This is an advanced worksheet, which assumes you have completed the Absolute Beginners’ Guide to R course, the Research Methods in Practice (Quantitative section) course, and the Intermediate Guide to R course.

This worksheet describes a full analysis pipeline for an undergraduate student dissertation which explored relationships between personality, imagery and creative problem solving. Forty-eight students were tested to address three hypotheses. First, the researchers predicted that participants with more open personality types would be better at solving a selection of problems requiring creative solutions. Second, they predicated that participants with more vivid mental imagery would be better at solving the problems. Third, they predicted a relationship between divergent thinking and an ability to solve the problems.

Personality was measured using a simplified version of Costa and McCrae’s (1992) “big five” personality questionnaire. Mental imagery was measured using the PsiQ Plymouth Sensory Imagery Questionnaire (Andrade et al., 2013). Divergent thinking was measured using a ‘flexible thinking task’, which measured fluency, flexibility and originality. The problems requiring creative solutions were taken from May (1987).

Open the `rminr-data`

project we used previously.

Ensure you have the latest files by asking git to “`pull`

” the repository. Select the `Git`

tab, which is located in the row of tabs which includes the `Environment`

tab. Click the `Pull`

button with a downward pointing arrow. A window will open showing the files which have been pulled from the repository. Close the `Git pull`

window. The `case-studies`

folder should contain the folder `jon-may`

.

Next, create a new, empty R script and save it in the `rminr-data`

folder as `cs-jon-may.R`

. Put all the commands from this worksheet into this file, and run them from there. Save your script regularly.

We start by loading the data.

**Explanation of commands:**

We clear the workspace, and load `tidyverse`

package, then read the four data files.

Problem booklet with 7 problems (solved=1, not=0, total=n solved)

```
Parsed with column specification:
cols(
subj = col_double(),
bridges = col_double(),
coins = col_double(),
greengrocer = col_double(),
wolves = col_double(),
cards = col_double(),
gorge = col_double(),
dots = col_double()
)
```

Big5 OCEAN questionnaire 50 items answered 1 to 5 (includes a data entry error)

```
Parsed with column specification:
cols(
.default = col_double()
)
```

`See spec(...) for full column specifications.`

```
#big5 <- read_csv('case-studies/jon-may/big5_total.csv', col_types = 'fiiiii')
oceankey<-read.csv("case-studies/jon-may/oceankey.csv")
scaleIDs <- oceankey$ScaleID # make a vector of the new variable names
names(scaleIDs) <- oceankey$ItemID # name each new name with the old name so it can be looked-up
ocean.scales<-ocean %>%
pivot_longer(S1:S50,names_to='Item', values_to='Value') %>% # put the 50 items into a column
mutate(ScaleID=scaleIDs[Item])%>% # lookup the new names from the vector
select(-Item) %>% # drop the columns we don't need
mutate(Value=ifelse(Value>5,NA,ifelse(Value<1, NA, Value))) %>% # screen for absurd values
mutate(Value=ifelse(grepl("r",ScaleID), 6-Value, Value)) %>% # reverse score items containg 'r' ...
mutate(ScaleID = sub("r", "", ScaleID)) %>% # ... and remove the 'r'
pivot_wider(names_from="ScaleID", values_from="Value") %>% # make the data wide again
select(subj,sort(names(.))) %>% # sort the columns by the new names
rowwise() %>% # for each participant...
mutate(openness=mean(c_across(o01:o10), na.rm = TRUE), # ... mean of 10 items in each scale
conscientiousness=mean(c_across(C01:C10), na.rm = TRUE),
extraversion=mean(c_across(E01:E10), na.rm = TRUE),
agreeableness=mean(c_across(A01:A10), na.rm = TRUE),
neuroticism=mean(c_across(N01:N10), na.rm = TRUE)) %>%
select(subj, openness, conscientiousness, extraversion, agreeableness, neuroticism)
```

