There are four different analysis techniques that we will discuss on these pages. We will be applying these four techniques to four different patterns. To make the most sense of things, we will send you through the first technique, Factor Effect, then give you choices of how you wish to proceed after that.

## FACTOR EFFECT

### DIRECT RELATIONSHIP

Here a comparison is being made between the first two data pairs. The second pair has a volume twice that of the first pair and the mass is also twice that of the first pair. As the volume doubles, the mass also doubles.

The third pair has a volume three times that of the first pair and has a mass three times that of the first pair. When the volume increases by a factor of three, the mass also increases by a factor of three.

Comparisons can be made within the same data table. The fourth data pair is larger than the second pair by a factor of two. When the volume increases by a factor of two, the mass also increases by a factor of two.

This comparison illustrates how the control variable can decrease. When the volume changes by a factor of one-half, the mass also changes by a factor of one-half.

## SUMMARY

In the factor effect pattern for a Direct Relationship, whatever factor change occurs for the control variable, the same factor change occurs for the dependent variable.

### INVERSE RELATIONSHIP

The second pair has a frequency twice that of the first pair and a period which is half. As the frequency doubles, the period is halved.

The fourth pair has a frequency four times the first pair, and a period which is a fourth that of the first. As the frequency changes by a factor of four, the period changes by a factor of one-fourth.

While the frequency changes by a factor of one-half, the period changes by a factor of two.

## SUMMARY

In the Factor Effect pattern for the Inverse Relationship, whatever factor change occurs for the control variable, the inverse of that factor is the factor change for the dependent variable.

NOTE: Inverse and Reciprocal have the same meaning, mathematically.

### SQUARE RELATIONSHIP

The second pair has a length twice that of the first pair and an area which is four times that of the first pair. As the length changes by a factor of two (or 2x) the area changes by a factor of four (or 4x or 22x).

While the length triples, the area increases by a factor of nine (9). The dependent variable increases by a factor which is the square of the control variable increase.

While the length changes by a factor of 1/3, the area changes by a factor of 1/9, or the square of 1/3.

## SUMMARY

In the Factor Effect pattern for the Square Relationship, whatever factor change that takes place for the control variable, the dependent variable changes by the square of that factor change.

### SQUARE ROOT RELATIONSHIP

The third pair has a Radius four times that of the first pair and a Period which is twice (or the square root of four times) that of the first pair. As the radius changes by a factor of four, the period changes by a factor of the Square Root of four.

As the radius changes by a factor of sixteen, the period changes by a factor of the Square Root of sixteen, or four. The dependent variable changes by a factor which is the Square Root of the control variable factor increase.

While the control variable changes by a factor of one-fourth, the dependent variable changes by a factor of the square root of one-fourth, which is one-half.

## SUMMARY

In the Factor Effect pattern for the Square Root Relationship, whatever factor change that takes place for the control variable, the dependent variable changes by the square root of that factor change.

## SELF TEST

 1. Which of the following is an example of Direct, Inverse, Square or Square Root Relationship? Click for ANSWER

 1. Which of the following is an example of Direct, Inverse, Square or Square Root Relationship? INVERSE SQUARE DIRECT SQUARE Click for NEXT QUESTION

 2. Which of the following is an example of Direct, Inverse, Square or Square Root Relationship? Click for ANSWER

 2. Which of the following is an example of Direct, Inverse, Square or Square Root Relationship? SQUARE ROOT INVERSE DIRECT SQUARE ROOT Click for NEXT QUESTION

 3. Which of the following is an example of Direct, Inverse, Square or Square Root Relationship? Click for ANSWER

3. Which of the following is an example of
Direct, Inverse, Square or Square Root Relationship?
NONE OF THESE
SQUARE

Hopefully you found that you can apply a general procedure for determining the nature of the relationship. You look at the control column, and identify two values that have a "nice" ratio like 2:1 or 3:1. Then you look at the ratio of the corresponding dependent values. If the ratio is the same - direct. If the ratio is just the reciprocal - inverse. If the ratio becomes the square of the control ratio - square. Finally, if the ratio becomes the square root - square root.

Note that it is handy to recognize the square root of some small numbers in order to use this technique more effectively.

 RATIO SQUARE ROOT 2 1.41 3 1.73 5 2.24

Now it's time to go on to the other three techniques. Remember, we are dealing with four relationships and learning four different techniques. The first technique is called FACTOR EFFECT.

Updated August 2001