Google PageRank (PR) vs. Alexa Traffic Rank Correlation (Regression) Analysis

Abstract: a statistical study (regression analysis) of a random sample of 102 websites has shown that a strong relationship (correlation) exists between Google PageRank and Alexa Traffic Rank.

Introduction

Google PageRank (GPR) and Alexa Traffic Rank (ATR) are two different measures of a website's success. As you know (shame on you if you don't), simply speaking, GPR measures the number of links to the site, while ATR measures the site's traffic. (Official detailed descriptions of these two indicators are available at Google Technology and Alexa Help pages.)

Correlation between ATR and GRP has become my concern after I visited two websites in a row, namely CSS Zen Garden and Mail.ru. The first one, a specialized CSS design project, has Google Page Rank of 8 and Alexa Traffic Rank of over 13 thousand. The second one, a huge Russian portal, had Page Rank of 6, yet ranked 23^rd in Alexa! The question occured, «does traffic affect link popularity?» Interestingly, although Mail.ru is a much more popular portal, CSS Zen Garden obviously had much more quality links pointing to it. This phenomenon can be explained with a look at the nature of CSS Z.G.; the site is oriented at designers, who are likely to have a site and give direct links. Users of Mail.ru, on the other hand, are mortals that want free email, videos, chat, news, etc, and are less likely to put links to the site.

Here is a comparative table:

Site            |  GPR  |   ATR
--------------------------------
CSS Zen Garden  |   8   | 13,138
Mail.ru         |   6   |   23  

This difference between the actual real popularity of a portal and the quality links pointing to it created this desire in me to test the statistical correlation between the inbound links and traffic, measured by Google PageRank and Alexa Traffic Rank respectively.

A copy of the original spreasheet is available, yet it does not contain graphs and charts.

The sample

The sample for this analysis consisted of 102 randomly picked websites. I tried to pick sites for this analysis as randomly as possible: I caught myself quering Google for such phrases that I would never ask for, such as "knitting", "nothing", "rotting" and other crazy queries. I tried to randomize the sample as much as I could. Yet I understand that there was a bias, because I was the only one who picked sites.

Many websites from the sample I like and visit daily, yet others I don't even know. To get some of the lower quality sites, I went to a lousy web design studio, and simply randomly clicked sites from their portfolio (most clone-looking 0-2 PR sites are their masterpieces). Note that there was a chance of humar error; my Google Toolbar might have malfunctioned or I could have simply overlooked the value. Complete list of websites is also available.

T-distribution (or Student's T distribution) table I used for my analysis offers .... 70, 80, 100, 150 ... degrees of freedom, among others. The key fact is that it does not offer 98 degrees of freedom. This information is important, since the formula I used needs n-2 degrees of freedom, where n is the sample size. Thus, I used exactly 102 observations purposefully (last two added later) so that I could find the accurate tabular values in Student's T distribution table (so that I deduct 2 from my sample and arrive at 100).

Each sample value (site) had three parameters (dimentions), namely URL, GPR, and ATR. In the initial spreadsheet, each observation also has an ID number and the date of measurement. (Please note, that some of the sites I am sure have changed since the study! Few of the them I run/manage/own/develop. Note the date of measurement.)

Google PageRank Distribution

Normally distributed! From GPR point of view, the sample was almost perfectly distributed, representing the bell-shaped curve. As you can see from the diagram, there was a very little skewness to the right. Mean average was 5.05 and median 5, with dispertion of 7. The coefficient of skewness was as low as 0.06, which means that the sample was quite normally distributed.

For the histogram above, I have chosen each of the 11 PageRank values for each class (exactly 11, not 10, remember that zero is also a separate value).

Alexa Traffic Rank Distribution

For Alexa TR, the distribution was much less normal. The entire sample was significantly skewed right, with as much as 73% observations representing one eighth of the possible values. This vast majority encompassed sites within the first 1,500,000 positions in the rank.

With mean average of 1,245,677.471 and meadian of 109,922, the sample had huge dispersion of 5351667608993.28, range of 10,960,325, and skewness coefficient of 1.47. I have divided the entire sample into 8 classes, with 1,500,000 as a class step, altogether ranging from 0 to 12,000,000.

Obviously, vast majority of the websites from the sample belonged to a minority group, which is a limitation of the study. I should have either gathered sites that were all in the top 2M range, or gathered more lower quality sites.