- We don’t have raw data for the ‘Flexible Thinking Test’ (overall scores mean of ftt1-3)

```
ftt <- read_csv('case-studies/jon-may/ftt.csv') %>%
rowwise() %>%
mutate(ftt = mean(c_across(ftt1:ftt3))) %>%
select(subj, ftt)
```

```
Parsed with column specification:
cols(
subj = col_double(),
ftt1 = col_double(),
ftt2 = col_double(),
ftt3 = col_double()
)
```

- the 35 PsiQ vividness of imagery items - 5 of each of 7 modalities (0 not at all to 10 as vivid as real life) (score = mean of all items)

```
psiq <- read_csv('case-studies/jon-may/psiq.csv') %>%
rowwise() %>%
mutate(psiq = mean(c_across(2:36))) %>%
select(subj, psiq)
```

```
Parsed with column specification:
cols(
.default = col_double()
)
```

`See spec(...) for full column specifications.`

The `psych`

library has a useful function `describe`

to obtain descriptive statistics.

```
Attaching package: 'psych'
```

```
The following objects are masked from 'package:ggplot2':
%+%, alpha
```

```
vars n mean sd median trimmed mad min max range
subj 1 48 24.50 14.00 24.50 24.50 17.79 1.00 48.00 47.00
openness 2 48 3.31 0.68 3.20 3.30 0.74 1.80 4.90 3.10
conscientiousness 3 48 3.51 0.72 3.50 3.51 0.74 2.20 4.90 2.70
extraversion 4 48 3.15 0.79 3.30 3.15 0.82 1.30 4.90 3.60
agreeableness 5 48 4.36 0.46 4.40 4.38 0.58 3.30 5.00 1.70
neuroticism 6 48 2.60 0.74 2.50 2.58 0.89 1.30 4.80 3.50
problems 7 48 1.58 0.92 1.00 1.57 1.48 0.00 4.00 4.00
ftt 8 48 6.29 1.96 6.17 6.34 1.73 0.67 10.00 9.33
psiq 9 48 6.89 1.48 6.77 6.91 1.65 3.57 9.77 6.20
skew kurtosis se
subj 0.00 -1.28 2.02
openness 0.17 -0.69 0.10
conscientiousness 0.02 -0.78 0.10
extraversion -0.05 -0.16 0.11
agreeableness -0.42 -0.85 0.07
neuroticism 0.46 -0.16 0.11
problems 0.40 -0.36 0.13
ftt -0.28 -0.06 0.28
psiq -0.14 -0.49 0.21
```

https://stackoverflow.com/questions/6967664/ggplot2-histogram-with-normal-curve

```
n_obs = sum(!is.na(data$problems))
bw = 1
mean <- mean(data$problems)
sd <- sd(data$problems)
data %>% ggplot(aes(problems)) +
geom_histogram(colour = "black", binwidth = bw) +
stat_function(fun = function(x)
dnorm(x, mean = mean, sd = sd) * bw * n_obs) +
xlab('Problems solved') + ylab('Count (participants)')
```

You learnt how to create a scatterplot and a best fit line in the regression worksheet.

``geom_smooth()` using formula 'y ~ x'`

The researchers predicted that participants with more open personality types would be better at solving the problems. In other words, we should expect a positive correlation between openness and problem solving. We test a directional hypothesis with a one-tailed correlation. See the More on relationships, part 2. worksheet for more details.

```
Pearson's product-moment correlation
data: data$problems and data$openness
t = 0.067585, df = 46, p-value = 0.4732
alternative hypothesis: true correlation is greater than 0
95 percent confidence interval:
-0.2309906 1.0000000
sample estimates:
cor
0.009964354
```

```
# note that this is a 2-tailed test
library(BayesFactor)
cor_o_problems_bf<-correlationBF(data$problems, data$openness)
cor_o_problems_bf
```

```
Bayes factor analysis
--------------
[1] Alt., r=0.333 : 0.3249778 ±0%
Against denominator:
Null, rho = 0
---
Bayes factor type: BFcorrelation, Jeffreys-beta*
```

**Explanation of commands:**

We use a Pearson correlation to look at the relationship between openness and the number of problems solved. We specify `alternative='greater'`

to indicate that we are predicting a positive correlation (one-tailed test). We also calculate a Bayes factor to test the evidence for the correlation.

