1. Counting and Measuring
PSYSTA1 – Week 2

2. Types of VARIABLES VARIABLE Quantitative Discrete Continuous
Qualitative

3. Some DEFINITIONS Qualitative Variables Quantitative Variables
indicates what kind of characteristic or quality an individual, object, or event possesses
measuring a quality or category
e.g. gender, occupation, experimental group/classification
Quantitative Variables
indicates how much or how many, that is, the quantity of a characteristic, an individual, object, or event possesses
measuring a quantity or amount
e.g. height, study time in hours, number of errors in a test

4. Some DEFINITIONS Discrete Variables Continuous Variables
those which there are no possible values between adjacent units on the scale
consist of separate, indivisible categories
e.g. number of children in a family, number of students attending class
Continuous Variables
those which theoretically can have an infinite number of values between adjacent units on the scale
divisible into an infinite number of fractional parts
e.g. weight of participants in a diet study, reaction time to a certain stimulus

5. A Note on CONTINUOUS Variables
Since a continuous variable may have an infinite number of values between adjacent units on the scale, all measurements made on a continuous variable are approximate.
rarely having two observations with exactly the same value!
measurements are given with real limits (recorded value±smallest unit)
ILLUSTRATION:
Consider two different individuals providing measurements of their weight. Suppose that both claim to be 150 lbs.

6. Example 1
Identify whether each variable is qualitative (QL) or quantitative (QN). If the variable is quantitative, determine whether it is discrete (D) or continuous (C).
marital status (single, married, etc.)
number of siblings
age (in years)
anxiety over public speaking, scored on a scale of 0–100 (assume that the difference in anxiety between adjacent units throughout the scale is not the same)
religion
proficiency in mathematics (categorized in poor, fair, and good)
verbal ability scored on a standardized scale of 0-100
evaluation ratings of professors by students on a 5-point Likert scale

7. Levels of MEASUREMENT SCALES
Ratio Scale
Interval Scale
Ordinal Scale
Nominal Scale

8. NOMINAL Scale one that has categories for the units
assigns categories with no intrinsic ordering
labels and categorizes observations, but do not make any quantitative distinctions between observations
e.g. political affiliation, brand of jogging shoes, room number

9. ORDINAL Scale
one in which the numbers on the scale represent rank orderings, rather than raw score magnitudes
consists of a set of categories that are organized in an ordered sequence
ranks observations in terms of size or magnitude
e.g. socioeconomic classification (upper, middle, lower), rank ordering of participants in a speech contest according to speaking ability (Top 1, Top 2, etc.), ranking of food preference (based on relative importance)

10. INTERVAL Scale
one in which the units represent raw score magnitudes, there are equal intervals between adjacent units on the scale, and there is no absolute zero point (i.e., arbitrary zero)
consists of ordered categories that are all intervals of exactly the same size, wherein equal differences between numbers on scale reflect equal differences in magnitude
differences between values are meaningful
e.g. Celsius scale of temperature, gambling position in terms of profit, standardized personality scores

11. RATIO Scale
one in which the units represent raw score magnitudes, there are equal intervals between adjacent units on the scale, and there is an absolute zero point (i.e., true zero)
an interval scale with the additional feature of an absolute zero point, where ratios of numbers do reflect ratios of magnitude
ratio of two vales are meaningful
e.g. Kelvin scale of temperature, weight of subjects, number of bicycles ridden by students

12. Levels of MEASUREMENT SCALES

13. A GUIDE on how to Determine Measurement Scale

14. A Note on LIKERT SCALES
What measurement scale do LIKERT SCALES belong to?
ORDINAL
Consider: The Satisfaction With Life Scale (Diener, Emmons, Larsen & Griffin, 1985) contains five questions (e.g. ‘The conditions of my life are excellent’, ‘So far, I have gotten [sic] the important things from life’), which you answer on a scale from 1 (strongly disagree) to 7 (strongly agree). Each person therefore has a score from 5 to 35.
Is the scoring scale 5 to 35 ordinal, interval, or ratio?
Suppose we compare two people whose scores are 25 and 20, respectively. Is the difference of 5 meaningful?

15. Example 2
Identify the scale of measurement of the following variables.
marital status (single, married, etc.)
number of siblings
age (in years)
anxiety over public speaking, scored on a scale of 0–100 (assume that the difference in anxiety between adjacent units throughout the scale is not the same)
religion
proficiency in mathematics (categorized in poor, fair, and good)
verbal ability scored on a standardized scale of 0-100
evaluation ratings of professors by students on a 5-point Likert scale

16. EXERCISE length of headache (in minutes)
Classify the following variables according to TYPE (qualitative, discrete quantitative, or continuous quantitative) and MEASUREMENT SCALE (nominal, ordinal, interval, or ratio).
length of headache (in minutes)
health rating (1 = Poor, 2 = OK, 3 = Good)
shoe color (1 = Black, 2 = Brown, 3 = Blue, 4 = Other)
intelligence quotient (IQ)
blood pressure (in mmHg)