SYS-CON MEDIA Authors: Carmen Gonzalez, Pat Romanski, Elizabeth White, Yeshim Deniz, Zakia Bouachraoui

Blog Feed Post

Using the Right Mean for Meaningful Performance Analysis

Performance analytics is a field which deals with huge discrete data sets that need to be grouped, organized, and aggregated to gain an understanding of the data. Synthetic and real user monitoring are the two most popular techniques to evaluate the performance of websites; both these techniques use historical data sets to evaluate performance.

In web performance analytics, it is preferred to use statistical values that describe a central tendency ( the odd numbermeasure of central location) for the discrete data set under observation. The statistical metric can be used to evaluate and analyze the data. These data sets have innumerable data points that need to be aggregated using different statistical approaches.

With the number of statistical metrics available, the big question is how do you determine the right statistical metric for a given data set. Mean, Median, and Geometric Mean are all valid measures of central tendency, but under different conditions, some measures of central tendency are more appropriate to use than others.

This article discusses different statistical approaches used in the world of web performance evaluation and the methods preferred in different contexts of performance analysis using real-world performance data.

Common Statistical Metrics

  • Arithmetic Mean (Average)

The average is used to describe a single central value in a large set of discrete data. The mathematical formula to calculate the average isThe average is equal to the sum of all data points divided by the number of items, where ‘n’ represents the number of data samples.

  • Median

Median is the middle score for a set of data that has been arranged in the order of magnitude. Let us consider a set of data point as [12, 31, 44, 47, 22, 18, 60, 75, 80]. To get the median of the data set the data points need to be sorted in ascending order.

12, 18, 22, 31, 44, 47, 60, 75, 80

The median for the above data set is ’44’ as the middle item is (n+1)/2 if odd number of items. The median would be n/2 if there is even number of items in the series.

  • Geometric Mean

Geometric mean is the nth positive root of the product of n positive given values. The mathematical formula to calculate the geometric mean for X containing n discrete set of data points is

  • Standard Deviation

Standard deviation is used for measuring the extent of variation of the data samples around the center. The mathematical formulae to calculate the standard deviation for a set of data samples is

Where ‘a’ denotes the average of ‘n’ data samples of value ‘x’.

Determining the Right Statistical Approach

The two graphs below illustrate the different data distributions we come across in web performance monitoring. Using the formulae explained above, we have derived the average, median and the geometric mean of the webpage load time for website A and B.

Webpage load time Website A

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat4-300x130.png 300w, http://blog.catchpoint.com/wp-content/uploads/2017/05/stat4-768x332.png 768w" sizes="(max-width: 993px) 100vw, 993px" />

 Webpage load time Website B

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat5-300x123.png 300w, http://blog.catchpoint.com/wp-content/uploads/2017/05/stat5-768x314.png 768w" sizes="(max-width: 994px) 100vw, 994px" />

Let us discuss a few use cases to understand how different statistical metrics are applicable in different scenarios.

USE CASE 1

G1 – Scatter plot showing webpage load time data set

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat6-300x227.png 300w" sizes="(max-width: 500px) 100vw, 500px" />

G2 – Histogram shown the distribution of data

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat7-300x223.png 300w" sizes="(max-width: 492px) 100vw, 492px" />

The graphs G1 and G2 plots data for webpage load time. The uneven distribution of the data points in the scatterplot and histogram helps us understand how inconsistent the load time is.

We can see a higher number of data points in the trailing end of the Gaussian distribution in the histogram (G2); this means that most of the data points are of higher value.

What would be a good statistical metric in such cases? Before answering this, lets us take an example. Consider the following data set

Data Set = [4,4.3,5,6.5,6.8,7,7.2,20,30]

If we use median it gives a value of 6.8. But most of the data points tend towards a higher range with 30 being the highest. So, taking the median value in cases with higher outliers is not an accurate estimate of the page load time. Median should be used for data sets with fewer outliers and values that are concentrated towards the center of the Gaussian distribution.

Now let us take the average for this same data set. This gives us a value of 27.4 which is slightly more skewed towards the outlier values. Once again, the average is not an accurate measure for web page load time.

Since median and average don’t apply to this set of data, let us consider the geometric mean. We get a value of 7.8 using geometric mean; this value is closer to the central value and is not skewed to the higher or lower values in the data set.

In this use case, we have determined the geometric mean as the most accurate statistical method to analyze the data.

