APPLIED STATISTICS COURSE CODE: ENEE1006IU Lecture 1:
Chapter 1: Data and Statistics
(3 credits: 2 is for lecture, 1 is for lab-work) Instructor: TRAN THANH TU Email: tttu@hcmiu.edu.vn tttu@hcmiu.edu.vn 1 1.1. DATA CLASSIFICATION
•Elements, Variables, and Observations •Scales of Measurement
•Categorical and Quantitative Data •Cross-Sectional and Time Series Data
A. ELEMENTS, VARIABLES, AND OBSERVATIONS
•Data are the facts and figures collected, analyzed, and summarized for
presentation and interpretation.
Elements are the entities on which data are collected.
A variable is a characteristic of interest for the elements. tttu@hcmiu.edu.vn 2
The set of measurements obtained for a particular element is called an B. SCALES OF MEASUREMENT
•Scales of Measurement: nominal, ordinal, interval, or ratio.
determines the amount of information contained in the data tttu@hcmiu.edu.vn 3
indicates the most appropriate data summarization and statistical analyses tttu@hcmiu.edu.vn 4 B. SCALES OF MEASUREMENT
•Scales of Measurement: nominal, ordinal, interval, or ratio tttu@hcmiu.edu.vn 5 tttu@hcmiu.edu.vn 6 B. SCALES OF MEASUREMENT
-Nominal scale: when the data for a variable consist of labels or names used to
identify an attribute of the element
a numerical code as well as a nonnumerical label may be used
-Ordinal scale: if the data exhibit the properties of nominal data and in addition, the
order or rank of the data is meaningful
-Interval scale: if the data have all the properties of ordinal data and the interval
between values is expressed in terms of a fixed unit of measure
Interval data are always numerical
-Ratio scale: if the data have all the properties of interval data and the ratio of two values is meaningful tttu@hcmiu.edu.vn 7
This scale requires that a zero value be included to indicate that nothing exists for
the variable at the zero point B. SCALES OF MEASUREMENT
-Nominal scale: when the data for a variable consist of labels or names used to
identify an attribute of the element tttu@hcmiu.edu.vn 8
a numerical code as well as a nonnumerical label may be used
Example: genotype, blood type, zip code, gender, race, eye color, political party, etc. B. SCALES OF MEASUREMENT
-Ordinal scale: if the data exhibit the properties of nominal data and in addition, the
order or rank of the data is meaningful tttu@hcmiu.edu.vn 9
Example: socio economic status (“low income”,”middle income”,”high income”)
education level (“high school”,”BS”,”MS”,”PhD”) income level (“less than
50K”, “50K-100K”, “over 100K”)
satisfaction rating (“extremely dislike”, “dislike”, “neutral”, “like”, “extremely like”), etc. tttu@hcmiu.edu.vn 10 B. SCALES OF MEASUREMENT
-Interval scale: if the data have all the properties of ordinal data and the interval
between values is expressed in terms of a fixed unit of measure
Interval data are always numerical (in which, zero still has the meaning)
Example: temperature (Farenheit), temperature (Celcius), pH, SAT score
(200-800), credit score (300-850), etc. tttu@hcmiu.edu.vn 11 B. SCALES OF MEASUREMENT
-Ratio scale: if the data have all the properties of interval data and the ratio of two values is meaningful
This scale requires that a zero value be included to indicate that nothing exists for
the variable at the zero point tttu@hcmiu.edu.vn 12
Example: enzyme activity, dose amount, reaction rate, flow rate,
concentration, pulse, weight, length, temperature in Kelvin (0.0 Kelvin
really does mean “no heat”), survival time, etc.
Time is interval scale: 0 is 12:00 noon
Duration is ration scale: 0 means no more time B. SCALES OF MEASUREMENT
Summary of data types and scale measures: tttu@hcmiu.edu.vn 13 tttu@hcmiu.edu.vn 14
C. CATEGORICAL AND QUANTITATIVE DATA tttu@hcmiu.edu.vn 15 tttu@hcmiu.edu.vn 16
C. CATEGORICAL AND QUANTITATIVE DATA
•A categorical variable is a variable with categorical data, and a quantitative
variable is a variable with quantitative data.
•If the variable is categorical, the statistical analysis is limited tttu@hcmiu.edu.vn 17
(when the categorical data are
identified by a numerical code,
arithmetic operations such as addition, subtraction,
multiplication, and division do not provide meaningful results) tttu@hcmiu.edu.vn 18
C. CATEGORICAL AND QUANTITATIVE DATA tttu@hcmiu.edu.vn 19 tttu@hcmiu.edu.vn 20