Case uitwerking
Assignment 2 (questions + answers) Statistics (GEO2-2217)
- Instelling
- Universiteit Utrecht (UU)
These are the questions and answers of assignment 2 of Statistics. It is due in the second part of the course.
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Assignment 2N.B.: For all ANOVA tasks, you can ignore the homogeneity of variance assumption.
1. ANOVA
The questionnaire contains several questions about the societal and scientific output of
the projects. As discussed by a group of scientific scholars, such impact of a project can be
measured with:
I. The number of scientific publications (variable Publ).
II. Presence in the media (variable Media)
During the first assignment you have practiced with the technological topic of the
projects. We want to examine whether the six technological topics (variable TechTop)
differ significantly in terms of the different types of output (variables Publ and Media).
Perform appropriate ANOVAs to analyze this.
Use = 5% give the experimental hypotheses as well as the null hypotheses in your answer.
a. Do the technological topics groups differ significantly on:
i. Publ
Figure 1. One-way ANOVA-table for variables TechTop and Publ
ii. Media
Figure 2. One-way ANOVA-table for variables TechTop and Media
Null hypothesis - 𝐻0: δ = 0
Experimental hypothesis - 𝐻1: δ ≠ 0
As can be seen in Figure 1 and Figure 2, the two-tailed p-value of variable Publ is equal to
𝑝 = 0. 0021% and for the variable Media this is equal to 𝑝 = 1. 9%. Each two-tailed p-value, thus, is
beneath α = 5%, which indicates that the technological topics groups differ significantly. As a result,
the experimental hypothesis H1 can be accepted and the null hypothesis H0 can be rejected.
b. Express the strength of the differences of question 1a in a measurement. Show
your calculations and interpret the results. (tip: for each of the ANOVAs you need to
provide a calculation and interpretation).
2 𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛
If we want to determine the strength of the differences, 𝑒𝑡𝑎 = 𝑆𝑆𝑡𝑜𝑡𝑎𝑙
has to be calculated for each
2 1102.951
variable. For the first variable, variable Publ, this is equal to 𝑒𝑡𝑎 = 14055.888 = 0. 078. In Appendix 4,
, this effect size is known as a medium effect. So the strength of the differences is in this case
moderate.
2 18669.063
For the variable Media, this is equal to 𝑒𝑡𝑎 = 115288.588
= 0. 162. This is known as a large effect,
Appendix 4. Therefore, the strength of the differences is large.
c. Based on question 1a we now know which ANOVA(s) is/are statistically significant.
We continue in this question with an ANOVA that was statistically significant in
question 1a. So, your first task is to select an ANOVA that is statistically significant.
Suppose we had no idea in advance which of the technological topics differ on the
different types of impact. Therefore, we will perform a post-hoc analysis according
to Tukey (α = 5%) for this selected ANOVA. Which technological topics differ
significantly? Describe both output tables of the post-hoc Tukey analysis in your
answer.
As indicated in question 1a, both the variable Publ and the variable Media differ significantly. In
comparison with the variable Publ, the variable Media has the lowest two-tailed p-value, which is why
we chose for the variable Media to be involved in the post-hoc analysis, as can be seen in Figure 3
and Figure 4.
Figure 4. Post-Hoc analysis Tukey
Subsets-table for variables TechTop and Media
Figure 3. Post-Hoc analysis Tukey for variables TechTop and Media
In Figure 4, the post-hoc analysis Tukey shows three subsets related to the different technological
project topics:
● In subset 1, the technological project topics ‘Plastic reduction’, ‘Agro technology’ and ‘Solar
energy’ are involved;
● Subset 2 consists of the technological project topics ‘Agro technology’, ‘Solar energy’,
‘Circular fashion’ and Wind energy’;
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