is also reliable and
unstable
B. Standard deviation-The counterpart of the mean,
used also when the distribution is normal or
symmetrical; Reliable/stable and widely used
C. Quartile Deviation or Semi-interquartile Range-
Defined as one- half of the difference between quartile
3(75th percentile) and quartile 1 (25th percentile) in a
distribution; Counterpart of the median; Used when
the distribution is skewed

15. III. Measures of Relationship
-describe the degree of relationship or
correlation between twovariables (academic
achievement and motivation). It is express in
terms of correlation coefficient from -1 to 0 to
10.

16. a. Pearson r
b. Spearman-rank-
order Correlation or
Spearman Rho

17. IV. Measure of Relative Position
-indicate where the score is in relation to all
other scores in the distribution; they make it
possible to compare the performance of an
individual in two or more different tests.

18. a. Percentile Ranks
b. Standard Scores
c. Stanine Scores
d. T-Scores