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Assignment 4

2022

Instructions

1) Please submit your solutions to this assignment in one PDF ﬁle in brightspace. Only one ﬁle will be accepted.

2) You can submit a PDF ﬁle more than once. However, only the last submission will be saved. If you want to modify your submitted assignment, that is ﬁne as long as it is before the deadline.

3) Late submissions of the assignment are not going to be marked.

4) In the second part of the assignment, you must use R for all of your computations. Please use R markdown to write the solutions for this part.

5) You can submit hand written solutions for part one of the assignment, but please combine images of your hand-written solutions with the PDF produced with R markdown as one PDF. (See https: //imagetopdf.com/ as a possible solution to combine images as one PDF).

6) Deadline: Before 11:59 pm on Wednesday, July 20

7) You can work in groups of up to four members.

Part one

You can provide hand-written solutions for this part, but it is not necessary. You are welcome to try to write your solutions with R markdown. For Part One, only use R to compute quantiles and probabilities from a t or F distribution.

1. Fill in the missing values in the following ANOVA table for a completely randomized design with two factors crossed factors (say A and B). A has 2 levels and B has 3 levels. The number of experimental units per treatment n = 3.

p-value

(a) Test for the signiﬁcance of the interaction eﬀects.

(b) Compute the partial eta square for each of the main eﬀects and for the interaction eﬀects.

(c) Based on the results from parts (a) and (b), is it reasonable to ignore the interactions in the description of the main eﬀects.

(d) Pool the ss for the interactions and the error, to obtain a table that corresponds to an additive model. With this modiﬁed table, test for the signiﬁcance of the A main eﬀects and test for the signiﬁcance of the B main eﬀects.

2. In a study of the eﬀect of applicant’s eye contact (factor A) and personnel oﬃcer’s gender (factor B) on the personnel’s oﬃcer’s assessment of likely job success of applicant, 10 male and 10 female personnel oﬃcers were shown a front view photograph of an applicant’s face and were asked to give the person in the photograph a success rating on a scale of 0 (total failure) to 20 (outstanding success). Half of the oﬃcers in each gender group were chosen at random to receive a version of the photograph in which there was not eye contact.

(a) Is the study experimental, observational, or mixed? Why?

(b) Identify all factors, factor levels, and factor level combinations.

Part Two

Please R for all computations, and for building graphs in this part of the assignment. Note that we also want answers to some of this questions, that do not involve R. R will only be used for the computation, and to produce graphs. For some of these questions, the R output will not be suﬃcient. You will need to interpret, to describe, and give conclusions.

3. Refer to Question 2. The data is in the ﬁle EyeContact .csv.

(a) Give an interaction plot. Does it appear that any factor eﬀects are present? Explain.

(b) Give group statistics, i.e. give statistics for each cell (mean, std dev, and sample size). It the study

balanced? Why?

(c) Fit a two-Factor ANOVA Model with interactions and ﬁxed eﬀects. Give the corresponding ANOVA table. For each of the 3 types of eﬀects compute the partial eta squared. Which of the three types eﬀects are the larger eﬀects?

(d) Test whether or not interaction eﬀects are present? Give the observed value of the test statistic, the p-value, and the conclusion at α = 5%.

(e) Test whether or not eye contact main eﬀects are present? Give the observed value of the test statistic, the p-value, and the conclusion at α = 5%.

(f) Test whether or not gender main eﬀects are present? Give the observed value of the test statistic, the p-value, and the conclusion at α = 5%.