The organizer of the seafood festival is hosting a clam chowder competition with the following conditions:
– There are twelve restaurants that are participating in this contest.
– As per the rules of the contest, each participant has to list all of its ingredients.
– The judge tastes the clam chowders and gives a rating on a scale of 1 to 10 on a notecard.
– Twenty-five note cards are selected by the organizer on a random basis.
– The organizer thinks that there is a relationship between the judge’s rating points given to each contestant and the number of ingredients used by the contest in making their respective clam chowders.
Which of the following statistical tests is the best option to determine above given relationship?
– Checking independence using the chi-square method
– Checking the difference of means using the 2-sample t-test
– Checking the proportion difference using the 2-sample z-test
– Checking the slope using the t-test of linear regression
– Checking the mean difference using the t-test of matched pairs
The aim of this question is to understand the above-given tests and identify which tests are most suitable for the given condition.
A chi-squared test is used to see if two clusters of data within a given population are statistically related or independent. A 2-sample t-test is used for checking the difference between the means of two clusters in a population. A 2-sample z-test uses the means of two clusters to see if they belong to the same population or not. A 1-sample t-test is used for checking whether the slope of the given data after regression/fitting is zero or not. A paired t-test is used to see if the mean difference between two clusters is the same or not.
Expert Answer
Based on the situation given, we can conclude that the organizer wishes to find whether the two given parameters are related or not. So based on the application areas described in the above paragraphs against each test type out of the given options, one can conclude that the chi-squared test of independence is the most suitable statistical test for this condition.
Numerical Result
A chi-squared test should be used.
Example
For the same scenario given above, let’s assume that the chi-squared test is positive and there exists a relationship between the ingredients of the clam chowders and the judge’s ratings. How can the organizer model this relationship?
To model the relationship between these two parameters, the organizer will have to perform a regression analysis. It can be a linear regression or a multi-variable regression depending on the fitting accuracy. However, he may have to perform some additional tests such as the 1-sample t-test described above.