How do we interpret the significance level and p-value under the concept of null hypothesis?

 

Significance level and P-value are related to the Type I error of Hypothesis testing, hence lets go back to basics.

Hypothesis testing is used to statistically validate a theory defined for a sample or among multiple samples. Unlike common belief, hypothesis testing does not help the researcher to choose between two options but researcher will always stick to null hypothesis unless there is significant evidence that alternate hypothesis is true.

Null Hypothesis (H0) is general ‘no effect’ hypothesis

Alternate Hypothesis (H1) is the condition that researcher is trying to prove right.

In hypothesis testing, there are two possible errors

1. Type I error: Rejecting null hypothesis when it is true.

For example, we are trying to validate if Average handling time (AHT) has improved post conducting refresher training.

Null Hypothesis: Refresh training has no effect on (AHT)

Alternate Hypothesis: AHT has improved post conducting refresher training.

Here, If a researcher is making type I error, s/he is acting assuming there is an effect. In our AHT example, company will start investing more on conducting refresher trainings assuming it will improve AHT.

Hence this error also referred as Producer’s risk.

The chances of making Type I error is denoted using α (alpha) symbol, which is the level of significance set for the hypothesis testing.

If α is 0.05, this means researcher is willing to accept 5% chances that s/he is wrong in rejecting the null hypothesis.

Statistical analysis generates a probability denoted as ‘p-value’ which refers the likelihood of rejecting the null hypothesis when it is correct.

Hence if the p-value is greater than α, we fail to reject null hypothesis considering that is the safest option for producer and we do not have enough evidence to prove that alternate theory is correct.

Now since we are taking about errors, let me complete article by adding bit explanation of Type II error as well.

2. Type II error: Failing to reject the null hypothesis when it is false.

Type II error is Consumer’s risk because even though there was an effect, the producer did not act on it hence the consumer did not get the better results.

The probability of making type II error is referred as β(Beta). The power of the test is in giving the correct result, i.e., accepting alternate hypothesis when null is false because that was the whole objective of conducting a hypothesis test. Hence the power of the test is referred using (1-β).

How do we interpret the significance level and p-value under the concept of null hypothesis?

What is Sigma Level and how to calculate it?

Sigma Level

Sigma level indicates the compliance rate of the process i.e. how effective process in avoiding defect or in other words is meeting client’s expectation. It is considered to be the positive way of representing the process capability

Short Term Sigma Level (Zst)

Short term sigma level is calculated using within standard deviation of the process. Zst represents the potential capability of the process i.e. how the process will perform if all short term variations are constant which is an ideal scenario.

Long Term Sigma Level (Zst)

Long term sigma level is calculated using the overall process standard deviation, hence representing the actual capability of the process. It is considered that over the period because of natural variation the short term sigma level is shifted by 1.5σ. Thus ZLT can also be calculated as

Sigma level can be calculated for both attribute data as well as continuous data.

Sigma Level for Attribute data

The sigma level for discrete data is calculated using DPU and DPMO.

The standard normal distribution (Z-distribution) is the tool referred to calculate the sigma level using DPMO.

Sigma Level

At 6σ level, the process is expected to make only 3.4 defects per million opportunities.

To calculate sigma level in Minitab, calculate compliance rate:

In Minitab, go to Calc -> Probability Distribution -> Normal, as we use standard normal distribution to calculate sigma level

Now, select ‘Inverse cumulative probability’ and updated compliance rate in ‘Input Constant.’ The ‘x’ value in the session window is the short term sigma level of the process if short-term attribute data is collected.

Sigma Level for Continuous data

Sigma level for continuous data is represented as the number of standard deviations (σ) can fit between the Mean and closest specification limit (SL). If Zst is six, that means six standard deviations (σ) can be accommodated between mean and SL. Higher Zst means lower the variation hence lower the DPMOs.

What is the difference between Lean Six Sigma and Six Sigma only?

What is the difference between Lean Six Sigma and Six Sigma only? by Shweta Ravi

Six Sigma is a data-driven methodology first introduced in the 1970s. Dr. Mikel Harry, the senior staff at Motorola, was first one to try statistical problem-solving. Later on Bill Smith, an engineer at Motorola designed six-step methodology to reduce variation and considered as the father of Six Sigma. Jack Welch then made it the center of business strategy at General Electrical. In today’s competitive world, Six Sigma has widely accepted as a philosophy for growth across different sectors.

Six Sigma is based on data analysis, hence helps in reducing risk which one of the many reasons that Six Sigma is still preferred over other improvement methodologies. The objective is to remove defects at the source and bring down performance to ‘six sigma’ level i.e. 3.4 defects for every one million opportunities. Continuous effort is made to achieve stable and predictable process.

Even before Six Sigma in 1930 in Japan, the owner of Toyota motors, Kiichiro Toyoda, asked Taiichi Ohno (Industrial Engineer) to look into Henry Ford, flow production model. This journey resulted in the introduction of Toyota Production System, which then became the foundation of ‘Lean Methodology,’ focused on reducing waste in the process.

In early 2000, the first concept of Lean Six Sigma introduced, which combines both the methodology to reduce waste and variation in the process.

Edward Deming has consolidated Six Sigma methodology in five step model widely known as DMAIC, (Define, Measure, Analysis, Improve, and Control), which continued for Lean Six Sigma as well. The objective of each step is now achieved using both statistical and lean methods.

What is the difference between Lean Six Sigma and Six Sigma only?