USE CASE 2

G3 – Scatter plot showing webpage load time data set

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat8-300x194.png 300w" sizes="(max-width: 462px) 100vw, 462px" />

G4 – Histogram shown the distribution of data

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat9-300x230.png 300w" sizes="(max-width: 483px) 100vw, 483px" />

In the graphs above (G3 and G4), most of the data points are close to each other with a higher population in the center of Gaussian surface. The difference between each of the data points are much less than the distribution considered in the previous scenario. This indicates a consistent page load time across different test runs.

Using average or median to evaluate the central tendency would be more accurate in this case as there are not many outliers so the average wouldn’t be skewed towards the outlier values.

USE CASE 3

  Website A

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat10-300x123.png 300w, http://blog.catchpoint.com/wp-content/uploads/2017/05/stat10-768x314.png 768w" sizes="(max-width: 832px) 100vw, 832px" />

Website B

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat11-300x123.png 300w, http://blog.catchpoint.com/wp-content/uploads/2017/05/stat11-768x316.png 768w" sizes="(max-width: 827px) 100vw, 827px" />

 

The above data distribution shows the webpage load time for two different websites. In performance analysis, we need to evaluate the consistency of a webpage. And if there is high volatility in the page performance then we should be able to measure the difference between the central value versus the outliers.

In this case, the standard deviation values are 9.1 and 1.7 seconds for website A and B respectively while the median for website A and B are 26.6 and 18.1 seconds. Based on the standard deviation values, we see there are data points for website A at 36 secs (median + SD) and website B at 20 secs (median + SD). This means that website A had high number of data points concentrated at 36 secs or more and website B had high number data points concentrated at 20 secs or more.

To know what percent of data had higher value when compared to the standard deviation we can use the cumulative distribution graph.

Website A                                                                     
http://blog.catchpoint.com/wp-content/uploads/2017/05/stat12-300x127.png 300w, http://blog.catchpoint.com/wp-content/uploads/2017/05/stat12-768x324.png 768w" sizes="(max-width: 850px) 100vw, 850px" />
 Website B

http://blog.catchpoint.com/wp-content/uploads/2017/05/stat13-300x127.png 300w, http://blog.catchpoint.com/wp-content/uploads/2017/05/stat13-768x325.png 768w" sizes="(max-width: 827px) 100vw, 827px" />

From the cumulative distribution graph shown above we can see that website A had almost 20% of data points higher than the standard deviation values whereas website B had 10% of data more than standard deviation value.

Standard deviation can be used for evaluating how far and consistent the data points are with respect to the central value of data distribution in performance analysis.

 

Median and average are applicable when the data points are concentrated towards the center of the Gaussian distribution. On the other hand, if there are more data points distributed towards the tail of the Gaussian distribution and there is a high difference between each data point then geometric mean would be a better choice. Standard deviation should be used to understand the variance of the data points from the median value and to gauge the consistency of the sites performance.

 

The post Using the Right Mean for Meaningful Performance Analysis appeared first on Catchpoint's Blog - Web Performance Monitoring.

Read the original blog entry...

More Stories By Mehdi Daoudi

Catchpoint radically transforms the way businesses manage, monitor, and test the performance of online applications. Truly understand and improve user experience with clear visibility into complex, distributed online systems.

Founded in 2008 by four DoubleClick / Google executives with a passion for speed, reliability and overall better online experiences, Catchpoint has now become the most innovative provider of web performance testing and monitoring solutions. We are a team with expertise in designing, building, operating, scaling and monitoring highly transactional Internet services used by thousands of companies and impacting the experience of millions of users. Catchpoint is funded by top-tier venture capital firm, Battery Ventures, which has invested in category leaders such as Akamai, Omniture (Adobe Systems), Optimizely, Tealium, BazaarVoice, Marketo and many more.

