Question

1. Why is using a single ANOVA preferable to running a series of independent t tests?

2 Determine the null and alternate hypotheses for the following statement:

People will eat more when their food is served on red plates than when it is served on blue or beige plates.

Answer 1

Answer(1):

For any hypothesis testing we may commit a type-I error with probability α which is also known as level of significance. If we conduct a independent t-test for comparison of each pair of treatments, there is 5% chance that we are making mistake in each t-test. Now, for example let’s say we conduct 3 independent t-test, there will be almost 15% chance of making type-I error which is not acceptable in research problems.

An ANOVA can control these errors because here we use only one time hypothesis testing to compare the several means and we can determine if all the means are equal or not with only 5% chance of committing a type-I error.

In ANOVA we can be more confident about our statistical results as the error remains on 5% while on running a series of independent t-test, the error increases manifolds. Due to this reason a single ANOVA is preferable to running a series of independent t tests.

Answer(2): The null and alternative hypothesis for given statement is as below:

H₀: food eaten by people on red plate is same as food eaten by people on blue or beige plates i.e. µ_red=µ_blue

H₁: food eaten by people on red plate is more than the food eaten by people on blue or beige plates i.e. µ_red>µ_blue