Why the null hypothesis (Ho) should never be ‘accepted’?

People may have some level of difficulty in making inferences using hypothesis testing.

Let me put forth a common mistake that we do while making conclusions.

We know that when the p-value is less than the level of significance (α), we reject the null hypothesis. Commonly we take α as 0.05. So when p< 0.05, we reject the null hypothesis.

But, when the p> 0.05 we can not reject the null hypothesis.

At this point, many of us tend to say that ‘we accept the null hypothesis‘ and this statement is not correct.


We make conclusions about the population based on a random chance that could say that Ho is true. But this random chance is at the chosen level of α. There is a possibility that some other randomly chosen sample gives a different conclusion at a different level of significance.

Thus, when p> α, we fail to reject Ho

When p is greater than α we should write the results in neutral language. For example,

Ho: Machine 1 is producing spindles with average length of 30 cm

Ha: Machine 1 is not producing spindles with average length of 30 cm

If p< 0.05, At the significance level of 0.05, we reject the null hypothesis that machine 1 is producing spindles with an average length of 30 cm. This also means that we accept (and not prove) the alternate hypothesis,  a nice explanation can be found here for this case.

When p> 0.05, at the significance level of 0.05, we can not reject the null hypothesis that machine 1 is producing spindles with an average length of 30 cm.

This simply means that at a significance level of 0.05, we can not conclude whether the machine is producing an average length of 30 cm or not.

So, we should always keep in mind that when we are not able to reject the null hypothesis, we should not conclude in any other way but in a neutral manner.

Do share in comments, your experience and other mistakes that you may have once committed/ witnessed.

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Sampling Basics

There are certain vital techniques which must be understood well if we want to understand the subject of statistics and measurements. Sampling is one such very important topic, which we’ll be covering in a couple of articles.

Some terminologies first…

To understand the concept, we should also understand a few frequent terms.

  • Element– an object on which a measurement is taken
  • Population– a collection of elements about which we wish to make an inference
  • Sampling units non-overlapping collections of elements from the population that cover the entire population
  • Sampling frame– a list of sampling units
  • Sample- a collection of sampling units drawn from a sampling frame
  • Parameter: numerical characteristic of a population
  • Statistic: numerical characteristic of a sample

What is Sampling?

The activity in which elements, from a population, are collected so as to represent the population. In this video, a very good introduction to sampling has been provided.

Why Sampling?

Most of the times, the population is too large to measure all of its elements, thus sampling is done. A sample reflects the characteristics of the population from which it is drawn. For example, a machine produces 1000 spindles a day. It may be difficult to measure all of them, so we take samples and measure them.

It is very crucial that samples are selected carefully. Incorrect sampling may lead to incorrect inferences about the population.

Sampling has many advantages over exhaustive sampling, which covers the whole population.

  • Sampling can save money
  • Sampling can save time
  • In case of destructive inspection, it is not prudent to do exhaustive sampling

In our next article, we’ll learn about the common sampling techniques.

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What is Six sigma?

If as a beginner in Six Sigma journey you are confused about exactly what is Six Sigma, you have come to the right place!

Six Sigma is a tool, methodology, a metric, a measure, a benchmark, a goal, a philosophy and a statistical term.

Let us see, how does ‘Six sigma’ fit into all these roles?

As a statistical term: 6σ is a statistical term in which σ is a Greek letter which denotes standard deviation. Standard deviation represents the variation of the process or the process spread around mean. A Six sigma process is a process in which the 6 standard deviations above or below mean are within the nearest specification limits.


In the above figure, the orange curve has high spread, i.e. high standard deviation; while the blue curve has lower standard deviation as compared to the orange one. In general terms, we can say process having blue curve is better since it is more clustered around the mean.

Let’s also consider the two vertical black lines now, which are the upper and lower specification limits. In this case, the blue curve is well within the specification limits. If we also assume that the 6σ spread above and below the mean are within these specification limits, the blue process is a Six Sigma process. In a six sigma process, there is a scope of 1.5σ shift towards upper/ lower specification limit.

As a Tool: 6σ is a set of existing tools used for business performance improvements, to design new processes & products, improve existing processes & product.

As a Methodology: 6σ comprises of methodologies like DMAIC, DMADV, DFSS etc. The most common methodology used for improving existing processes/ products is DMAIC, which stands for five phases of a 6σ project, Define, Measure, Analyse, Improve & Control.

As a Measure: We use Sigma Level as a measure to state the capability of the process. As soon the sigma level increases (which means that more of the process spread squeezes between specification limits) the probability of getting defects decreases. A 6σ process has a probability of getting only 3.4 defects per million opportunities.

As a Metric: There are various metrics which are used in a six sigma project and serve various purposes. Ex: Defects per unit (DPU), Defects per million opportunities (DPMO), Rolled Throughput Yield (RTY), First Time Yield (FTY) etc.

As a Benchmark: 6σ level companies are world-class benchmarks. Their processes are so effective and efficient that the cost of poor quality and probability of defects is very low.

As a Goal: An organisation can make a Goal to attain the 6σ level. Though reaching to this high level of sigma is considered very challenging than to attain 2 sigma level, where simply doing standardisation can help. As sigma level goal increases, the complexity increases and more sophisticated tools are required to attain such a high capability.

As a Philosophy: Six Sigma, if followed religiously, brings a cultural change. Like it has changed the DNA of GE — “it is now the way we work — in everything we do and in every product we design.”

In whatever form you understand Six sigma, adopting six sigma brings a cultural change across the organization, with use of some simple and some sophisticated tools, in a systematic and data-driven approach to bring out the continuous improvements.

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The three D’evils!

What is it that comes as the biggest challenge in the way of an organisation towards success?


There are, and can be, an infinite number of reasons. But the three D’s, or the three Devils, look to pose a serious threat for an organisation to succeed.

 1. Defects:


When the effort and money go in fixing things which should have been done ‘right first time’, it is definitely going to cost an organization way more than it can assess! With every defect in the delivered item, it is losing the faith of the customer and it is needless to mention that eventually, it’ll lose the business.

Even, if an item is not delivered yet, then also the employees are on fixing spree, which is consuming time as well as money that could be better spent serving customers and strengthening the bottom line.

2. Delays:


Just like defects impact business, delays are also not taken positively by the customers. Delays between the process steps cost time and money and can negatively impact  the productivity and profitability.

Within the organisation, delays may lead to frustration of the employees and when the delivery is impacted, it may frustrate the customer as well.

3. Deviation


When the product or services have small to the large difference in the output, the confidence of meeting customer specifications/ needs goes down.

Think of the scenario where you are going to tighten a nut…but the bolt is not of the right size. It is going to stop your work. There are parts which are just right, while sometimes we get some parts which are too big or too small to be used.

Deviations are the unwanted difference in the output of the same process. Some amount of deviation is inherent and can be lived with…but when the deviation is beyond certain agreed limits, called the specification limits, it starts causing the problem.


So, any organization, irrespective of their industry, must be cautious of the three Devils and always work in the direction to keep these away.