**Explanation of output:**

Contrary to the first hypothesis, there is no evidence for a positive correlation between openness and creative problem solving (*r* = 0.01, one-tailed, *BF* = 0.32).

Correlation matrices are covered in the Better tables worksheet.

```
library(apaTables)
apa.cor.table(data %>% select(conscientiousness:problems), filename='table1.doc', table.number = 1)
```

```
Table 1
Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2 3 4
1. conscientiousness 3.51 0.72
2. extraversion 3.15 0.79 -.01
[-.29, .28]
3. agreeableness 4.36 0.46 .20 .43**
[-.09, .46] [.17, .64]
4. neuroticism 2.60 0.74 .28 .13 .07
[-.00, .52] [-.16, .40] [-.22, .34]
5. problems 1.58 0.92 -.12 -.19 .02 -.14
[-.39, .17] [-.45, .10] [-.26, .30] [-.41, .15]
Note. M and SD are used to represent mean and standard deviation, respectively.
Values in square brackets indicate the 95% confidence interval.
The confidence interval is a plausible range of population correlations
that could have caused the sample correlation (Cumming, 2014).
* indicates p < .05. ** indicates p < .01.
```

**Explanation of output:**

There were no correlations between the other four personality factors and problem solving. Note that these are 2-tailed correlations, as it’s not possible to specify 1-tailed tests with `apa.cor.table()`

.

```
Pearson's product-moment correlation
data: data$problems and data$ftt
t = 2.118, df = 46, p-value = 0.0198
alternative hypothesis: true correlation is greater than 0
95 percent confidence interval:
0.06214013 1.00000000
sample estimates:
cor
0.2980887
```

```
# note that this is a 2-tailed test
library(BayesFactor)
cor_f_problems_bf<-correlationBF(data$problems, data$ftt)
cor_f_problems_bf
```

```
Bayes factor analysis
--------------
[1] Alt., r=0.333 : 2.172511 ±0%
Against denominator:
Null, rho = 0
---
Bayes factor type: BFcorrelation, Jeffreys-beta*
```

```
Pearson's product-moment correlation
data: data$problems and data$psiq
t = -0.19137, df = 46, p-value = 0.5755
alternative hypothesis: true correlation is greater than 0
95 percent confidence interval:
-0.2667972 1.0000000
sample estimates:
cor
-0.02820461
```

```
# note that this is a 2-tailed test
library(BayesFactor)
cor_v_problems_bf<-correlationBF(data$problems, data$psiq)
cor_v_problems_bf
```

```
Bayes factor analysis
--------------
[1] Alt., r=0.333 : 0.3296407 ±0%
Against denominator:
Null, rho = 0
---
Bayes factor type: BFcorrelation, Jeffreys-beta*
```

**Explanation of commands:**

As for Openness, we use Pearson correlations to look at the relationship between the number of problems solved, Flexible Thinking and Vividness. We specify `alternative='greater'`

to indicate that we are predicting a positive correlation (one-tailed test). We also calculate a Bayes factor to test the evidence for the correlations.

**Explanation of output:**

There is evidence for a positive correlation between flexibility and creative problem solving (*r* = 0.3, one-tailed, *BF* = 2.17). There is no evidence for a positive correlation between imagery vividness and creative problem solving (*r* = -0.03, one-tailed, *BF* = 0.33).

Pairs plots are are covered in the Better graphs worksheet.

Andrade, J., May, J., Deeprose, C., Baugh, S.-J., & Ganis, G. (2014). Assessing vividness of mental imagery: The Plymouth Sensory Imagery Questionnaire British Journal of Psychology, 105(4), 547–563.

Costa, P. T., & McCrae, R. R. (1992). Neo personality inventory-revised (NEO PI-R). Psychological Assessment Resources Odessa, FL.

May, J. (1987). The cognitive analysis of flexible thinking. Unpublished PhD thesis, University of Exeter.

This material is distributed under a Creative Commons licence. CC-BY-SA 4.0.