Six Sigma is an applied methodology for improving business and organizational performance. It is used for minimizing mistakes and maximizing value. Six Sigma takes effort and requires you to go through the discomfort of change. But soon the pain is transformed into improved performance, lower costs, more success, and happier customers.

• Six Sigma is a problem-solving methodology. It is the most effective problem-solving methodology available for improving and organizational performance.
• Six Sigma performance is the statistical term for a process that produces fewer than 3.4 defects (or errors) per million opportunities for defects.
• A Six Sigma improvement is when the key outcomes of a business or work process are improved dramatically, often by 70 percent or more.
• A Six Sigma deployment is the perspective rollout of the methodology across an organization, with assigned practices, roles, and procedures according to generally accepted standards.
• The Six Sigma toolset is the collection of methods and tools, including statistics and analytics, that Six Sigma practitioners use to consistently achieve breakthrough levels of improvement.

A specification is the value separating acceptable from unacceptable performance. To evaluate the appropriateness of any specification, the following should be considered:

• Reasonable: is the specification based on a realistic assessment of the customer's actual need? Does the specification relate directly to the performance of the characteristic?
• Understandable: is the specification clearly stated and defined so that no one can misinterpret it?
• Measurable: can you measure the characteristic's performance against the specification? If not, a lot of debate will ensue between you and your customer as to whether the specification has been met.
• Believable: Have you bought into the specification setting? Can you and your coworker peers strive to meet the specification?
• Attainable or achievable Can the level and range of the specification be reached?

Quality is on-target performance with as little variation as possible.

The Six Sigma DMAIC (Define, Measure, Analyze, Improve, Control) methodology can be thought of as a roadmap for problem solving and product/process improvement. A summary of DMAIC tools and links to examples is given below.

Prior knowledge of the tools and techniques is necessary in determining which tools are useful in each phase. Remember, the appropriate application of tools becomes more critical for effectiveness than correctness, and you don't need to use all the tools all the time.

The chart below show seven Statistical Analysis or methods in which you can study the data you have. Which method you choose will depend of the Data Type (Nominal or Interval/ratio), The Number of Samples ( 1, 2 or 1 sample with 2 measures) you have and the Purpose of your study. Open the imange below in a new tab and use the up and down arrows to view how these tests are categorized.

Other Statistical Analysis or Tests that are used in Business and other applications are listed below.

Test/Analysis	Application Area
t-test	A t-test allows us to compare the average values of two data sets, and determine if they came from the same population. A t-test is used to determine the difference between two sample means from two normally distributed populations with unknown variance. The graph below shows the different t-tests available and when to use them. The null hypothesis (Ho) always assume that there is no difference between the mean of the 2 data sets (mu=0) and the t-test should tell us whether this assumption should be rejected. The alternative hypothesis (Ha) is that there is a difference between the 2 means (mu≠0).
z-test	for something
KS-test	Kolmogorov-Smirnov Test is used in the
f-test	under construction

R Studio is a popular application that allow you to Upload, manipulate and Analyse data files. Imagine the file below exist. This file is going to be used to illustrate the different functions of R Studio.

• Type getwd() to display the current working directory of your project in the Console window. To change the current working directory go to Session > Set Working directory > Choose directory.
• To assign the content of the file "one.csv" to the variable "data" you may type: data <- read.csv ("one.csv").
• Type print(data) to print the content of the file in the Console window.
• Check that the structure of "one.csv" conform to R data frame requirements; Type is.data.frame(data), then the response TRUE should appear in the Console window.
• Type print(data$Name) the names Peter, James, John should be listed in the Console window.
• Type print(max(data$Salary)) the number 12000 should be listed in the Console window.
• Type d <- subset(data.Salary == 9500) then type print(d) the number 9500 should be listed in the Console window.

The following is a t-test performed in R Studio with the file shown below.

• Type help(t.test) or ?t.test to display helpful content to understand the this analysis tool.
• Type LungCapData <- read.table(file.choose(), header=T, sep="\t") to load the data into the LungCapData varible
• Type attach(LungCapData) for some reason.
• Type names(LungCapData) to list the column categories of the table.
• Type class(LungCap) to print the class of data type under LungCap: numeric.
• Type class(Smoke) to print the class of data type under Smoke: factor.
• Type levels(Smoke) to print the levels of data under Smoke: yes and no.
• Type boxplot(LungCap ~ Smoke) to print a box plot of the relationship between Lung Capacity and Smoking.
• Type a comment starting with # saying the null hypothesis (Ho) the one the analyst support, is the the mean lung capacity of smokers and non-smokers is the same.
• Type t.test(LungCap~Smoke, mu=0, alt="two.sided", conf=0.95, var. eq=F, paired=F) to create the t-test
• Type the alternative command t.test(LungCap~Smoke) to create the t-test, all the other varibles are in default setting.
• Type the alternative command t.test(LungCap[Smoke=="no"], LungCap[Smoke=="yes"]) to create the t-test.
• Check out the variance of each group to decide whether "var. eq" ir TRUE or False: Type var(LungCap[Smoke=="yes"]) and var(LungCap[Smoke=="no"]) then compare the values.
• Very small p-values (e.g. 0.00034) indicate that the null hypothesis (Ho) must be rejected.