Chapter 2

nominal scale

A scale of measurement (also called a categorical scale), that labels observations rather than quantifying observations.

1.All measurement scales have one or more of the following three attributes

1.Magnitude. 2.Equal intervals between adjacent units. 3.Absolute zero point.

Limits/Real Limits

All measurements on a continuous variable are approximate. They are limited by the accuracy of the measurement instrument. When a measurement is taken, one is actually specifying a range of values and calling it a specific value. The real limits of a continuous variable are those values that are above and below the recorded value by 1/2 of the smallest measuring unit of the scale (e.g., the real limits of 100C are 99.5 C and 100.5 C, when using a thermometer with accuracy to the nearest degree).

Rounding

If the remainder beyond the last digit is greater than 1/2 add one to the last digit. If the remainder is less than 1/2 leave the last digit the same. If the remainder is equal to 1/2 add one to the last digit if it is an odd number, but if it is even, leave it as it is.

Discrete variables

In this case there are no possible values between adjacent units on the measuring scale. For example, the number of people in a room has to be measured in discrete units. One cannot reasonably have 6 1/2 people in a room.

Significant figures

The number of decimal places in statistics is established by tradition. The advent of calculators has made carrying out laborious calculations much less cumbersome. Because solutions to problems often involve a large number of intermediate steps, small rounding inaccuracies can become large errors. Therefore, the more decimals carried in intermediate calculations, the more accurate is the final answer. It is standard practice to carry to one or more decimal places in intermediate calculations than you report in the final answer.

Ratio scales

These scales have the most useful characteristics since they possess attributes of magnitude, equal intervals, and an absolute zero point. All mathematical operations can be performed on ratio scales. Examples include height measured in centimeters, reaction time measured in milliseconds. (Kelvin Scale is a ratio scale)

Interval scales

This scale possesses equal intervals, magnitude, but no absolute zero point. An example is temperature measured in degrees Celsius. What is called zero is actually the freezing point of water, not absolute zero. Can do same determinations as ordinal scale, plus can determine if A - B = C - D, A - B > C - D, or A - B < C - D.

Continuous variables

This type can be identified by the fact that they can theoretically take on an infinite number of values between adjacent units on the scale. Examples include length, time and weight. For example, there are an infinite number of possible values between 1.0 and 1.1 centimeters.

Ordinal scales

possess a relatively low level of the property of magnitude. The rank order of people according to height is an example of an ordinal scale. One does not know how much taller the first rank person is over the second rank person. Can determine whether A > B, A = B or A < B.