Module 1 - Terminology and Scales of Measurement

Module 1 will consist of the following topics:

1. Some terminology for statistics
2. Assignment 1
3. Quiz 1

Discussion

Some terminology for statistics

1. Qualitative versus quantitative variable

Qualitative variable - data typically in narrative form; gathered by use of observations and interviews; results contextual - unique to individual and setting.

Quantitative variable - data numerical; gathered by quantifying observations, administering tests and other instruments;attempts to find laws, generalizations.

1. Measurement -assigning numbers to observations according to rules.

1. Variables a measured characteristic that can assume various values or levels.

Discrete variables - have only certain values (whole numbers for example).

Continuous variables - can take any value (accuracy of measurement).

1. Constant -has only a single value. A certain characteristic can be a variable in one study and a constant in another study.
2. Scales of measurement

Nominal scale - naming, used to label, classify, or categorize data (gender, SSS number , locker number, address).

Ordinal scale - classification function plus observations are ordered, distance between adjacent values not necessarily the same (olympic medals, finishing place in a race, class rank).

Interval scale - classification, ordered plus equal intervals between adjacent units (all test scores are assumed to be at the interval scale, temperature Fahrenheit, temperature Centigrade).

Ratio scale - all of the above plus the scale has an absolute zero, a meaningful zero. Most physical measures are at the ratio level of measurement (height, weight, distance, time, pressure, temperature on the Kelvin scale - absolute zero is -273 degrees Centigrade).

1. Descriptive and inferential statistics

Descriptive statistics are a way of summarizing data - letting one number stand for a group of numbers, can also use tables and graphs to summarize data.

Inferential statistics - research statistics, a measure of the confidence we can have in our descriptive statistics, the statistics we use to test hypothesis.

1. Parametric and nonparametric statistics

Parametric statistics - used with interval and ratio data and usually with data that were obtained from groups randomly assigned, normally distributed, and with equal variability between groups - preferred statistics to use, they are more "powerful" than nonparametric statistics. Examples we will study are t-tests, analysis of variance, and Pearson correlation coefficient.

Nonparametric statistics - used with nominal and ordinal data and sometimes with interval and ratio data when other assumptions can not be met. Examples we will study are the chi-square test and the Spearman rank difference correlation coefficient.

Assignment 1

For this first lesson, the assignment is to provide the following information about your self. As you provide this information you should think about what level of measurement would be involved with each item.

1. Name

2. Email Address

3. Student Number

4. Gender

5. Course

6. Name of your major subject.

7. The distance from your home to school (answer to the nearest whole kilometer).

8. Favorite color

9. Color of your eye

10. Name of the last book you read (or are reading) which is not a required book for a class.

11. Title of the last movie you saw.

Quiz 1

Selectthe best answer to each test item.

1. The scores on this test would be an example of measurement at the

a. Nominal level. b. Ordinal level.

c. Interval level. d. Ratio level.

2. You measure the width (in inches) of a number of fabric samples. This would be an example of measurement at the:

a. Nominal level. b. Ordinal level.

c. Interval level. d. Ratio level.

3. What level of measurement would be involved in recording a person's social security system number?

a. Nominal level. b. Ordinal level.

c. Interval level. d. Ratio level.

4. A variable that can only take certain values (like whole numbers) is referred to as a

a. Continuous variable. b. Discrete variable

c. Constant d. Statistical variable

5. What kind of statistics would we probably be required to use with data at the nominal or ordinal level?

a. Variable statistics b. Constant statistics

c. Parametric statistics d. Nonparametric statistics

-end-