Question

Each student in a statistics class had a randomly assigned bag of candies and counted the number of each color​ (Blue, Red,​ Orange, Green,​ Brown, Yellow). The bags were all the same size. The investigators claimed to use a randomized block​ design, with Bag as the blocking factor. They counted the number of candies of each color in each bag. Their results are reproduced in the given ANOVA output. Complete parts (a) through (c).

Source Degrees Sum of Mean F-ratio P-value
of Freedom Squares Square
Bag 13 4.726 0.364 0.10 1.000
Color 6 350.679 70.136 18.72 <0.001
Error 65 243.488 3.746
Total 83 598.893

(a) Was this an observational or experimental study?
(b) What was the treatment? What factors were manipulated?

A. The factors were color and bag and the treatments were all possible combinations of those two factors.
B. The factors were bag and student and the treatments were all possible combinations of those two factors.
C. The factors were color and student and the treatments were all possible combinations of those two factors
D. There is no treatment. No factors were manipulated.

(c) What was the response variable?

Answer 1

Explanation:

Hello!

a)

An observational study is one where the investigator has no control or intervenes on it. He just defines the variable of interest and merely collects and documents the information. These types of studies are usually made as precursors to a more formal experimental study, to have an idea of what's to be expected from the population.

An experimental study or experiment is one where the investigator intervenes by defining the variable of interest and artificially manipulates the study factor. It is also one of its characteristics the randomization of cases or subjects in groups (two or more, depending on what is the hypothesis of study).

In this example, the investigators used a randomized block design with "Bag" as the blocking factor and assigned the bags randomly to the students of the statistic class.

The researchers manipulated all confounding factors in this experiment leaving only "the number of candies per color per bag" as the only random variable. This is an experimental study.

b)

This is an ANOVA with two factors, "Bag" and "Colour" and the treatments are all possible combinations between these two factors.

Correct Option A.

c) The response variable is the "number of candies per color per bag"

Colors: Blue, Red, Orange, Green, Brown and Yellow.

I hope you have a nice day!