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This worksheet relies on the follwing pacakges: teachingtools, tidyverse, afex, emmeans, and psych. To make sure that these packages are loaded, run the following code in your console. 

xfun::pkg_attach2("psych","afex","ggbeeswarm","emmeans","teachingtools","tidyverse")

If you need to install teachingtools then follow the instructions in the introduction.

This worksheet covers the material from the follwing sessions: Reading data into R, RStudio Project files, Analysis of Variance with afex, and Simple mediation.

Creating a RStudio project

Problem 6.1

Create a new RStudio project. Inside the project folder, create two sub-folders. One should be called data and the other should be called scripts.

Problem 6.2

Create a new R script, and save it into the scripts folder of your project.

Problem 6.3

Download the following two files and save them into your data folder of your project.

aov_data1.csv

mediate_data1.csv

Reading in data

The following problems should be solved by writing code into the file in your scripts folder

Problem 6.4

Write code to read in the data stored in the files aov_data1.csv and medaite_data1.csv. The data in the file aov_data1.csv should be stored in a variable called aov_data, and the data in mediate_data1.csv should be stored in a variable called mediate_data.

Get a hint
  • You’ll need to use two functions to solve this
  • Use the here() function for finding directions
  • Use the read_csv() function for reading in data
Solution 
aov_data <- readr::read_csv(file = here::here("data","aov_data1.csv"))
mediate_data <- readr::read_csv(file = here::here("data","mediate_data1.csv"))

Analysis of Variance

The following questions will require the aov_data data set you’ve just imported. This data set contains data from a working memory task. It was undertaken by 60 participants: 20 Engineering students, 20 Psychology Students, and 20 Maths students (Degree.Type). The students performed the working memory task under two conditions (Task). Their performance is recorded in value.

aov_data
# A tibble: 120 x 4
   SubjectCode Task  Degree.Type value
   <chr>       <chr> <chr>       <dbl>
 1 s01         Angle Engineering 0.358
 2 s01         Color Engineering 0.305
 3 s02         Angle Engineering 0.151
 4 s02         Color Engineering 0.164
 5 s03         Angle Maths       0.268
 6 s03         Color Maths       0.250
 7 s04         Angle Engineering 0.209
 8 s04         Color Engineering 0.131
 9 s05         Angle Psychology  0.206
10 s05         Color Psychology  0.189
# … with 110 more rows

Problem 6.5

Conduct a 2 x 3 mixed ANOVA on the aov_data data set. Save the model output as aov_wm

Get a hint
  • You’ll need to specify within and between factors.
Solution 
aov_wm <- afex::aov_ez(id = "SubjectCode",
                    dv = "value", 
                    between = "Degree.Type",
                    within = "Task",
                    data = aov_data)
aov_wm
Anova Table (Type 3 tests)

Response: value
            Effect    df  MSE         F  ges p.value
1      Degree.Type 2, 57 0.00      0.79 .021    .458
2             Task 1, 57 0.00 57.32 *** .199   <.001
3 Degree.Type:Task 2, 57 0.00   5.03 ** .042    .010
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

Problem 6.6

Output a summary ANOVA table that includes the partial \(\eta^2\) effect size, rather than the default generalised \(\eta^2\).

Get a hint
  • You might find the anova() function useful
  • Partial \(\eta^2\) is pes
Solution 
anova(object = aov_wm, es = "pes")
Anova Table (Type 3 tests)

Response: value
                 num Df den Df       MSE       F     pes    Pr(>F)    
Degree.Type           2     57 0.0034893  0.7924 0.02705  0.457692    
Task                  1     57 0.0011455 57.3198 0.50140 3.556e-10 ***
Degree.Type:Task      2     57 0.0011455  5.0305 0.15003  0.009729 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Problem 6.7

As your first question you’re interested in whether their is a difference in performance on the Color Task and the Angle Task in each of the three degree type. That is, you want to know the Task difference in each degree type.

Get a hint
  • Answering this will take two steps
  • In the first step will require estimating the marginal means and the second step will require performing pairwise comparisons.
Solution 
emmeans::emmeans(aov_wm, specs = "Task", by = "Degree.Type") %>% 
  pairs()
Degree.Type = Engineering:
 contrast      estimate     SE df t.ratio p.value
 Angle - Color   0.0413 0.0107 57 3.858   0.0003 

Degree.Type = Maths:
 contrast      estimate     SE df t.ratio p.value
 Angle - Color   0.0260 0.0107 57 2.429   0.0183 

Degree.Type = Psychology:
 contrast      estimate     SE df t.ratio p.value
 Angle - Color   0.0731 0.0107 57 6.826   <.0001

Problem 6.8

Now that you know the difference in each degree type, you’d like to compare this difference across the degree types. That is, you’d like to compare the task difference between Engineering and Maths, Engineering and Psychology, and Maths and Psychology.

Get a hint
  • This just requires adding another call to your previous answer
  • You’ll need to set the simple argument
Solution 
emmeans::emmeans(aov_wm,  spec =  "Task", by = "Degree.Type") %>% 
  pairs() %>% 
  pairs(simple = "Degree.Type")
contrast = Angle - Color:
 contrast1                estimate     SE df t.ratio p.value
 Engineering - Maths        0.0153 0.0151 57  1.011  0.5733 
 Engineering - Psychology  -0.0318 0.0151 57 -2.099  0.0991 
 Maths - Psychology        -0.0471 0.0151 57 -3.109  0.0081 

P value adjustment: tukey method for comparing a family of 3 estimates

Problem 6.9

Finally, you’d like to draw a plot. Draw any plot you feel is sensible.

Solution (One possible solution) 
afex_plot(aov_wm, 
          x = "Degree.Type", 
          panel = "Task", 
          error = "none", 
          dodge = 0, 
          data_geom = geom_boxplot)

Mediation Analysis

The following questions rely on the mediate_data data set which you imported at the start. This is data set, from Pollack et al (2012), has data from 262 entrepreneurs who were part of the Business Networking International group.

mediate_data
# A tibble: 262 x 7
   tenure estress affect withdraw   sex   age   ese
    <dbl>   <dbl>  <dbl>    <dbl> <dbl> <dbl> <dbl>
 1  1.67      6     2.6      3        1    51  5.33
 2  0.580     5     1        1        0    45  6.05
 3  0.580     5.5   2.4      3.66     1    42  5.26
 4  2         3     1.16     4.66     1    50  4.35
 5  5         4.5   1        4.33     1    48  4.86
 6  9         6     1.5      3        1    48  5.05
 7  0         5.5   1        1        0    51  3.66
 8  2.5       3     1.16     1        0    47  6.13
 9  0.5       5.5   1.33     2        1    40  5.26
10  0.580     6     3        4        1    43  4   
# … with 252 more rows

Problem 6.10

Pollack et al (2012), proposed that economic stress estress led to a desire to withdraw from entrepreneurial activities (withdraw) and that this was mediated by the depressed affect affect caused by this stress. Perform this mediation analysis. Save the model as med_with

Get a hint
  • You’ll need to use the psych::mediate() function
Solution 
med_with <- psych::mediate(y = "withdraw", 
                           x = "estress", 
                           m = "affect", 
                           data = mediate_data, 
                           plot = FALSE)

Problem 6.11

The find the bounds of the bootstrapped 95% CI of the indirect effect (ab).

Get a hint
  • The model object is a list
  • This list has a named element called boot than contains information about the bootstrapped results
Solution 
med_with$boot$ci.ab[,1]
      2.5%      97.5% 
0.06980001 0.20213655

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