# The Math of Tuning

This chapter will discuss the statistics involved - it can be arduous, but it's important, so the author encourages the reader to grin and bear it.

## Throwing Away Part of the Data

There is no absolute answer in statistics - outside of the hard sciences, most studies are geared toward a level of confidence that's around 95% - and even that is based on cleaning the data before analyzing it. Of importance: data cleaning does not mean throwing out data that does not support a foregone conclusion - but in the "real world," there's dirt and grit that needs to be set aside.

One example of data cleaning is dealing with a biased sample. You may want to get rid of all data pertaining to traffic from a specific ad in order to get a better idea about the general audience - or you might want to throw away all data from the general audience to concentrate on the impact of a specific ad. Or if your company is mentioned in a news program one day, you may want to remove that data as being unusual and unrepresentative.

Some data collection also excludes certain responses due to technology ro behavior. One example is using JavaScript to determine monitor sizes. Users who turn JavaScript off (about 4% of the universe) will not be counted. This is an inherent bias. Likewise, an analysis of search terms shows only topics of interest to visitors who prefer to use search engines as their primary mode of navigation.

## Basics of Statistical Analysis

The author provides some basics about statistical analysis. I don't think he quite understands the topics he's meaning to teach others, because he's getting a lot of things wrong here, and probably misinforming the reader.

However, some key concepts are worth preserving:

Of key importance to marketing is probability theory: the creation of a model that results in a number of predictable outcomes ("events") and assigns a probability to each outcome based on statistical inputs.

Inputs to the equation are quantifiable measurements that are (more-or-less) objective. Some statistics are based on qualities (a person's level of income) and others are based on preceding events (a person entered a store).

Statistical analysis consists of:

- Analyzing data, a propos of nothing, to identify correlations
- Developing a hypothesis that a given correlation is significant
- Testing that hypothesis to determine its reliability

In the context of conversion, the most important goal of statistical analysis is to discover causality - such that altering some of the factors of the equation can be expected to produce a desirable outcome.

## Reliability

Reliability is the goal of statistical modeling, but there are a number of common problems that can undermine that reliability:

- Collecting insufficient data - Statistics based on small sample sizes tend to be very inaccurate. The "level of confidence" and "probability of error" should be calculated and considered
- Sample Bias - In spite of the best efforts to select a good sample and clean the data, there is inherent bias. In any survey, the conclusions are skewed because people who don't answer surveys are not included in the results.
- Missing important data - Statistical analysis is based on the data present, but there may be factors that were not observed that influence behavior, and overlooking them can lead to bad conclusions
- Misinterpreting Correlation - Just because there is a correlation does not mean that there is causation
- Insufficient Analysis - Drawing a conclusion based on facile analysis without checking the conclusions by methods such as tightening the level of confidence or testing the null hypothesis.

## Variable Interactions

Generally, the outcome of a statistical study is a conclusion, or at least the implication, that by doing X, we will influence outcomes in a favorable way, and that the outcome is mathematically predictable.

The problem is that this is based on an assumption of stasis: if nothing else changes. This is seldom the truth - and when you change multiple factors, or there are external influences, the interactions between changes in each factor may have a combined result.

## Application to the Web

Some random notes about applying statistical methods to the Web, important because he will use these terms later, I suppose:

- The input and output variables are measured and observed through analysis of the user's behavior on the site (how many arrived on the page, how many converted)
- The variables are assumed to be the content of the Web page itself (e.g., the color, size, placement, and wording of the action button)
- The values are the possible "states" of a given variable quality (a button color can be blue, green,. Or red)
- The branching factor describes the number of different combinations (page with a blue button, page with a green button) - it can become complex if multiple parameters are changed
- The combination of factors tested is referred to as a "recipe"
- The search space size is the number of possible variations, given the recipes. If factor one has three values, factor two has three, and factor three has five, the search space is 45 recipes (3 x 3 x 5)