Parameters Hypothesis Testing

In the Analyze stage of a Six Sigma DMAIC project, Hypothesis Testing is done to statistically validate if our alternate assumption is correct or null hypothesis is correct. Alternate hypothesis involves statistically validating if there is difference between the population data and the target or there is difference between the parameters of two or more population data. On the other hand, Null Hypothesis involves statistically proving that no such difference exists. Lots of statistical tests are used to perform hypothesis tests using various parameters such as mean, median, variance, proportion etc as the basis. Practically speaking, it helps a Six Sigma professional to decide the direction in which he has to focus his energy in order to improve the target(y).

Parameters Hypothesis Testing

There are various parameters to test this, namely:
• Mean
• Median
• Variance
• Proportion
• Regression
• Chi Square

Mean base tests
Mean is the ideal form of performing hypothesis testing as it represents the average of the sample data, based on which we can predict the Confidence Interval of the population data. But one of its most important pre-requisite is that data should be normal and there is a centering issue. Its most important weakness is that it can be affected by the presence of outliers.

Median based tests
Median is another form of centering which is used for hypothesis testing. It represents a powerful way for statistically validating as Median represents 50th percentile of the sample data which leads to the formulation of Confidence Interval of population data. Median based tests are used when data is not normal and there is a centering issue.

Variance base test
Variance based tests are used when there is variation issue in the data. Even if the process is performing within the prescribed limits, technically it seems to be under control but practically it is not. It is very difficult to make predictions about the future performance as the process is performing all over the place due to variation.

Proportion base test
Proportion based tests are used to check the proportion of the data which is performing as per the expectations. A proportion of sample data is taken to check this and based on this, Confidence Interval of the whole population is formulated. Proportion is the best parameter to check if the data to be checked is categorical, preferably binary data.

Regression base test
Regression is a very powerful way of performing hypothesis testing. It analyzes and mathematically validates the relationship between two or more variables and clearly shows the magnitude of impact that one or more factors are having on the target(y). It helps in the statistical validation of assumption and helps in deciding which factor(x) is having the maximum impact on y.

Chi Square
Chi Square tests represent another powerful way of performing hypothesis testing. They are used to compare the observed values of a factor with its expected values