# how to calculate interaction effect?

#### random512

##### New Member
Hello - I'm trying to understand how to calculate interaction effect. The question and answer below the dotted line below are for the following run chart:

https://www.dropbox.com/s/7pn6iz0uule6fs9/Photo Sep 07, 9 35 44 AM.png

A formula appears to be provided in the question but I seem to having problems interpreting the formula. The formula seems to read: ((sum of positive A's) * (sum of positive B's)) - ((sum of negative A's) * (sum of negative B's)). However, this interpretation yields a number that is way off from the number provided in the answer.

So, based on this information, can you help me understand how the provided interaction formula is actually applied?

=====

QUESTION:
Calculate the interaction effect A × B (i.e., A × B+ – A × B– ).

A. 1.5
B. 205
C. –5
D. 17
E. –17

ANSWER:
C

Last edited:

#### Miner

##### TS Contributor
If you multiply the A levels time the B levels to obtain the AB levels (i.e. -1 (A) * -1 (B) = 1 (AB)), then calculate the effect for AB, you will obtain -5.

#### rogojel

##### TS Contributor
hi,
the formula is basically correct, you sum the elements where the product AB is positive and substracr the sum of the elements where the product is negative but then you have to divide the result by two..

that would give you (129+80-(133+86))/2=-5.

regards
rogojel

#### random512

##### New Member
Thanks rogojel - Your explanation really helped me better understand interaction effect at a conceptual level.

#### rogojel

##### TS Contributor
oh,
BTW the number two is the number of measurements that contribute to a level , so in this case you have two values for the level of AB+ and two levels for AB- thats why you divide by 2. If you had 3 factors, the number to divide with would be 4 and so on. It is basically the average output for the given level.

regards
rogojel

#### random512

##### New Member
sorry rogojel - now I'm a little confused. You're describing:

* 2 values for the level of AB+
* 2 levels for AB-

I'm not clear on the differences between these 2 points. For your point #2 why wouldn't you instead say "2 values for the level of AB-"?

"If you had 3 factors, the number to divide with would be 4"

You were previously referring to "values" and "levels." Can you please help me understand what a "factor" would be in this context?

#### gentle

##### New Member
sorry rogojel - now I'm a little confused. You're describing:

* 2 values for the level of AB+
* 2 levels for AB-

I'm not clear on the differences between these 2 points. For your point #2 why wouldn't you instead say "2 values for the level of AB-"?

"If you had 3 factors, the number to divide with would be 4"

You were previously referring to "values" and "levels." Can you please help me understand what a "factor" would be in this context?
sorry rogojel - now I'm a little confused. You're describing:

Now for 2 level , 2 factor experiment , total experiment is 4. Now 2 cases will have interaction sign positive eg high pressure , high temperature / low pressure, low temperature whereas in other case interaction is negative high pressure, Low temp / High Temp, Low pressure. Now for calculating interaction calculate average of positive-average of positive.
For 2 level , 2 factor you will have 2 positive and 2 negative so divide by 2 required for average calculation.
For 2^3 experiment that is 2 level 3 factors there are 4 positive, 4 negative interaction , so divide by 4. Similarly it would follow for different DOE.