Q 584 -

1 - Variance Test is a lesser-known statistical test. Explain its utility with some examples.

 

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1 Variance Test

 

In General, Chi -Square test is called 1 variance test.

This test is used to basically compare the variation of a sample which is also known as population.

It is also used to test hypothesis about the population variance, and this is usually based on the sample which is drawn from normally distributed population.

This is also used find out if a that if a variance of single sample is significantly different from a particular value which is generally known as hypothesized variance. This is a non-parametric test.

 

It has two hypotheses:

·       Null Hypothesis (Ho)

·       Alternative Hypothesis (Ha)

 

The Chi-square test is very useful in various scenario:

·       Quality Control – Lets assume a manufacturing company wants to make sure that the variance of a specific product remains within specific limits. So, company can collect a sample of available products and can test of variance.

·       Environmental Studies – If scientists want to check air and water quality in weather condition and pollutant concentration in a specific region. So, they can use variance test.

·       Psychological Studies – Researcher might want to check the anxiety level in any patient.

 

1 variance test is used to compare variance of sample to a known population, with the assumption that sample is drawn from a normally distributed population. This analyses the difference between an observed process std deviation and a specified std deviation. It determines whether the population variance differs from hypothesized value specified in the test

 

Example 1:

Let us take a Timber company ships its high quality products through sea to high priced markets of European countries.

The quality analyst at the receiving country wants to determine whether the variance of the moisture content in the shipment

Has increased from that of the specified value. If the variance is greater than maximum acceptable variance , analyst uses the confidence interval to determine how is the difference and whether this difference  has practical significance.   

A test of single variance can be left tailed or Right tailed. Here in this case Let us assume if the moisture content variance specified is 0.1 gm/cc, it means our Null hypothesis is the population variance = specified variance and Alternate hypothesis is that population variance should be less than specified .

Here the word “Less” indicates that it is left tailed test.

 

Example 2:

If the doctor wants to know the variation of Diastolic (low) Blood pressure levels in patients is more than 60mm /hg.

In this case the word “more” indicates that it is right tailed test.

 

The following Data considerations need to be satisfied when applying the chi – square test:

1> The sample must be randomly drawn from the population

2>The data needs to be ensured for normal distribution

3> Each observation should be independent from all other observations.

 

How to derive the Test statistic for 1 variance? is given below:

 

 

The question mentions that the 1-Variance Test is a lesser-known statistical tool. 

 

Some of the answers that have not been approved are because they explained two variance tests and their variations. 

 

From the published answers, Venkateswaran Kazhagamani's answer has been selected as the winner for giving relevant examples.