So, the next thing we're going to examine with conjoint analysis

is determining how important each of the attributes are in the overall decision process.

So, is price a very important attribute or, sort of,

just a minor attribute when people make decisions.

Now look at this formula.

This is big and ugly but it's actually quite intuitive.

I bet you figured out by now that the difference between the effects

or the utility levels tells you something about how much more

or how much less people prefer a particular level of a given attribute.

That's true.

It's also true that you can look at the spreads between the highest

and the lowest preferred level of any different attribute and those spreads

will give you an indication of how important the attribute is all in the choice process.

So, for example, if I looked at brand, the highest preferred level is 0.56

and that's with the high flyer probrand.

The least preferred is the long shot at -0.60.

Suppose, instead of 0.56 and 0.60 all those numbers were very close to zero.

What that would mean is, it doesn't make much difference,

one way or the other which brand that you choose.

People don't really care.

It doesn't add a lot to utility and it doesn't subtract a lot from utility.

So, intuitively that tells you that the higher the spread between the most preferred

and least preferred level, the more important the attribute is.

So, how do we do that mathematically?

Typically, in conjoint analysis, the way that's done,

is to take any individual attribute, and let's call that attribute K.

It could be any attribute.

And look at the value of the most preferred level.

So, for brand that would be 0.56 and subtract from

that the value from the least preferred level.

Now, the least preferred level, because these always add up to 0,

is typically going to be a negative number.

So, it's going to be minus, minus a number.

Right?

It's minus a negative number so that this whole numerator will be a positive number.

That's the numerator.

What's this in the denominator, this big ugly summation?

That's just the sum of the spreads of all the different attributes

in your conjoint analysis, including the attribute that was included in the numerator.

So, in our output this would include brand, it would include the spread for distance,

and it would also include the spread for price.

So let's take this big, ugly, messy looking thing and apply it to some data.

So, in our golf ball example,

the attribute importance of distance is, okay, where did I get that?

For distance, the least preferred level is 0.48.

The most preferred level is 0.36 and that is the difference between that positive

and negative number and remember that turns into an addition.

And, then in the denominator, you have the spread for the distance.

You also have the spread for the brand is sitting here and you have the utility spread

for the price and that gives you 0.24.

And mathematically, I suspect a lot of you can intuitively understand

that that number always has to be between 0 and 1

because whatever is included in the numerator is also always included in the denominator

and that bounds that number between 0 and 1.

And because of that, the typical way that this is interpreted

is this is the percent decision weight of a particular attribute.

So distance in our example receives 24 percent of the decision weight.

So it's not real high.

It's not real low.

It's just kind of somewhere in the middle in terms of attribute importance.