Latest Stories
The dream is universal: heuristic driven, global business operations without interruption so that nobody has to wake up at 4am to solve a problem. Building upon Nutanix Acropolis software defined storage, virtualization, and networking platform, Mark will demonstrate business lifecycle automation with freedom of choice and consumption models. Hybrid cloud applications and operations are controllable by the Nutanix Prism control plane with Calm automation, which can weave together the following: ...
FinTech is a disruptive innovation that denotes the adoption of technologies that have changed how traditional financial services work. While FinTech is now embedded deeply into the financial services ecosystem, the rise of digital age has paved way to FinTech 2.0 - which is rolling out innovative solutions through emerging technologies at a disruptive pace while maintaining the tenets of security and compliances. Blockchain as a technology has started seeing pilot adoption in FinTech around ...
Now is the time for a truly global DX event, to bring together the leading minds from the technology world in a conversation about Digital Transformation. DX encompasses the continuing technology revolution, and is addressing society's most important issues throughout the entire $78 trillion 21st-century global economy. DXWorldEXPO® has organized these issues along 10 tracks, 22 keynotes and general sessions, and a faculty of 222 of the world's top speakers.
Atmosera delivers modern cloud services that maximize the advantages of cloud-based infrastructures. Offering private, hybrid, and public cloud solutions, Atmosera works closely with customers to engineer, deploy, and operate cloud architectures with advanced services that deliver strategic business outcomes. Atmosera's expertise simplifies the process of cloud transformation and our 20+ years of experience managing complex IT environments provides our customers with the confidence and trust tha...
92% of enterprises are using the public cloud today. As a result, simply being in the cloud is no longer enough to remain competitive. The benefit of reduced costs has normalized while the market forces are demanding more innovation at faster release cycles. Enter Cloud Native! Cloud Native enables a microservices driven architecture. The shift from monolithic to microservices yields a lot of benefits - but if not done right - can quickly outweigh the benefits. The effort required in monitoring,...
SUSE is a German-based, multinational, open-source software company that develops and sells Linux products to business customers. Founded in 1992, it was the first company to market Linux for the enterprise. Founded in 1992, SUSE is the world's first provider of an Enterprise Linux distribution.
Intel is an American multinational corporation and technology company headquartered in Santa Clara, California, in the Silicon Valley. It is the world's second largest and second highest valued semiconductor chip maker based on revenue after being overtaken by Samsung, and is the inventor of the x86 series of microprocessors, the processors found in most personal computers (PCs). Intel supplies processors for computer system manufacturers such as Apple, Lenovo, HP, and Dell. Intel also manufactu...
Blockchain has shifted from hype to reality across many industries including Financial Services, Supply Chain, Retail, Healthcare and Government. While traditional tech and crypto organizations are generally male dominated, women have embraced blockchain technology from its inception. This is no more evident than at companies where women occupy many of the blockchain roles and leadership positions. Join this panel to hear three women in blockchain share their experience and their POV on the futu...
Artifex Software began 25-years ago with Ghostscript, a page description language (PDL) interpreter software prevalent in printing and related applications requiring rendering and/or conversion from one software language to another. Founded by renowned computer scientist Dr. L. Peter Deutsch, our company has thrived on the basis of our sharp focus on this area of expertise, a zealous commitment to quality and a strong customer service orientation. Over 100 OEM partners representing some of th...
As the digitization of business accelerates the move of critical applications and content to the cloud, the network has never been as critical to business success. Consuming everything ‘as-a-service' requires new levels of network automation, agility and security. Discover how Enterprises can take advantage of Digital Platforms, directly connecting to an extensive ecosystem of digital partners and flex their service at the click of a button.
Alan Hase is Vice President of Engineering and Chief Development Officer at Big Switch. Alan has more than 20 years of experience in the networking industry and leading global engineering teams which have delivered industry leading innovation in high end routing, security, fabric and wireless technologies. Alan joined Big Switch from Extreme Networks where he was responsible for product strategy for its secure campus switching, intelligent mobility and campus orchestration products. Prior to Ext...
In today's always-on world, customer expectations have changed. Competitive differentiation is delivered through rapid software innovations, the ability to respond to issues quickly and by releasing high-quality code with minimal interruptions. DevOps isn't some far off goal; it's methodologies and practices are a response to this demand. The demand to go faster. The demand for more uptime. The demand to innovate. In this keynote, we will cover the Nutanix Developer Stack. Built from the foundat...
In an age of borderless networks, security for the cloud and security for the corporate network can no longer be separated. Security teams are now presented with the challenge of monitoring and controlling access to these cloud environments, as they represent yet another frontier for cyber-attacks. Complete visibility has never been more important-or more difficult. Powered by AI, Darktrace's Enterprise Immune System technology is the only solution to offer real-time visibility and insight into ...
Financial enterprises in New York City, London, Singapore, and other world financial capitals are embracing a new generation of smart, automated FinTech that eliminates many cumbersome, slow, and expensive intermediate processes from their businesses. Accordingly, attendees at the upcoming 23rd CloudEXPO, June 24-26, 2019 at Santa Clara Convention Center in Santa Clara, CA will find fresh new content in full new FinTech & Enterprise Blockchain track.
Every organization is facing their own Digital Transformation as they attempt to stay ahead of the competition, or worse, just keep up. Each new opportunity, whether embracing machine learning, IoT, or a cloud migration, seems to bring new development, deployment, and management models. The results are more diverse and federated computing models than any time in our history.