# PSYC 210 Chapter Notes - Chapter 2: Random Number Table, Exclusive Or, Dependent And Independent Variables

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Basic Concepts

•In statistics everything we do begins with the measurement of whatever it is we

want to study

•Measurement = the assignment of numbers to objects

•Example we use paw-lick latency as a measure of pain sensitivity, we are

measuring sensitivity by assigning a number (a time) to an object (a mouse) to

assess the sensitivity of that mouse

•Black depression inventory is the most popular measure of depression

•Depending on what we are measuring and how we measure it, the number we

obtain may have different properties and those different properties of numbers

often are discussed under the specific topic of scales of measurements

2.1 scales of measurement

•Scales of measurement = characteristics of relations among numbers assigned to

objects

•Realize that statistics as a subject is a set of facts put together with a variety of

interpretations and opinions

•S. S. Stevens defined 4 types of scales: nominal, ordinal, interval and ratio

Nominal scales

•Nominal scales = numbers used to only distinguish among objects

•Not really a scale at all, because it doesn’t scale items along any dimension but

rather label items

•Frequently these numbers have no meaning whatsoever other than as convenient

labels that distinguish the players or their positions from one another

•Gender is a nominal scale (1 = male and 2 = female)

•Could also use letters or pictures of animals

•Nominal scales generally are used for the purpose of classification categorical

data

•Quantitative data are measured on the other 3 types of scales

Ordinal scales

•The simplest true scale is an ordinal scale = numbers used only to place objects

in order

•Example the class standings of people graduating from high school OR Homles

and Rahe’s scale of life stress

•These 2 examples of ordinal scales differ in the numbers that are assigned. In the

first case we assigned the ranks 1,2,3 … whereas in the 2nd case the scores

represented the number of changes rather than ranks

•No information is given about the differences between points on the scales

Interval scales

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•Interval scales = scale on which equal intervals between objects represent an

equal difference – differences are meaningful

•Example Fahrenheit scale of temperature in which a 10-point difference has the

same meaning anywhere along the scale

•You can find the meaning anywhere along the scale

•However we still don’t have the ability to speak meaningfully about ratios no

true 0 point

•Example the measurement of pain sensitivity is a good example of something

that is probably measured on an interval scale

Ratio scales

•Ratio scales = a scale with a true 0 point ratios are meaningful

•A 0 must be a true 0 point and not an arbitrary one such as 0°F or 0°C

•A true 0 point is the point that corresponds to the absence of the thing being

measured

•Example common physical ones of length, volume, time, etc.

•Important fact: it is the underlying variable being measured not the numbers

themselves that define the scale

•Because there is usually no unanimous agreement concerning the scale of

measurement employed it is up to you to make the best decision about the nature

of the data

The role of measurement scales

•There is a difference in opinion as to the importance assigned to scales of

measurement

•Argument for the example of room temperature wherein the scale (interval or

ordinal) depended on whether we were interested in measuring some physical

attribute of temperature or its effects on people

•In other words we have an interval scale of the physical units but no more than an

ordinal scale for comfort

•Because statistical tests use numbers without considering the objects or events we

can carry out standard mathematical operations regardless of the nature of the

underlying scale

•The problem comes when its time to interpret the results of some form of

statistical manipulation ask if there are meaningful statistical relationships

•Now dealing with a methodological issue

•Statistical tests can be applies only to the numbers we obtain and the validity of

the statements about the objects or events depends on our knowledge of the

object or event not to the scale of measurement

•Do our best to ensure that our measures bear as close relationships as possible to

what we want to measure, but our results are ultimately only the numbers we

obtain and our faith in the relationship between those numbers and the underlying

objects or events

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