When most people hear of the word "mathematical", they usually cower and go in fetal position. Yes it's true that it's a tough discipline- Calculus was never my favorite subject. But a lot of the techniques and analyses that successful companies use for marketing are often integrated with various mathematical and statistical methods. In this week's post, we'll go over some of the most popular math methods used in marketing research.

**Conjoint Analysis**

Conjoint analysis (with the emphasis on the "joint") is an unnecessarily intimidating algorithm used to optimize the attractiveness and value of a product or service based on consumer judgments of different combinations of their specific attributes. Although conjoint analysis originated from the deep bowels of mathematical psychology, it is used in many of the applied social sciences today, one of them namely product marketing. And within marketing, conjoint helps in product positioning, product design, and assessing appeal of products.

The easiest example to give on conjoint implementation is for a mobile phone. Say the marketing team at a popular cellphone company needed to do some research on how consumers would respond to a new model. The researchers choose to analysis the following attributes: weight, battery life, and price. They hypothetically invent a Phone A, which weighs 3 grams, has a battery life of 13 hours, costs $250, and a Phone B, which weighs 4 grams, has a battery life of 15 hours, and costs $300. Then, they ask potential consumers to rank order what mix of attributes they prefer from either Phone A or Phone B. Which ever phone the consumers rank highest, theoretically has the more "valued" attributes. Of course you can expand this design with more attributes and levels within the attributes with more hypothetical phones, but I think you get the picture.

**Factor Analysis**

This type of analysis is mostly associated with segmentation. Since everyone knows that the process of defining your consumer segments is so important, it's safe to say that doing a proper factor analysis is just as crucial. A factor analysis is a statistical method used to infer correlation and relationships among many variables. The point of using this method is to find groups of people with common characteristics, beliefs, and attitudes so they can be seen as one entity instead of individually. This way, market researchers can cater to a specific consumer group rather than aim at millions of individual people.

Let's go back to the cellphone company example. Say the company needs to define their consumer segments so they can produce the right ads for each one of them. A factor analysis of their entire consumer sample uncovers three main groups:

*The Busy Businessmen*, who use their cellphones strictly for business during the 9-5 work block and are conservative with texting;

*The Social Students*, who are comprised of a younger crowd, see their cellphones as a window of communication to their friends, and tend to over text all the time; and finally

*The Perturbed Parents*, who have cellphones only for emergencies and to reach their family members. By gaining these segments, researchers are able to give their consumers personalities and anticipate what each group value and desire in a cellphone.

**Bayesian Statistics**

Sounds like the scariest and craziest thing next to a David Lynch movie. Well, it kind of is, but it's useful! The most simple definition of Bayesian analysis is the assessment of prior information through statistical and probabilistic models to infer the likelihood of a particular outcome. Bayes theorem mostly deals with uncertainty. But for the purposes of applying it to marketing research, we'll discuss the inference part of Bayesian analysis. You can think of it in terms of predicting the future. For instance, if the weather has been sunny and hot for the past 30 days, a Bayesian inference will tell you that there's a high chance that its going to be sunny and hot tomorrow. However, if you say the same information but also note that it's actually winter time and supposed to be gloomy and freezing, a Bayesian model will account for that extra information on the season and lower the probability that tomorrow's going to be sunny and hot. With that being said, Bayesian analysis does a good job in factoring extra information into the output.

As you can imagine, being able to predict the future is a great tool that any situation could benefit from. This is why Bayesian analysis can be applied to a diverse set of problems. However in marketing, it could help with predicting consumer behavior given past information of purchases (e.g., through scanner card data from grocery stores) and even predicting marketing environments (Rossi & Allenby, 2002). Although it's a bit difficult to calculate (you need a math model and at least three months of your life), Bayesian analysis yield powerful outcomes if you do it right. With Bayesian analysis, the sky is the limit...

So conquer your fears in math. Because math is so important to getting quality data and insight to a successful marketing campaign.

*Sources:*

*Rossi, P. & Allenby, G. (2002). Bayesian Statistics and Marketing. Marketing Science, 22, 3, 304-328.*