M2 L3: Levels of Measurement, Frequency Distributions & Graphical Illustrations

Question 1

What is a measurement?

Answer 1

Measurement is defined as “the assignment of numerals to objects or events according to rules” (Stevens 1951, cited in Kerlinger 1986, 391).

Question 2

Conceptualiation vs. Operationalization

Answer 2

Conceptualization – the researcher’s abstract/general idea about the variables under study.

Operationalization – the process of turning abstract concepts into measurable observations.

Question 3

What are the different levels of measurement?

Answer 3

1. Nominal- Used for observations that have categories, or names, as their values. Eg: Demographics, types
2. Ordinal- A variable used for observations that have rankings (that is, 1st, 2nd 3rd …) as their values with no precise numerical meanings. Eg: Attitudes
3. Interval- In addition to incorporating orderings, interval scales have a specific numerical distance between each pair of levels. This allows greater comparison than the ordinal level. Eg: Income level
4. Ratio- The data have all the properties of the interval level of measurement with one exception – there is a meaningful zero point as a response option. This scale must contain a zero value that indicates that nothing exists for the variable at the zero point. Eg: Hours spent= 0

The level determines the amount of information
contained in the data.

Question 4

What is frequency distribution?

Answer 4

Frequency distribution is an organized graphical representation of the number of individuals in each category on the scale of measurement. Its purpose is to organize our raw scores.

Two kinds:
* Ungrouped
* Grouped frequency distribution

Question 5

What is a frequency table?

Answer 5

A visual depiction of data that shows how often each value occurred, that is, how many scores were at each value. Values are listed in one column, and the number of individuals with scores of the value are listed in the second column.

Score= x
Frequency= f
Sum of frequencies (sample size)= ∑ f

Question 6

Ungrouped vs Grouped Frequency Tables

Answer 6

Ungrouped:
Relative frequency= f / ∑ f
Percentage= x 100
Cumulative Frequency= +f

Grouped: indicates the numbers of participants within particular intervals, rather than at particular scores.

Question 7

Types of graphical illustrations

Answer 7

• Pie Chart- a circular chart in which the circle is divided into sectors (nominal & ordinal)
• Bar Graph- different values of X is represented by the height of a bar (nominal & ordinal)
• Histogram- a rectangle is used to represent frequencies of observations within each interval (interval & ratio)
• Frequency Polygon- uses a single point rather than a bar to represent a class interval on a graph.