# Statistics

Question 1.
Below is a SPSS output from a two-way ANOVA of a small subsample (n=24) of the full data set (n =133) that we analyzed in Workshop 3.

1. Interpret the results
2. Provide an estimate of and comment the effect size
Univariate Analysis of Variance
Between-Subjects Factors
Value Label N
Type Of Lost Product -1 Phone 12
1 Laptop 12
Age Of Lost Product -1 New 12
1 Old 12

Descriptive Statistics
Dependent Variable: Nr_of_B_choices (i.e. Nr of attempts to contact the lost property office)
TypeOfLostProduct AgeOfLostProduct Mean Std. Deviation N
Phone New 3,17 ,983 6
Old 2,83 ,983 6
Total 3,00 ,953 12
Laptop New 2,17 1,329 6
Old 3,83 ,408 6
Total 3,00 1,279 12
Total New 2,67 1,231 12
Old 3,33 ,888 12
Total 3,00 1,103 24

Tests of Between-Subjects Effects
Dependent Variable: Nr_of_B_choices (i.e. Nr of attempts to contact the lost property office)
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 8,667a 3 2,889 2,989
Intercept 216,000 1 216,000 223,448
TypeOfLostProduct ,000 1 ,000 ,000
AgeOfLostProduct 2,667 1 2,667 2,759
TypeOfLostProduct * AgeOfLostProduct 6,000 1 6,000 6,207
Error 19,333 20 ,967
Total 244,000 24
Corrected Total 28,000 23

Question 2

1. Describe one case (including real variables) when ANCOVA is appropriate to use and one when it is not. Explain from a statistical point of view why (2p).
2. What is the power of an mixed design? Provide an example where you illustrate this (2p).
3. Instead of using a repeated measure design, you could choose another design to test the same research question. What is that design, and what type of ANOVA-test would you use to analyze the results? (2p)
Question 3. Imagine a two-group experiment with a continuous dependent variable, in which you are investigating a hypothesis that one group tends to score higher on the dependent variable than the other. Given this design and hypothesis, in what situations might you prefer a non-parametric approach vs. a parametric approach to statistically test the hypothesis?

Question 4.

Imagine you wanted to bootstrap the median difference of a continuous dependent variable between two groups in an experiment. What factors would need to be considered when assessing the appropriateness of this statistical approach? What assumptions should you check?
Question 5.
The z-test, t-test and one way-ANOVA all compare groups.
What are main difference between a z-test and a t-test and why do we use df:s when calculating t-test but not z-test? (2p)
Why is a one way-ANOVA preferred to a t-test if we have more than two groups to compare? (1p)
When do we use a planned contrast instead of an post hoc test in a one way-ANOVA? (1p)
Question 6.
What is the substantive problem linked to invalid use of ANCOVA? Provide an example from your own field.

Question 7.
There are two different types of designs where repeated measures are relevant to use. Field provide an example of one such type. Describe an example from your own field of these two types of designs where you would use repeated measure ANOVA.

Question 8.
Provide an example of an 2 x 3 x 4 mixed design. How many different effects of interest would you get in your mixed design ANOVA output? If you only were allowed to focus on half of the given effects in the outputs, what effects would you prioritize to highlight?

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