Chapter 9 One-way designs

One way designs

(James et al., 2015)

James, E. L., Bonsall, M. B., Hoppitt, L., Tunbridge, E. M., Geddes, J. R., Milton, A. L., & Holmes, E. A. (2015). Computer game play reduces intrusive memories of experimental trauma via reconsolidation-update mechanisms. Psychological Science, 26, 1201-1215. Obtained from journals.sagepub.com/doi/abs/10.1177/0956797615583071

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• Download the SPSS data set (wide format)

• Download the Excel/R data set (wide format)

9.1 Sanity checks

## 
##  Kendall's rank correlation tau
## 
## data:  .$post_within_z and .$Day_Zero_Number_of_Intrusions
## z = 4, p-value = 3e-05
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##   tau 
## 0.361

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

9.2 Visualization

## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.

## `summarise()` ungrouping output (override with `.groups` argument)

## 
##  Fligner-Killeen test of homogeneity of variances
## 
## data:  Days_One_to_Seven_Number_of_Intrusions by Condition
## Fligner-Killeen:med chi-squared = 6, df = 3, p-value = 0.1

Model statistics
Multiple \(R^2\)	0.143
Multiple \(R^2_{adj}\)	0.106
\(F_{3,68}\)	3.795
Sig. (\(p\))	0.014
Resid. SD	3.176
Resid. df	68

Analysis of Variance table
Term	SS	d.f.	MS	\(F\)	Sig. (\(p\))	\(\eta^2\)	\(\eta^2_p\)
Condition	114.819	3	38.273	3.795	0.014	0.143	0.143
Residuals	685.833	68	10.086

Tukey's HSD post-hoc tests
Contrast	Null	Estimate	Sig. (\(p\))
React.-No task	0	−0.278	0.994
React.-Tetris	0	0.944	0.809
Tetris-No task	0	−1.222	0.657
Tetris-R. & T.	0	2.000	0.242
React.-R. & T.	0	2.944	0.034
R. & T.-No task	0	−3.222	0.017

9.3 Transformation

9.3.1 Logarithmic

Because 0 is a possible count, and \(\log(0) = -\infty\), we cannot use a log transformation to reduce the skew. There are other possibilities, such as \(\sqrt{x}\). Here I will use a simple modification of the log transformation: \(\log(1+x)\). Adding 1 means that we no longer have the problem with the 0 counts, because \(log(1 + 0) = 0\).

As you can see in the dotplot below, the problematic skew is reduced.

## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.

Model statistics
\(\log(1+x)\)-transformed DV
Multiple \(R^2\)	0.202
Multiple \(R^2_{adj}\)	0.167
\(F_{3,68}\)	5.744
Sig. (\(p\))	0.001
Resid. SD	0.600
Resid. df	68

Analysis of Variance table
\(\log(1+x)\)transformed DV
Term	SS	d.f.	MS	\(F\)	Sig. (\(p\))
Condition	6.205	3	2.068	5.744	0.001
Residuals	24.485	68	0.360

Tukey's HSD post-hoc tests
\(\log(1+x)\)-transformed DV
Contrast	Null	Estimate	Sig. (\(p\))
React.-No task	0	0.039	0.997
Tetris-No task	0	−0.148	0.881
React.-Tetris	0	0.187	0.787
Tetris-R. & T.	0	0.547	0.039
R. & T.-No task	0	−0.695	0.005
React.-R. & T.	0	0.734	0.003

9.3.2 Rank

## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.

Model statistics
Rank-transformed DV
Multiple \(R^2\)	0.191
Multiple \(R^2_{adj}\)	0.155
\(F_{3,68}\)	5.350
Sig. (\(p\))	0.002
Resid. SD	19.046
Resid. df	68

Analysis of Variance table
Rank-transformed DV
Term	SS	d.f.	MS	\(F\)	Sig. (\(p\))
Condition	5,822.500	3	1,940.833	5.350	0.002
Residuals	24,667.500	68	362.757

Tukey's HSD post-hoc tests
Rank-transformed DV
Contrast	Null	Estimate	Sig. (\(p\))
React.-No task	0	1.833	0.992
Tetris-No task	0	−4.944	0.864
React.-Tetris	0	6.778	0.710
Tetris-R. & T.	0	16.056	0.064
R. & T.-No task	0	−21.000	0.008
React.-R. & T.	0	22.833	0.003

9.4 Nonparametric

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Days_One_to_Seven_Number_of_Intrusions by Condition
## Kruskal-Wallis chi-squared = 14, df = 3, p-value = 0.004

Dunn's nonparametric post-hoc tests
Sorted by significance
Contrast	Z statistic	Sig. (\(p\))
React. - Tetris	0.981	0.979
No task - Tetris	0.716	0.948
No task - React.	−0.265	0.791
R. & T. - Tetris	−2.324	0.080
No task - R. & T.	3.040	0.012
R. & T. - React.	−3.306	0.006

References

James, E. L., Bonsall, M. B., Hoppitt, L., Tunbridge, E. M., Geddes, J. R., Milton, A. L., & Holmes, E. A. (2015). Computer game play reduces intrusive memories of experimental trauma via reconsolidation-update mechanisms. Psychological Science, 26(8), 1201–1215. Retrieved from https://journals.sagepub.com/doi/abs/10.1177/0956797615583071

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