## Why Head and Shoulders Has Less Variations For Sale

8 November, 2009 § 1 Comment

Not too long ago, Proctor & Gamble marketed Head and Shoulders shampoo with twenty-six variations. Sales were good, but not maximal. To increase sales of their shampoo, they decided to *reduce* the number of variations from twenty-six to fifteen. Result: Sales increased 10% [1].

But does that make sense? Popular notion would seem that the more choices an individual can make, the happier they will be. Don’t you like to have the option to choose between a small, medium, large, or extra-large drink? It turns out that the popular notion isn’t wrong, sometimes it’s just applied at the wrong times.

When given the option to choose, increasing the number of options from 2 to 6 increases the satisfaction of the individual and reduces the amount of time to make said decision [1]. But at what point does the addition of options have diminishing returns? George Miller, a cognitive psychologist at Princeton in 1956, found that the optimal number of choices are 7, plus or minus 2 [2].

This 7 ± 2 rule has been widely cited, and it may be the reason that many fast food restaurants have pared down the number of value meals that are offered to fit within this range. When the number of options is higher than 9, individuals will feel overwhelmed and burdened by the worry that comes with making a “wrong” choice.

Residents of the United States are faced with so many decisions on a daily basis, including decisions that are likely to affect loved ones, that the decision-making process becomes demotivating [3]. Up to this point (2000), there has been research that focused on the 7 ± 2 rule, options ranging from 2 to 6, but no research on options ranging in count from 6 to 24 or 6 to 30.

A study by Sheena Iyengar of Columbia University and Mark Lepper of Stanford University specifically looks at the effects of choice and has interesting findings. Iyengar and Lepper performed three studies observing participants initial reaction, satisfaction, and decision-making when presented with extensive and limited selections.

One of their studies focused on the sale of exotic jams. They stationed a sample booth in a gourmet grocery store and offered varying numbers of jam to sample. If a customer approached the sample booth, they received a coupon towards a jam, and purchases of the jam were recorded to determine the effect of the sampling booth.

Table 1

Extensive Selection | Limited Selection | Total |
---|---|---|

24 flavors | 6 flavors | |

386 shoppers | 368 shoppers | 754 shoppers |

242 encountered | 260 encountered | 502 encountered |

145 stopped/sampled | 104 stopped/sampled | 249 stopped/sampled |

4 purchased | 31 purchased | 35 purchased |

Those results show the following percentages:

Table 2

Extensive Selection | Limited Selection |
---|---|

66% encountered | 63% encountered |

60% stopped | 40% stopped |

3% purchased | 30% purchased |

These results are very interesting. Although the number of customers that approached the extensive selection (60%) was much higher than the limited selection (40%), these customers did not purchase the jam. In fact, the customers that approached the limited selection were **10 times more likely** to purchase.

Given those percentages, **can we turn the data on its head and determine the effect that the number of flavors presented had, given that the customer was going to purchase the jam?**

To answer the question, we can use the naïve Bayes theorem [4]. The naïve Bayes theorem provides a way to find the posterior probability given a pre- and post-condition. We can use the percentages given in Table 2 and apply them to the theorem:

The probabilities for purchasing without sampling were not given, and thus we will use a weighted average of the purchasers to estimate the probability at 0.095 *((4/386) + (31/368))*. These numbers are chosen because we will have to assume that regardless of the number of flavors present at the sample booth, these customers were already going to make a purchase. *Ideally, we would have in our data set the number of customers who purchased regardless of stopping at the sample booth.*

*P _{6}(sample|purchase) = (P_{6}(purchase|sample) * P_{6}(sample))/(P_{6}(purchase)) = (0.3 * 0.4)/0.095 = 1.26*

P_{24}(sample|purchase) = (P_{24}(purchase|sample) * P_{24}(sample))/(P_{24}(purchase)) = (0.03 * 0.6)/0.095 = 0.19

Using the naïve Bayes Theorem, we are able to find that when customers were buying jam, they were **663% more likely** to stop and sample jam if the sample booth only contained 6 flavors compared to 24 flavors. The increase in choice may have at first glance brought many more customers to the sample booth, yet the customers that approached the booth when 24 flavors were presented may never have intended on purchasing the jam.

So Miller’s rule says that 7 ± 2 is the right number of choices, and Iyengar and Lepper make a case that happiness does not increase with choices. Right now, we are encountering *too many* choices. Most of us would probably choose the same options, so we might as well be happier about our choices. Therefore, if our goal is to make the customer happier, the selection should be limited before they encounter their decision. In the end, we will all be happier.

[1] http://www.columbia.edu/~ss957/articles/Choice_is_Demotivating.pdf

[2] http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two

[3] http://www.ucpress.edu/books/pages/5572001.php

[4] http://en.wikipedia.org/wiki/Naive_Bayes_classifier