The chi-square (χ2) distribution is a probability distribution resulting from the sum of the squares of standard normal variables. It is used in hypothesis testing, specifically to assess goodness of fit, independence, and homogeneity of population variances. A chi-square distribution’s degrees of freedom indicate the number of independent observations used to calculate it.
You can use the following formula to calculate the chi-square distribution:
χ2 = ÎŁ(Oi – Ei)^2/Ei
where Oi denotes the observed frequency of an event, Ei denotes the expected frequency of an event and is the total number of events.
In manufacturing and service process improvement projects, the chi-square distribution is used to determine if observed and expected frequencies in a process differ significantly. Assume a manufacturer produces a batch of 100 items and wants to know if the number of defects differs between two production runs. They can collect data on the number of defects in each run and use a chi-square test to see if there is a significant difference between the observed and expected defect frequencies. If the calculated chi-square value is greater than the critical value for the desired significance level, the manufacturer can conclude that the two production runs differ significantly and take corrective action to improve the process.
In conclusion, the chi-square distribution is an effective tool for determining the statistical significance of differences between observed and expected frequencies in manufacturing and service process improvement projects.
The variance of a chi-square distribution with 5 degrees of freedom equals twice the number of degrees of freedom, which in this case is 10. (variance = 2 x df)
