Analysis of Variance Archives - 6sigma https://6sigma.com/tag/analysis-of-variance/ Six Sigma Certification and Training Fri, 28 Feb 2025 12:41:41 +0000 en-US hourly 1 https://6sigma.com/wp-content/uploads/2021/03/cropped-favicon-blue-68x68.png Analysis of Variance Archives - 6sigma https://6sigma.com/tag/analysis-of-variance/ 32 32 How to Use Analysis of Variance (ANOVA) https://6sigma.com/use-analysis-variance-anova/ https://6sigma.com/use-analysis-variance-anova/#respond Fri, 20 Jul 2018 14:00:03 +0000 https://opexlearning.com/resources/?p=26624  

If you take a Six Sigma Green Belt or Black Belt training class, Analysis of Variance (ANOVA) is a core analysis tool that is taught. It is used to split variability from a data set into two key groupings: random factors (noise) and systemic factors (significant).

The ANOVA test is […]

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The total variation (orange) is broken up into 4 different factors using Analysis of Variance (ANOVA)

 

If you take a Six Sigma Green Belt or Black Belt training class, Analysis of Variance (ANOVA) is a core analysis tool that is taught. It is used to split variability from a data set into two key groupings: random factors (noise) and systemic factors (significant).

The ANOVA test is a useful tool that helps you establish what impact independent variables (inputs) have on dependent variables (outputs) within a regression model, experimental design or multi-variable study. For instance, ANOVA can be used to determine differences in the average Intelligence Quotient (IQ) scores of people from different countries (e.g. Spain vs. US vs. Italy vs. Canada).

In this example, the IQ scores would be considered the dependent variable, and countries would be an independent variable.

ANOVA provides a statistical test of whether the averages of several groups are equal, and therefore generalizes the traditional t-test to more than two groups, referred to as an F-test. If there were statistical differences between the average IQ scores within each country, then we would conclude that country is a systemic (significant) factor in explaining variation in IQ scores.

Many statistical packages can perform ANOVA analysis and help you determine which of your independent variables are significant, which makes the calculations much easier these days.

The History and Purpose of ANOVA

For the purpose of this type of comparison test, which was developed during the 20th century, t-tests were the primary analysis tools available to analysts until 1918, the year when Ronald Fisher created ANOVA.

However, the term only became a buzzword in 1925 after it appeared in his book, Statistical Methods for Research Workers.’ Initially, the method found application in experimental psychology, but was later employed to wider applications such as farming and manufacturing. As a nod to its creator, the test is also known as the Fisher Analysis of Variance.

The ANOVA test is the first step when analyzing the factors that affect a data set, after assumptions have been validated. After the test has been completed, you can perform further tests on the factors which contribute to the variability, or discover that there are more factors not captured in your data that are missing from your analysis.

From the ANOVA analysis, a percentage of explained variation can be calculated (called an R-squared value), which is a number between 0% and 100%. If your analysis shows a percentage of only 33%, likely you are missing some important variables from your data set, and should find ways to gather additional data and re-run your analysis.

Types of ANOVA

Analysis of variance comes in two distinct forms: one-way and multiple. In a one-way ANOVA, the evaluation carried out is with regard to the impact of a single factor on only one dependent variable. This analysis helps to determine if all categories or groups studied are the same within that variable (such as each country). The purpose of the one-way ANOVA is to establish if there are statistically significant differences in the average of two or more unrelated groups within your dependent variable.

The multiple ANOVA extends the one-way ANOVA to two or more dependent variables. An example of a multiple ANOVA is where a company seeks to compare productivity of its workers on the basis of four independent variables…

Dependent: Productivity (average number of quality documents produced per hour)

Independent:

  1. Age (Under 30, 30-50 years old, over 50)
  2. Job experience in company (less than 5 years, 5-10 years, over 10 years)
  3. Previous related work experience or education (no or yes)
  4. Education Level (no high school degree, high school educated, college educated)

In addition to determining which of the 4 variables influence the productivity, it can also identify if any of the variables interact with each other, creating a more complicated relationship. An interaction in this example might be where previous related work experience does not matter for workers with over 10 years experience in the company, but makes a big difference for workers who are under 30 years old and with the company less than 5 years. The impact on productivity changes when you look at the groups of another variable (it’s not consistent across the board).

