## The Hidden Math of Internet Marketing

Photography: tkamenick

Success at marketing online will demand a talent for copywriting (or at least the ability to hire a good copywriter when you see one), a feel for the market, and the ability to create and offer good products that people want to buy. It also requires math. Lots of math. Some of it, really, really hard math.

It’s starts simply enough. Build a website and you’ll quickly find yourself looking at your Google Analytics reports and following your traffic. If you’re paying attention to the search engine optimization, building links and promoting the site, then the numbers of views and visitors will rise, and with them, your income.

At that point you might start wondering how much traffic you need in order to earn the kind of revenue you want from your website. That’s a fairly easy sum. The Effective Cost Per Mille (eCPM) is a measure of the amount of revenue a site earns for each thousand impressions. Each visitor though may generate more than one impression so to calculate your target number of visitors you’d need to multiply your target earnings by 1,000 and divide by the sum of your eCPM multiplied by the average of the number of page views each visitor generates.

ConversationMarketing.com, a blog by Internet marketing expert Ian Lurie, makes it all a lot easier by supplying a useful online calculator. Enter the figures, hit “Calculate” and you’ll be able to see your traffic target. The site also supplies more calculators to estimate the click values for lead-based marketers and retail businesses. Each of those is affected by conversion rates, more figures that have to be factored into the equation.

**Calculating a Test Sample Size**

They might not sound it, but those are pretty simple calculations. And in practice, they’re unlikely to be made too often. You might have a target income that would make your efforts feel worthwhile, but for most online marketers the overall target is “as much as possible,” a figure that’s harder to work into a mathematical formula.

Something that will crop up more often in the development of an Internet business though is the results of tests.

Frequent testing is a vital form of any aspect of marketing. It’s only by testing that you can tell which ad layouts deliver the best results, which types of content most engage your users, which landing pages lead to the most conversions. The principle of A/B testing is clear enough: show two different versions to an audience and compare the results. Google makes it simple for AdSense publishers to test two different ad formats by using Javascript to randomly swap two blocks of code. But all tests need an audience size that’s large enough to deliver statistically significant results. That minimal size is much harder to figure out and relies on the use of standard deviation, a measure of variation from the mean used frequently in statistics.

LucidView, a firm that brings scientific testing to the world of marketing, explains that all sample size calculations are based on the equation:

where *N* is the sample size. To calculate the standard deviation, you’d need to calculate the mean of a set of data, compute the difference between each data point and the mean, and square the result of each. Applying that equation to marketing though requires factoring in “alpha risk,” a 5% chance that a significant result is random, and the chance of missing a significant result — or 31.38.

That produces the equation

where is the value of standard deviation.

That’s useful for large online stores in which each customer buys a unique basket of goods. If five customers to a software site with a dozen different products spent the following sums:

$33.95

$24.95

$75.95

$49.95

$33.95

then the mean sale per customer would be $43.75 and the standard deviation would be $18. If the store owner wanted to see whether a new design would raise that average sale value to $50 then the equation needed to calculate the size of his test sample would be:

^{ }

or 260.3. The marketer then would need to make sure that the total sample size of people who actually bought a product — both control members and those seeing the new design — numbers at least 260.3.

To test response rates, LucidView offers an equation that’s no less fun. Thankfully though, the site also sums up the results in a table that shows that to test a promotion you hope will deliver a 5% lift in response rate (from 1% to 1.05%), you’d need 12,500 responses. Each subsequent 5% rise would require a total of 3,100, 1,380, 780 and 500 responses respectively.

**Are Your Results Significant?**

Of course, those equations will only tell you whether the sample size is big enough. They won’t tell you whether the result is significant. To find that out, you’ll need to use either Pearson’s Chi-square test or the G-Test. Alternatively, you can save yourself a headache and toss the figures into this useful spreadsheet created by SEO expert Simon Griffiths.

So much for the basic math. Things get really complicated when you start looking for real money-making opportunities online. AdSense Arbitrage works by buying traffic at a low cost per click from one source and selling it through higher value ads to other advertisers. It requires spotting gaps between bid values that are large enough for a publisher to be confident of making a profit on the clicks even though only a small percentage of the users he buys will click through. According to SEO expert Michael Gray, the equation required for spotting those opportunities looks like this:

Thankfully, he doesn’t try to explain that equation, and even more thankfully Smart Pricing and the end of Overture’s Keyword Tool have done a pretty good job of wiping out AdSense Arbitrage for all but the most risk-happy and dedicated publishers.

And that just leaves one more number for any online marketer to focus on: the revenues. Because ultimately, the number on the check is the only figure that really counts.

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