Analysis and methods

The initial idea was to test whether the ATR actually correlates to GPR. Thus, the null hypothesis H₀ was, «no relationship exists between traffic popularity measured by Alexa Traffic Rank and link popularity measured by Google Page Rank». The alternative hypethesis H_f was, «there is a correlation between Google PageRank and Alexa Traffic Rank». The purpose of the study was to reject the null hypothesis and to prove there truly is a correlation between the two site success indicators. (I must remind that the initial CSS vs. Mail encounter that pushed me toward this analysis showed that there was hardly any correlation between these indicators.)

Simple regression analysis and t-distribution significance test was used for the study.

Regression analysis

The two arrays of data (each of 102 observations) showed rather high negative correlation. The ultimate r (correlation coefficient) was equal to -0.5. The best fit line's equation was y = -439630,50x + 3469690,61. I had Alexa TR on the Y axis (and Google PR on X axis, respectively).

The data points are concentrated vertically at the 11 imaginary lines of PageRank values, because Google's rank only has 11 possible values. This phenomenon creates huge gaps in this discrete data array. Still, the tendency is obvious! There is a strong visible correlation between the two sets of data.

Hypothesis testing (significance test)

Regardless of the visual correlation, I had to test whether this was a chance occurrence, or a statistically significant phenomenon. As I mentioned earlier, I used t-distribution for significance test. The test statistic was r/√[(1-r²)/(n-2)], where r is the regression coefficient and n is the sample size. The number of degrees of freedom is n-2. I used standard significance level α=0.05. The table value of t_{0.05; 100df} appeared 1.984. Thus, with a two-tailed test, if the absolute value of the calculated value of t is greater than the absolute value of tabular t, I can reject the null hypothesis (hypotheses are described above). The calculated value of t was -5.83125. |-5.83125| is greater than |1.984|, and therefore we reject the null hypothesis, and prove that there is statistical significance to claim that correlation between Google PageRank and Alexa Traffic Rank truly exists and is not a random chance phenomenon.

Outliers and interesting observations

Two potential outliers are at the top of the graph; one at point [6; ~11,000,000] and the other one (yet less likely to be considered an outlier) at [3; ~10,400,00]. These two, however, are potential graphical outliers, visible with the naked eye.

Three questionable points, which are not that visible, yet are very hard to believe in, are concentrated near the origin. Especially the one right next to the origin (the bottom point on the Y axis), which is a website with zero Page Rank, yet relatively high traffic. This is an interesting phenomenon, which shows a popular website, with nearly no inlinks. (The site is Red Bean, and at the date measurement on Nov 29th, 2007, it had 0 PR and 27,214 ATR. Yet, at the moment of writing this article, I see it has PR of 7.)

Conclusion

Regardless of the limitations of the test, the study showed very strong relationship between Google PR and Alexa Traffic Rank.

If you notice errors of typos, please leave a comment. The copy of the original spreadsheet is available at Google Spreadsheets.

What Does Your Alexa Rank Mean?

Alexa is a funny little ranking engine. Your fluctuations in rank can be pretty dramatic until Alexa gets a handle on your site.

They have changed their algorithm to, supposedly, better reflect and predict all your traffic. This means they no longer depend on simply guestimating your rank based on Alexa toolbar users who visit your site.

After the update I went from 32,000 to 60,000+ and now I believe they rank me well over 100,000. Yet, my traffic continues to grow.

The important thing to remember is that Alexa is one of several indicators of your site’s traffic health. Of course, you know the exact number of uniques you get each day from your own stats. That’s the main indicator, above all else, you should use to gauge how you’re doing.

It is quite possible Alexa doesn’t know enough about the traffic that is hitting your site because it is too low at this point to estimate more accurately in their rankings.

With the traffic level you have now, my focus would be on more marketing, deeply important and interesting posts (linkbait) for your niche, more commenting and networking on other blogs and social sites, and link building.

Regardless of the quirks in Alexa’s particular ranking system, you want to set a benchmark of a solid 100 visitors per day and then shoot for 500, 1000 and beyond.

Eventually Alexa should reflect this progress in their rankings.

There's More to SEO than Rankings

Perhaps one of the biggest misconceptions in SEO is that ranking at Google and Yahoo is all that counts in search engine optimization. Potential clients come to me with a single goal: "Get me a top-ten ranking at Google." Some will also mention MSN, and a few will rhyme off a list of search engines and want to rank well at the top 200 of them.

