# Comparing Proportions

Comparing proportions is the statistical method to find out if one proportion is truly different from another. This comparison of proportion from two or more samples is carried out by implementing the chi-square statistics. The comparison is made by contrasting the experimental proportions to the proportion which are estimated to find out whether there are any variations between the samples. If the experimental result is larger than the estimated result, it is said that there is a considerable difference in the sample proportions.

In six sigma, we often find that there are a number of cases in point when the analyst wants to make a comparison between the proportions of items that are distributed among several categories. The things might include operators, techniques, and materials or may be some other alliance of interest. Among the groups, a sample is chosen which is evaluated and placed into one of a number of categories, viz high class, marginal quality, refuse quality. The outcome of this can be presented as a statistical table with rows showing the number of groups of interest and there are columns that are showing the categories. Such tables can be described as an answer to the question if the groups may vary with regards to the quantity or proportion of items in the categories.

Chi-square test is implemented with the sole intention to compare the frequencies or the proportions of various groups. This sort of test is undertaken in order to find out the difference in proportions. It also acts as a means to verify the frequency of the real happenings against the frequency of the expected occurrences to help decide whether any important change has taken place. The chi-square test evaluates the grouping or lack of independence in a two way categorization of the other variable.

The formula for Chi-Square is the summation of the squared distinction between the real and estimated data which is then divided by the estimated data. Some important rules for using Chi-square formula are as follows. It is crucial to keep in mind two important rules while making use of Chi-Square formula. These are as follows:

**•** Chi-Square has to be calculated by using only arithmetical values and not by using percentage or ratios.

**•** Chi-Square should not be calculated in the situation when the estimated value is less than 5 in any category.

**Few Examples of Chi-Square Tests:**

Chi-square test plays an essential part in statistical analysis. Some of the most general examples of chi-squared tests used in statistical analysis are as follows:

**•** Pearson’s chi-square test

**•** Mantel-Haenszel chi-square test

**•** Yates chi-square test

**•** Linear-by-Linear grouping chi-square test

**•** Sample variance test.

Pearson’s chi-square test is also regarded as Goodness-of-Fit test or Test for Independence. This was first introduced by Karl Pearson. The test is one of the most extensively used chi-square method.

Chi-square is one of the major tools of six sigma. Chi-square test is a statistical test used in the methodology of six sigma. Within the range of Chi-square test, analysis of three types is included. These are:

**•** Goodness of Fit

**•** Homogeneity Test

**•** Independence Test

The Test of ‘Goodness of Fit’ finds out that if a sample for investigation was taken into account out of population which may pursue a particular distribution. The 2nd analysis, the Homogeneity Test, is undertaken to establish the statement saying that there are a number of homogeneous populations in accordance with some common characteristics. The ultimate analysis proves that the Independence Test is there to look at the null hypothesis asking the two standards of classification are independent when it is applicable to subject’s population. If they are dependent and having connection in between them, chi-square test is the right and most accepted method of dissimilar data hypothesis testing.

**Synopsis of the Chi -Square Test**

Chi Square tests, and contingency tables, are the two responsible tests that are entitled to answer several questions in relation to six sigma methodology. Furthermore, it is implemented to verify whether counts, or size, are consistent with some particular distribution of population or not.

**Following are some of the frequently asked questions:**

**• **Whether the mass who have seen an advertisement, are interested to acquire a product or not?

**•** If the people of a particular type are in a group or not?

**•** Last of all, in the above examples, whether the tests would find out the distinctions could be analyzed, or whether they show that the factor that was considered influenced the result?

Chi-square test depends upon mathematical assessment of the number of experimental counts against the estimated number of counts to find out if there is a difference in the productivity counts derived from the input category. The hypothesis is made as follows:

**H0 **– the sample match with the particular distribution

**H1** – the sample does not match with the distribution

Test of proportion is used to work out the difference in two groups of “BINOMIAL” data whereas T- test is carried out on “VARIABLE” data set to measure the variations between two sets of data.