How Is ANOVA Used?

You will find ANOVA tables displayed in the these 3 popular Six Sigma tools: Regression Analysis, Gage Repeatability and Reproducibility (R&R) studies, and Design of Experiments (DOE).

For instance, a researcher could test students from different colleges in order to find out if the students attending one college are consistently outperforming those from the rest of the colleges. Another example of the applications of the ANOVA test is a researcher testing two different manufacturing processes to find out if one process used to create a product is more cost effective than the other.

You could even compare the beer consumption between regions of the world to see if they are similar or different.

Here is an example of an ANOVA analysis. The bottom section represents the ANOVA table, showing the Region, Error and Total terms. We will not go into the details of this calculation in this article.

Conclusion

If you are familiar with the traditional t-test, you will be excited to learn that the ANOVA test can replace the t-test, as it can handle more complex analyses that are difficult or impossible to perform with the t-test alone. Due to the increase in computing speed over the last few decades, ANOVA has become one of the most popular techniques used to compare group averages, which is needed to understand many research reports and conduct successful Six Sigma projects.

If you would like to learn more about t-tests, F-tests and ANOVA, sign up for Six Sigma Green Belt training with 6sigma.US >>>

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Top 10 Reasons for Six Sigma Green Belt Training https://6sigma.com/21391-2/ https://6sigma.com/21391-2/#respond Tue, 11 Jul 2017 17:37:41 +0000 https://6sigma.com/?p=21391 Six Sigma is well-known within countless businesses and corporations for its effective process improvement capabilities. Using Six Sigma, you can isolate problems and correct them with ease, streamlining your operations to make them more efficient and profitable. Moreover, Six Sigma relies on a belt-based hierarchy, and one of the most integral of all practitioners is […]

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Six Sigma is well-known within countless businesses and corporations for its effective process improvement capabilities. Using Six Sigma, you can isolate problems and correct them with ease, streamlining your operations to make them more efficient and profitable. Moreover, Six Sigma relies on a belt-based hierarchy, and one of the most integral of all practitioners is the Six Sigma Green Belt.

But why invest the time and money in Green Belt training? How will it benefit you in the long- and short-term? Today, we shed light on how Green Belt training can be highly advantageous for individuals or corporations. Here are our top 10 reasons why you should sign up for a Six Sigma Green Belt training course.

 

Top 10 Reasons for Six Sigma Green Belt Training

 

  • 1. Positive Change.

    By training employees to become Six Sigma Green Belts, they will master Six Sigma methods in the workplace. This can only be a benefit for your organization, as they can then make positive changes from within.

 

  • 2. Time-Effective Training.

    Green Belt training provides a wide-ranging, intensive study of Six Sigma methodology in an accelerated timeframe. Green Belts aren’t required to take on the same level of management responsibility as Black Belts, so training requires significantly less time investment.

 

  • 3. Incentive for Promotion.

    With promotion comes new responsibilities and required skills as well as numerous benefits. As an employer, you can use Six Sigma Green Belt training as an incentive for promotion. Moreover, as an employee, Green Belt training will grant you additional knowledge and skills to help bolster your job progression.

 

  • 4. Impress Employers.

    Companies all over the world use Six Sigma, and job candidates with Six Sigma certification are in high demand. Equally, Green Belts are one of the most versatile and effective Six Sigma practitioners. Show employers why they should hire you through your resumé.

 

  • 5. Pathway to Black Belt Training.

    Six Sigma doesn’t end with the color Green, and Green Belt training can also open doors for Black Belt progression. With the combined knowledge and capabilities of Green and Black Belts on your staff, you will reach optimum efficiency in no time.

 

  • 6. Teambuilding.

    Don’t just train one Green Belt. Train a whole group of them. Green Belts typically train in groups, and by investing in multiple employees, their training also builds team spirit and group work skills.

 

  • 7. Flexible Training Plans.

    Your Six Sigma Green Belt training, when given in-company, is flexible enough that you can adjust it to suit your needs. It can focus on the most pressing areas affecting your company so that you can get the most benefit.

 

  • 8. Easy to Evaluate.

