# Contingency Table

Contingency tables are used in the application of the chi-square test that is implemented to evaluate the connection between two variables. This table provides an effective way of arranging attribute data while permitting us to eagerly find out relative probabilities. To quote an example, contingency tables can be made to use in place of the fraction out of the ordinary control chart to analyze a group of preliminary samples for not having enough of control.

When some items are grouped on the basis of two or greater than two criteria, it’s always hard to decide if these criteria functions independently of each another. Thus, a diagram is drawn to put together the test results into many groups in order that when calculating the comparison between them, one can easily find out if there is a difference in the grouping for any given level of confidence.

It is obligatory to establish a baseline measurement as a point of reference to give a support to the given confidence level.

Let us suppose, if we want to sort defects discovered in biscuits manufactured in its plant; first, as per the defect category and, second, as per the shift of production during the production of biscuits is carrying on. If the extent of the diverse range of defects is found to be stable from shift to shift, the categorization following defects is free of the categorization. Conversely, if the extent of the diverse range of defects found different from shift to shift, the categorization following defects is dependent on the shift categorization and classifications are reliant.

In the system to evaluate whether a mode of categorization is dependent on another, it’s expected to view the information by employing a cross categorization in the face which may consist of ‘r’ no. of rows and ‘c’ no. of columns (where r and c are numbers) and can be defined as contingency table. An analysis into the test of independence is put to determine whether the two variables are in a contingency table, or are autonomous of each other when a couple of examination is performed.

The Objective of Contingency Tables:

• It aims to identify the merits of using contingency tables in finding out statistical significance.
• This table is used to recognize examples of contingency tables that are properly constructed.
• Contingency table is used to determine statistical significance.

As contingency tables are an application of Chi-Square test, so, it is essential to have a clear idea about it. A careful analysis of this material could impact how you think about Chi-Square test. This test is most commonly implemented to determine what results are found out by making comparison between given data and the expected data. This test is taken to establish that there will be no change or difference between actual and expected data. The Chi-Square formula is the result of the four-way difference between the definite and predictable data, divided by the predictable data.

A thorough study into the subject of Chi-Square test is quite important. It is one of the major six sigma tools. This is a statistical test generally used in six sigma methodology. There are three different types of analyses included in this test.

These are:

• Goodness of fit
• Homogeneity test
• Test of independence.

Summary of the Chi- Square Test:
Chi Square tests, and contingency tables, are the in charge of responding different queries connected with six sigma methodology. Further, the test is undertaken to examine whether counts, or extent, are constant with some precise distribution of population or not. The questions that are frequently asked are as follows:

• People who see the advertisement are probable to purchase a product or not.
• Whether the people who belong to a particular type under, or over symbolized may belong to a group or not
• Finally, in the above two examples, the tests would find out if the dissimilarities could be described coincidentally, or if the show that the factor that was investigated would affect the result.

The Chi-Square 'Goodness of Fit' examination is used to check, if a sample is represented from a group of population that match with a specified distribution or not. Therefore, the proposition is made in the following manner:

H0 the sample match with the precise distribution
H1 the sample does not match with the distribution

It is of vital importance to follow up two major rules while using Chi-Square formula. They are:

• Chi-Square is needed to be calculated using only numerical values & not percentage or ratios.
• Chi-Square should not be planned if the probable value in any category is less than 5.

There are some of the most common examples of chi-squared tests which are most commonly implemented in Statistical analysis. These are:

• Pearson's chi-square test
• Yates chi-square test
• Mantel-Haenszel chi-square test
• Linear-by-Linear association chi-square test
• Sample variance test.

Pearson's test is regarded as Goodness-of-Fit test or Test for Independence. This test was first developed by Karl Pearson. This is one of the most frequently used chi-square method.

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