Statistics are not the dragon you think it is.

For many people, the field of statistics is a dragon in disguise and like dragons, most people shy away from statistics.

I have found that Neil Salkind’s book “Statistics for People Who (Think They) Hate Statistics” a good reference for understanding the basics of statistics.  The 4th edition is due out in September 2010.  This book  isn’t intimidating; it is easy to understand; it isn’t heavy on the math or formulas; it has a lot of tips.   I’m using it for this column.  I keep it on my desk along with Dillman.

Faculty who come to me with questions about analyzing their data typically want to know how to determine statistical significance.  But before I can talk to faculty about statistical significance, there are a few questions that need to be answered.

• What type of measurement scale have you used?
• How many groups do you have on which you have data?
• How many variables do you have for those groups?
• Are you examining relationships or differences?
• What question(s) you want to answer?

Most people immediately jump to what test to use.  Don’t go there.  Start with what measurement scale do you have.  Then answer the other questions.

So let’s talk about scales of measurement.  All data are not created equally.  Some data are easier to analyze than other data.  Scale of measurement makes that difference.

There are four scales of measurement and most data fall into one of these four. They are either categorical (even if they have been converted to numbers) or numerical (originally numbers).  They are:

• nominal
• ordinal
• interval
• ratio

Scales of measurement are rules determining the particular levels at which outcomes are measured.  When you decide on an answer to a question, you are deciding on the scale of measurement, you are agreeing to the particular set of characteristics for that measurement.

Nominal scales name something. For example–gender is either male, female, or unknown/not stated; ethnicity is one of several names of groups.  When you gather demographic data, such as gender, ethnicity, or race, you are employing a nominal scale.  The data that result from nominal scales are categorical data–that is data resulting from categories which are mutually exclusive from each other.  The respondent is either male or female, not both.

Ordinal scale orders something; it puts the thing being measured in order–high to low; low to high.  Salkind gives the example of ranking candidates for a job.  Extension professionals (and many/most survey professionals) use ordinal scales in surveys (strongly agree to strongly disagree; don’t like to like a lot).  We do not know how much difference is between don’t like and likes a lot.  The data that result from ordinal scales are categorical data.

Interval scale is based on a continuum of equally spaced intervals along that continuum. Think of a thermometer; test score; weight.  We know that the intervals along the scale are equal to one another.  The data that result from interval scales are numerical data.

Ratio scale is a scale with absolute zero or a situation where the characteristic of interest is absent–like zero light or no molecular movement.  This rarely happens social or behavioral science, the work that most Extension Professionals do.  The data that result from ratio data are numerical data.

Why do we care?

• Scales are ordered from the least precise (nominal)  to the most precise (ratio).

• The scale used determines the detail provided by the data collected; more precision, more information.
• The more precise scale is a scale which contains all the qualities of less precise scales (interval has the qualities of ordinal and nominal).

Using an inappropriate scale will invalidate your data and provide you with spurious outcomes which yield spurious impacts.