    You can evaluate the success of your Six Sigma Green Belts’ work based on their awarded certification, completed project work, and demonstration of Six Sigma knowledge. This also makes it easy to measure the success and capabilities of your Green Belts for specific tasks.

 

  • 9. Productivity Prevents Problems.

    Green Belt training encourages high productivity and continuous improvement culture. Six Sigma Green Belts can implement preventative measures to ensure problems do not continue to recur. Moreover, this helps you reach a state of near-complete operational excellence.

 

  • 10. Hone Your Analytical Skills.

    Much of Six Sigma involves varying levels of data analysis. Especially for techniques like DMAIC and Analysis of Variance. Furthermore, Six Sigma Green Belt training allows you to develop these key analytical skills. From basic comparisons to quantifying profits. With their range of skills, Green Belts are also prime management material.

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Industry: Drop Shipping and Six Sigma https://6sigma.com/industry-drop-shipping-six-sigma/ https://6sigma.com/industry-drop-shipping-six-sigma/#respond Wed, 21 Jun 2017 21:20:02 +0000 https://6sigma.com/?p=21311 Drop shipping is booming and supply chain managers all over the world are currently using Six Sigma to improve their delivery businesses. But first, it’s important we define what drop shipping means before we can understand how it works with Six Sigma. Drop shipping, while it does involve physical shipping of items, is more a […]

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Drop shipping is booming and supply chain managers all over the world are currently using Six Sigma to improve their delivery businesses. But first, it’s important we define what drop shipping means before we can understand how it works with Six Sigma. Drop shipping, while it does involve physical shipping of items, is more a retailing strategy between retailers and wholesalers. It has garnered great esteem thanks to sites like Alibaba, Overstock, and Amazon, both of which use drop shipping in their operations.

Drop shipping involves a retailer making an arrangement with a wholesale distributor to ship their product after a customer has purchased it. The retailer sells it, and the wholesaler distributes it with the retailer’s label on the item’s packaging. This is a mutually advantageous relationship in which both parties benefit. The wholesaler acquires more product sales and new outlets for retail. Similarly, the retailer benefits from the percentage they earn from each sale. A further advantage for the retailer is that they don’t have to concern themselves with the shipping or carrying of inventory. The wholesaler takes care of it all on their behalf. Today, we look at some of the advantages of drop shipping and how Six Sigma ideas can help you make the most of it.

Why is Drop Shipping Beneficial?

Drop shipping is beneficial as it does not require retailers to maintain an inventory. Not does it require them to handle shipping. They can simply buy at wholesale prices and sell directly to the customer at retail prices, with the distributor supplying product information as well as new products. Amazon, Alibaba, and Overstock all use drop shipping in their online operations. Using this method has helped them cultivate a prosperous online business presence with virtually no initial inventory investment required. By having wholesalers source and dispatch the items they sell, Amazon makes substantial revenue to dominate the online market.

When a retailer sets up a website to sell goods, customers buy the goods, paying the retailer plus any shipping costs. For example, a $10 item may necessitate $3 shipping. It’s then up to the retailer to contact the wholesale distributor, informing them of the details regarding the order. The wholesaler can then package and ship the item to the customer using the retailer’s label. The retailer pays the wholesale price of the product(s) and shipping while retaining a 30% profit. This is how sites like Amazon have managed to make billions of dollars.

Going Where No Retailer Has Gone Before

Certain markets regularly become flooded as multiple retailers try to woo customers with competing products. There is a way around this, though, and Amazon is a great example of ingenuity here. Moreover, Amazon has gone a step further than most as they are both retailers for external products and wholesaler for their own-branded goods. But not only that, Amazon is not just a retailer and distributor, but also a manufacturing and technology giant too. The AmazonBasics line of products aims to provide affordable alternatives to a vast array of everyday essentials. Everything from batteries and phone chargers to backpacks and fashion items. Using Six Sigma principles, they have managed to significantly streamline their manufacturing, distribution, and retail processes for their own-branded products. This affords them a substantial market advantage over competing vendors. Why pay more when you can pay less?

