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 (except for the single site I got from my wife, which is likar.info).

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.

see too about pagerank algorithm

20 Ways to Increase your Alexa Rank

see too about google pagerank secret
Here is a collection of methods you can use to boost your Alexa Rank. Most of these tips are derived from several fellow webmasters I know who claimed to have derived positive results through their experiments with the Alexa Rankings.

Some of the other tips were derived articles and sources, which I have duly referenced at the end of this post.

Do these tips work? According to some, yes they definitely do work. But do note that most of them require active effort of some sort and hence, they will work as long as long as you are consistently performing specific actions.

To increase your Alexa rank in the long run, I would highly recommended that one focus on developing quality content which attracts and maintains a large audience instead of purely focusing on artificially increasing your Alexa Rank.

Great link-worthy content will leads to an natural increase in site traffic and is an excellent way to passively increase your Alexa rank.

It is important to emphasize that you should devote most of your efforts in growing your site audience alongside integrated implementation of any of the following tips below.

1. Install the Alexa toolbar or Firefox’s SearchStatus extension and set your blog as your homepage. This is the most basic step.
2. Put up an Alexa rank widget on your website. I did this a few days ago and receive a fair amount of clicks every day. According to some, each click counts as a visit even if the toolbar is not used by the visitor.
3. Encourage others to use the Alexa toolbar. This includes friends, fellow webmasters as well as site visitors/blog readers. Be sure to link to Alexa’s full explanation of their toolbar and tracking system so your readers know what installing the toolbar or extension entails.
4. Work in an Office or own a company? Get the Alexa toolbar or SS Firefox extension installed on all computers and set your website as the homepage for all browsers. Perhaps it will be useful to note that this may work only when dynamic or different IPs are used.
5. Get friends to review and rate your Alexa website profile. Not entirely sure of its impact on rankings but it might help in some way.
6. Write or Blog about Alexa. Webmaster and bloggers love to hear about ways to increase their Alexa rank. They’ll link to you and send you targeted traffic (i.e. visitors with the toolbar already installed). This gradually has effects on your Alexa ranking.
7. Flaunt your URL in webmaster forums. Webmasters usually have the toolbar installed. You’ll get webmasters to visit your website and offer useful feedback. It’s also a good way to give back to the community if you have useful articles to share with others.
8. Write content that is related to webmasters. This can fall in the category of domaining and SEO, two fields in which most webmasters will have the Alexa toolbar installed. Promote your content on social networking websites and webmaster forums.
9. Use Alexa redirects on your website URL. Try this: http://redirect.alexa.com/redirect?www.atur4ku.blogspot.com . Replace doshdosh.com with the URL for your website. Leave this redirected URL in blog comments as well as forum signatures. This redirect will count a unique IP address once a day so clicking it multiple times won’t help. There is no official proof that redirects positively benefit your Alexa Rank, so use with caution.
10. Post in Asian social networking websites or forums. Some webmasters have suggested that East Asian web users are big Alexa toolbar fans, judging by the presence of several Asia-based websites in the Alexa Top 500. I suggest trying this only if you have the time or capacity to do so.
11. Create a webmaster tools section on your website. This is a magnet for webmasters who will often revisit your website to gain access to the tools. Aaron Wall’s webpage on SEOTools is a very good example.
12. Get Dugg or Stumbled. This usually brings massive numbers of visitors to your website and the sheer amount will have a positive impact on your Alexa Rank. Naturally, you’ll need to develop link worthy material.
13. Use PayperClick Campaigns. Buying advertisements on search engines such as Google or Exact Seek will help bring in Traffic. Doubly useful when your ad is highly relevant to webmasters.
14. Create an Alexa category on your blog and use it to include any articles or news about Alexa. This acts as an easily accessible resource for webmasters or casual search visitors while helping you rank in the search engines.
15. Optimize your popular posts. Got a popular post that consistently receives traffic from the search engines? Include a widget/graph at the bottom of the post, link to your Alexa post or use Alexa redirection on your internal URLs.
16. Buy banners and links for traffic from webmaster forums and websites. A prominent and well displayed ad will drive lots of webmaster traffic to your website, which can significantly boost your rank.
17. Hire forum posters to pimp your website. Either buy signatures in webmaster forums or promote specific articles or material in your website on a regular basis. You can easily find posters for hire in Digital Point and other webmaster forums.
18. Pay Cybercafe owners to install the Alexa toolbar and set your website as the homepage for all their computers. This might be difficult to arrange and isn’t really a viable solution for most. I’m keeping this one in because some have suggested that it does work.
19. Use MySpace . This is a little shady so I don’t recommended it unless you’re really interested in artificially inflating your Alexa Rank. Use visually attractive pictures or banners and link them to your redirected Alexa URL. This will be most effective if your website has content that is actually relevant to the MySpace Crowd.
20. Try Alexa auto-surfs. Do they work? Maybe for brand new sites. I think they are mostly suitable for new websites with a very poor Alexa rank. Note that there be problems when you try to use auto surfs alongside contextual ads like Adsense. They aren’t also long term solutions to improving your Alexa Rank so I suggest using with caution.