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To undertake hypothesis testing it is necessary to go through these following stages:

1. Decide on the null hypothesis, H0.
2. Decide on the alternate hypothesis, H1.
3. Decide on the significance level.
4. Calculate the appropriate test statistic, using the sample data.
5. Calculate the p-value.
6. Compare the p-value with the significance level, and decide whether to reject or accept the null hypothesis, H0.

The null hypothesis is a statement about the population value that will be tested - “no change” statement. The alternative hypothesis is the hypothesis that includes all population values not covered by the null hypothesis - “some change” statement

There are several different types of hypothesis tests. Specifically, this post concentrates on the one sample t-test.

What is a one sample t test?
The one sample t-test is used to test the null hypothesis that the mean of the population from which the data sample is drawn is equal to a hypothesized value.

Hypotheses:

• Null: There is no significant difference between the sample mean and the population mean.
• Alternate: There is a significant difference between the sample mean and the population mean.

Assumptions
Before running a one sample t-test you need to establish if the data violates any assumptions by using these tests. Generally, the test assumes that the sample values are independent and are all identically normally distributed (same mean and variance). If your data do not come from a normal distribution:

• transform the values to make the distribution more normal
• use a nonparametric test instead, for example, a one-sample sign test. This is potentially the best option if the distribution is highly skewed
• use the t test anyway, knowing that the t test still works well if the underlying distribution
  is symmetric, unimodal, and continuous.

A fuller description of the possible alternatives can be found here.

One of the advantages of the t-test is that it can be applied to a relatively small number of cases. It was specifically designed to evaluate statistical differences for samples of 30 or less. However, although the assumption of normality is not too important with large samples, it is important with small sample sizes, for example less than 10.

You also need to be aware that statistically significant does not mean the same as practically significant.

Minitab
To run a one sample t-test for a hypothesis concerning a single mean in Minitab:

Stats -> Basic Statistics -> 1 sample t -> Variables (enter data columns)-> Check “Test of Mean” (enter value in the box).

Minitab will respond with Test of mu = (value you entered) vs mu not = (value you entered). Below this will be printed the N, mean, standard deviation, standard error, T statistic, and P value.

This link takes you to the Minitab training material for a one-sample t-test. Alternatively, this or this provide a nice summary. If you don’t have Minitab use this site.

P-value
P is the probability that the mean for the data equals the value you were comparing it to. The Prism site has a great summary about how to think about results from the one-sample t test.

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We must understand variation.

- W. Edwards Deming

Image via Wikipedia

Wikipedia says that:

Multivariate analysis (MVA) is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time. In design and analysis, the technique is used to perform trade studies across multiple dimensions while taking into account the effects of all variables on the responses of interest.

So multi-vari analysis is a technique for viewing multiple sources of process variation. Different sources of variation are categorized into families of related causes and quantified to reveal the largest causes. Instead of telling you just that shift is a factor and machine is a factor, multi-vari analysis provides a breakdown for you to say, for example, that machine B on shift 1 is causing the most variation. It won’t quantify the variation…just show you where it is. Once you’ve narrowed your list of inputs, you know where to go take more data, do more training, plan further studies, etc. Pareto analysis won’t get you to that level of detail.

Multi-Vari is the perfect tool to determine where the variability is coming from in your process (lot-to-lot, shift-to-shift, machine-to-machine, etc.), because it does not require to manipulate the independent variables (or process parameters) as you would with design of experiments.

Because it provides a great way of analysing the effects of multiple factors multi-vari analysis is widely used in six sigma projects.

You can display the effect of categorical type inputs on a response on a multi-vari chart. It is one of the tools used to reduce the trivial many inputs to the vital few. In other words it is used to identify possible Xs or families of variation, such as variation within a subgroup, between subgroups, or over time.

Although simple in nature, such a chart has considerable power. It can help you isolate the major (dominant) family of variation. For example, does most of the variation in downtime occur within-machine, machine-to-machine, within-operator, operator-to-operator, within shift, shift-to-shift, within-location, or location-to-location?

Once you have determined where the major source of variability is coming from, then you can target more efficiently your experimental designs (DOE) to reduce that particular source of variation.

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Dr. W Edwards Deming was an advocate of achieving Quality through Process Management. He has described the adverse effects of tampering with a stable process in his book titled ‘Out of the Crisis’. He demonstrated through the famous Funnel Experiment how adjustment of a stable process can lead to an increase in process variation.

Symphony Technologies have hosted a Deming’s Funnel Simulator on their web site. The Simulator is free to use.

The Deming’s Funnel Simulator simulates the four rules of adjustment described by Deming. In addition it also calculates the process variation associated with each. The simulator is strong in graphics and explains the four types of process adjustments in details.

It can be used by trainers to train others in the Principles of Variation and Process Management. It can be used by students to explore Deming’s principles of process adjustment and overadjustment.

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