Supply Chain Management

Supply chain managers have a lot on their plate. Their work is often externally focused, requiring them to work with outside partners to source goods or parts to produce products. This is integral to the way modern retailing works. For wholesale distributors and delivery companies, supply chain managers source the inventory retailers require, selling it to them so that they can sell it on again to make a profit. Supply chain managers often work for large corporations, particularly online stores and retail giants like Alibaba and Amazon. They negotiate contracts with distributors to maintain inventory on in-demand goods. Using Six Sigma, you can make a real difference to your wholesalers and how you deal with them. This will help improve efficiency and increase revenue for both.

Improving Delivery Businesses with Six Sigma

As a retail supply chain manager, it’s up to you to decide which products you want to sell. Six Sigma uses raw data to make justifiable decisions about process changes. Without a strong plan to follow, you won’t make the most of Six Sigma strategy. Think about the market you are targeting. Make certain that the products you want to sell are in demand. Search engine analytics are a great way to shed light on what is trending, on which products and services people want. The more you know, the more prepared you are to drive successful change. The more data you have, the greater control you have over the value chain, allowing you to predict potential future demand.

It’s important to utilize reliable drop shippers to ensure success. Be wary, though, as there are plenty of charlatans out there masquerading as good drop shippers. If you chance upon a bad egg, get rid of it quickly, as they will cause more problems for you later. A reliable drop shipper demands lots of pertinent information to do their job. This is your golden ticket. You can expect them to ask for references from other suppliers as, remember, they want to benefit from the arrangement just as much as you do. Once you get going, we recommend applying tools like Root Cause Analysis and DMAIC as regular assessments of your business operations.

Additional Six Sigma Improvement Tools

If you keep running into similar problems, like missing product information and shipping alternative or defective items, apply Root Cause Analysis to identify the source of the issue. Similarly, DMAIC can help you take control of inefficiencies to improve your business processes. It can also help you locate sources of variation that lead to defective products using Analysis of Variance. Applying Lean principles will also help eliminate sources of waste such as over-processing and human error. Black Belt-led improvement projects can also actively seek out inefficiencies and replace them with innovative solutions. All these tools and techniques coalesce to make significant improvements across the board. Cultivating a Kaizen culture of continuous improvement is also a beneficial strategy to stay on top of these problems and ensure future success. This not only benefits the customer but, of equal importance, you as well.

Learn more about our training and Courses

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Glossary of Six Sigma Terms: Letters A – C https://6sigma.com/six-sigma-glossary-c/ https://6sigma.com/six-sigma-glossary-c/#respond Wed, 19 Apr 2017 19:32:47 +0000 https://6sigma.com/?p=20984 A
  • Acceptable Quality Level.

    The term acceptable quality level, abbreviated as AQL, is a concept appearing in Six Sigma sampling inspection. The concept describes the maximum percentage of defects that is acceptable for a long-term average. Six Sigma practitioners use AQL to put a cap on allowable defect when inspecting a batch […]

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    • Acceptable Quality Level.

      The term acceptable quality level, abbreviated as AQL, is a concept appearing in Six Sigma sampling inspection. The concept describes the maximum percentage of defects that is acceptable for a long-term average. Six Sigma practitioners use AQL to put a cap on allowable defect when inspecting a batch of items. As per the basics of sampling inspection, the batch is either then accepted or rejected based on its suitability.

     

    • Accuracy. 

      When we talk about accuracy, it is usually as a term of measurement. Accuracy describes the difference in average or means of numerical readings, as well as the true / target value. It is essentially the same as bias when used for measurement. The difference between observed measurements and the true value, based on the reference standard. Any Six Sigma practitioner or statistician will use accuracy to discover data biases. In process variation, practitioners aim to create accuracy by adjusting the process mean.

     

    • Activity Network Diagrams.

      ANDs or activity network diagrams display information about Six Sigma activities and how they are interdependent. ANDs are only ever used in complex projects to help with planning, scheduling, and identifying critical pathways. Critical pathways are activities that would suffer from delay, ultimately impacting project completion. The most commonly used activity network diagram is a project evaluation and review technique, or PERT. In PERT, nodes or circles represent milestones in a project, interlinked by numbered lines to show duration.

     

    • Analysis of Variance.

