1. Measurement in Statistics
Chapter 2
Measurement in Statistics

2. Data Types and Levels of Measurement
Qualitative data
Non-numerical categories
Quantitative data
Counts or measurements
Discrete – only particular values
Continuous – any values in a given interval
GED111/CDS111 Statistics in Modern Society

3. GED111/CDS111 Statistics in Modern Society
Levels of Measurement
Nominal
Characteristic, name, label, category
The data are qualitative and cannot be ranked or ordered
Ordinal
Qualitative data that can be arranged in order (low, medium, high)
It generally does not make sense to do computations with data in this level
Interval
Intervals are meaningful
Arbitrary zero point
Ratio
Quantitative data that have a true zero point
GED111/CDS111 Statistics in Modern Society

4. Example: software usage
Do you use MS Office?
YES/NO
How often do you use MS Office?
Not at all, not often, sometimes, a lot, always
How often do you use MS Office (per week)?
0-3hrs; 4-7hrs; 8-11hrs; >11hrs
What is your usage of MS Office in terms of hours per week?
____hrs/week
GED111/CDS111 Statistics in Modern Society

5. GED111/CDS111 Statistics in Modern Society
Exercise
Ex 29 – 40 p58
Ex 49 – 56 p59
GED111/CDS111 Statistics in Modern Society

6. GED111/CDS111 Statistics in Modern Society
Dealing with Errors
Random
Unpredictable
Systematic
Affects all measurements in the same way
GED111/CDS111 Statistics in Modern Society

7. GED111/CDS111 Statistics in Modern Society
Size of Errors
Absolute
The exact difference (by subtraction)
Relative
Difference in terms of percentage
GED111/CDS111 Statistics in Modern Society

8. GED111/CDS111 Statistics in Modern Society
Describing results
Accuracy
How closely a measurement approximates a true value
Precision
The amount of detail in a measurement
GED111/CDS111 Statistics in Modern Society

9. GED111/CDS111 Statistics in Modern Society
Exercise
Ex31-38, p66-67
GED111/CDS111 Statistics in Modern Society

10. Uses of Percentages in Statistics
The rate of smoking among 10th graders jumped 45 percent, to 18.3 percent, and the rate for 8th graders is up 44 percent, to 10.4 percent.
GED111/CDS111 Statistics in Modern Society

11. Using Percentages to Describe Change
Absolute change
The actual increase/decrease from a reference value to a new value
Absolute change = new value – reference value
Relative change
The size of the absolute change in comparison to the reference value and can be expressed as a percentage
Relative change = absolute change/reference value x 100%
GED111/CDS111 Statistics in Modern Society

12. “Of” versus “More Than”
The new population is 200% more than the original population. This is a relative change in the population. Of
The new population is 300% of the original population, which means it is three times the original population. This is a ratio of the new population to the original population
GED111/CDS111 Statistics in Modern Society

13. Percentages of Percentages
The bank increases the interest rate on your savings account from 3% to 4%.
The interest rate increases by 1%(percentage point)
The interest rate increases by 33%
Change/difference expressed in percentage points
Absolute change/difference
Change/difference expressed in a percentage(%)
Relative change/difference
GED111/CDS111 Statistics in Modern Society

14. GED111/CDS111 Statistics in Modern Society
Index Numbers
A simple way to compare measurements made at different times or in different places. The value at one particular time (or place) must be chosen as the reference value (or based value)
GED111/CDS111 Statistics in Modern Society

15. Making Comparisons with Index Numbers
Consumer Price Index (inflation/deflation)
Hang Seng Index
When the Hang Seng Index was first published, its base of 100 points was set equivalent to the stocks' total value as of the market close on July 31, Its all-time low is points, reached retroactively on August 31, 1967, after the base value was established but before the publication of the index. The Hang Seng passed the 10,000 point milestone for the first time in its history on December 10, 1993 and, 13 years later, passed the 20,000 point milestone on December 28, In less than 10 months, it passed the 30,000 point milestone on October 18, Its all-time highs, set on October 30, 2007, are 31, points during trading and 31, points at closing.
GED111/CDS111 Statistics in Modern Society

16. GED111/CDS111 Statistics in Modern Society
Hang Seng Index
GED111/CDS111 Statistics in Modern Society

17. GED111/CDS111 Statistics in Modern Society
Focus on Politics
Who Benefits from a Tax Cut? Pp84-85
GED111/CDS111 Statistics in Modern Society