Question

Discussion post

Not all distributions are normally distributed. Statisticians have developed methods to allow us to solve for non-normally distributed data and also at the nominal level of measurement!

In our study of Statistical Quality Control we have become familiar with control charts for variables and attribute control charts.
Use this discussion posting to give a personal/work related scenario on either how a chi-square goodness of fit test can be employed or select a control chart and give an example of how this statistical tool will be beneficial in your current or future line of work.

Answer 1

χ2 test of goodness of fit:

A chi-square goodness of fit test is a hypothesis test used to determine if the sample data are consistent with a hypothesized or pre-decided distribution. The test is valid only under the assumption of simple random sampling, with the size of the population at least 10 times as large as the sample.

While an independent t- test is used to determine if a sample statistic (say mean) differs considerably from a hypothesized population parameter or to examine if two populations have significantly different parameters, the χ2 goodness of fit test is used to compare a given distribution with a hypothesized one.

As an example from real life, suppose that my friend, who is a ready-made clothes distributor is required to deliver a large quantity of sweaters to a foreign consignment in India. The dealer has ordered 47% sweaters to be white, 33% black, and 20% green. A random sample of 300 sweaters was selected by an inspector and 150 white, 85 black, and 65 green sweaters were counted. The test of goodness of fit can be used to determine if the consignment delivered was as per the order or whether it deviated considerably from the order.