      Also known as ANOVA, analysis of variance is a statistical technique used by Six Sigma project leaders. You can use ANOVA to compare whether samples are taken from populations with the same mean, or if their population means possess significant differences. ANOVA analyzes variation in data sets to deduce how much variation has contributed to each factor. You should use a hypothesis test to work out how much variation is statistically significant per each source. Once you have proven or disproven your hypothesis, you can use ANOVA, provided each process conforms to normal distribution.

     

    • Analytical Statistics.

      Six Sigma Belts use analytical statistics, sometimes known as inferential statistics, to draw conclusions about populations based on their sample data. For instance, three sets data values, at 4, 8, and 9, might refer to the number of years three homeowners have owned their homes. You would use analytical statistics to make inferences about the mean amount of time your sample participants have owned their homes, which would be 7 Using such a small sample would be impractical, which is why a full-scale study involving a sufficient sample size is necessary. During your study, you would use analytical statistics to ensure your sample is representative of the population.

     

    B

    • Balanced Scorecard.

      Six Sigma project leaders use the balanced scorecard strategy to increase performance and accountability when both are lacking. Using balance scorecard, you can develop performance measures based on four categories. Financial, the most common focus for performance. Customer, based on the known needs and potential expectations for future demand. Business processes, how efficient your operations are. Learning and growth, how you cultivate knowledge and expertise in your employees. The balance scorecard system states that practitioners place too much importance on financial measures. As such, short-term focus on the bottom line of expense operations is more critical to success in the long-term.

     

    • Bayes Theorem.

      Bayes Theorem is an important concept in probability theory. It is a statistical method to calculate conditional probabilities. This means that the likelihood of an event occurring is dependent on how probable the event is, along with the accuracy of your measuring instrument. Six Sigma Belts use it in quality improvement projects to probe probabilities. You can also use it in manufacturing environments to detect the probability of errors. When using Bayes Theorem, your probabilities are the probability of a positive result, the prior probability of the problem, the probability of a positive result with the problem and without it, plus the probability of the problem with a good result.

     

    • Benchmarking. 

      Benchmarking can be used by any Six Sigma practitioner to strategically improve systems by comparing your current system to an equivalent one. You may wish to compare the system used by a competitor, a company from another industry, or between divisions in your organization. Benchmarking improves critical systems that are not the primary focus of the company. For example, a manufacturing industry may wish to use benchmarking to enhance its distribution system.

     

    • Box and Whisker Plots.

      Six Sigma practitioners use box and whisker plots to display small data sets, depending on their relevance to the project. You can create a box and whisker plot by plotting your first and third quartile onto a graph, with each quartile represented by the width sides of a rectangle. The length sides represent your interquartile range, while a vertical line through the middle represents your median. The whiskers are horizontal lines that extend to the largest and smallest data values, but only those that are not outliers. Your outliers are plotted using an asterisk. Outliers are usually more than 1.5 times the interquartile range above your third quartile, but below the first. You can use box and whisker plots in process improvement projects.

     

    C

    • Calibration Standard.

      Your calibration standard should be used in measurement systems to calibrate your measuring devices for Six Sigma projects. Calibration standard refers to a point of known accuracy that you can trace according to the national standard. In the US, the National Institute of Standards and Technology provides the standard on which to base your work.

     

    • Cause and Effect Diagram.

      The Cause and Effect diagram is also known as an Ishikawa diagram or a fishbone diagram. Six Sigma Belts use it to represent and categorize information about a problem. The diagram resembles a fish skeleton, with a central line (the spine) representing a problem, usually a production issue. Additional lines branch off the problem line, creating categories for methods, personnel, materials, and equipment. Each additional line then branches off to narrow down the potential causes. You use Cause and Effect diagrams in process improvement and root cause analysis to determine the source of an issue. Once you have found the cause, you can correct the issue and put preventative measures into place.

     

    • Central Limit Theorem.

      Six Sigma project leaders use CLT, or central limit theorem,  in statistical process control. CLT relies on how well data conforms to normal distribution, stating how even if a process is non-conforming, the sample means taken will still be normal. In other words, the larger the sample you work with, the greater the tendency for conformity. You use CLT by taking many samples and calculating the means of each one. When represented in a graph, the data should display a different shape for each population formed by each sample mean.

     

     

     

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