Week 5 Discussion

Goodness-Of-Fit Tests

Download: Video Transcript (PDF 156.38KB) (media/transcripts/SU_W5L1.pdf?

_&d2lSessionVal=413TjsBLZG4ot5goGhUoGZTkm&ou=84108)

Goodness-Of-Fit tests are considered to be tests that allow for the analysis of categorical data. For example, are all of the soft drinks of a

particular beverage company equally likely to sell? One key observation here is that we are no longer limited to comparing two values to

one another. Rather we can now look at a collection of statistics simultaneously. In the soft drinks example, if 500 people were to

02:19



purchase one of �ve soft drinks, we might hypothesize that there is no difference in the number of people who will order particular soft

drinks. With this logic, we would expect approximately 100 people to order each of the �ve available soft drinks.

If 375 people order the same soft drink, 75 more order the second soft drink, and the other 50 people are divided among the remaining

three soft drinks, we would probably suspect that the number of people purchasing each soft drink would not be the same for each soft drink. However, how do we statistically determine this to be the case? In other words, how do we prove (statistically) that the rate at

which soft drinks are purchased is not the same for all of the �ve beverages?

While the data given in the preceding paragraph makes it seem fairly obvious that there are differences in the rates at which the soft

drinks are purchased, what if each of the �ve soft drinks was purchased by somewhere between 80 and 120 people (out of the 500 that

we are considering)? Would we still be able to conclude that there were differences in the numbers of people who ordered the particular

soft drinks? Goodness-Of-Fit tests allow us to draw statistically valid conclusions about such questions.

Goodness-Of-Fit tests are an example of nonparametric tests, which are tests that do not require the data to follow a distribution with

which we have experience working (like the normal, binomial, Poisson, Student's t, etc.) These methods are particularly use for working

with data that are classi�ed or categorized in some way.