It is time to separate fact from fiction.

Yes, I can get you a top-ten placement at Google. But...

1. If the placement is for "dirty brown shoes", it probably won't help your shoe store one bit, even if I get you the first place ranking. Few people are actually searching for that term.

2. Being number ten might not help much either, depending on the term. People searching for "Essential Nectar liquid vitamins", will probably click on the first result they see, or at least on one of the "above-the-fold" results that do not require scrolling. On the other hand, someone searching for "liquid vitamins" might check through two pages of results to familiarize herself with the options available.

3. If your title tag reads like a cheap list of search terms, it will not be enticing. For instance, if it reads: "vitamins, liquid vitamins, multivitamins, multi-vitamins", you might skip over it in favor of the next result that reads "Liquid vitamins from the Liquid Vitamin Supplements Store".

4. If your description tag is a mess, people will more likely skip over your listing, even if it does rank number one, in favor of one that sounds like what they are looking for. Google and others use the description tag usually when the term searched for is found in it, so make sure to include your key search terms in a description tag that actually reads well.

Predicting traffic from SEO results

I recently responded to a forum question, which went something like this: My site ranks number one for this term at this engine. The term is searched this many times per day, and the engine has this percentage marketshare. Can I expect this many visitors?

That's not an SEO challenge; that's a math problem: searches x marketshare = visitors

I responded with a few factors that override mathematics in the SEO game, including the site's title tag and description tag, as well as whether the term lends itself to scrolling. I also pointed out that it depends on the title tags and description tags of the competition, too.

Another factor that makes predicting traffic difficult is the abandonment factor - how many people click on none of the results because they get interrupted or confused, or abandon the search for a new one because they find themselves off-topic or searching too broadly.

It also depends on how many sponsored links there are and how they are marked. Often at Yahoo and Lycos, for example, there are so many ads that the average searcher might never scroll a screen or two to see the organic (natural) results.

And, of course, it also depends on the color of the walls in the room the searcher is clicking from, the weather outside and how well they slept last night. But there is little you can do about that.

What you can do is to work with your SEO consultant to choose the most effective search terms for your business and make sure he develops a title tag and description tag that sell to both humans and the search engines. Then make sure he is monitoring not just the rankings for your key search terms, but also the description used by each of the search engines.

A good ranking at Google and Yahoo is just one measure of your SEO consultant's success. A more complete evaluation is that he is your partner in building long-term, targeted traffic

The Fatal Attraction of Online Marketers

Suppose you were offered 263 links coming into your website from 263 other websites all in one fell swoop. Everybody knows that the more inbound links you have, the higher you will rise in the search engine rankings.

Suppose further that these were real links from real websites that actually sold real products and services - no cheap FFAs throwing come-ons on a street corner on the bad side of town.

Suppose further that this offer included the reciprocal linking code for all 263 sites that just had to be cut and pasted into your website. Piece of cake.

Does it get any sexier than this? Are you drooling yet? Does the sweet perfume of "ka-ching!" float around your head? Is this love at first site?

Well, no, it's actually a fatal attraction, one you had best resist. One that could infect your website with deadly communicable diseases.

I resisted this very offer not long ago, and you should resist anything similar. Here's why:

1. The link pages on these sites are essentially link farms. The more links on a page, the less value they have in a search engine's eyes, especially when you start approaching or even passing 100 links. And don't expect any direct traffic from this kind of link, either.

2. There is a technical term for identical pages within a site or on multiple sites. It is called "duplicate content", and it is strictly verboten by the search engines. Here is what Google says about them: "Don't create multiple pages, subdomains, or domains with substantially duplicate content."

3. Do some quick math. You have 289 outgoing links, 263 of them are labeled "bad neighborhood websites" by the search engines ... so bad that they might even have been banned. What do you think will happen to your rankings?

Sadly, many webmasters fall for such tantalizing come-ons without thinking carefully about what the repercussions might be.

There is a lot of truly bad advice floating around the Internet on how to trick the search engines or find a short-cut to high rankings. This is one example of how following poor advice and hopping into bed with the wrong partner could kill your business.

Here is a good rule of thumb. Two's company. Three's a crowd. Four or more will get you arrested. OK, so I just made that up, and it's not very elegant. But it will keep you from falling for that inevitable offer with the come-hither eyes and the deadly communicable disease.