Chapter 11 Mixed designs

Designs with fixed and a single random factor

Four trials of the absolute judgment task.

Stimulus sets used in the experiments. The bottom shows white lines on black, as the participants say, as well as the relative size of the lines to the screen (black 4:3 rectangle).

Figure 11.1: Stimulus sets used in the experiments. The bottom shows white lines on black, as the participants say, as well as the relative size of the lines to the screen (black 4:3 rectangle).

11.1 Sanity checks

## `summarise()` regrouping output by 'set_first', 'line' (override with `.groups` argument)
Overall proportions of confusions in blocks 2-5. The presented line is on the $x$ axis., and the response is on the $y$ axis. Proportions sum to 100% vertically. If a cell lacks a number, the proportion was less than 0.5%. 'NA' represents an invalid response. Stimuli within the two vertical dashed lines (dark red) are the target stimuli.

Figure 11.2: Overall proportions of confusions in blocks 2-5. The presented line is on the \(x\) axis., and the response is on the \(y\) axis. Proportions sum to 100% vertically. If a cell lacks a number, the proportion was less than 0.5%. ‘NA’ represents an invalid response. Stimuli within the two vertical dashed lines (dark red) are the target stimuli. 

## `summarise()` regrouping output by 'set_first' (override with `.groups` argument)
Accuracy by stimulus in blocks 2-5, before the (potential) set switch. The shaded region shows the target stimuli.

Figure 11.3: Accuracy by stimulus in blocks 2-5, before the (potential) set switch. The shaded region shows the target stimuli. 

## `summarise()` ungrouping output (override with `.groups` argument)
Frequency of lines presented
Tabulated across all 81 participants
Line label Frequency
1 5427
2 5427
3 5427
4 5427
5 5427
6 5427
7 5427
8 5427
9 5346
10 5346
11 5346
12 5346

11.2 Visualizations

## `summarise()` regrouping output by 'id' (override with `.groups` argument)
## `summarise()` regrouping output by 'condition' (override with `.groups` argument)
## `geom_smooth()` using formula 'y ~ x'

## Note: re-fitting model with sum-to-zero contrasts
## `geom_smooth()` using formula 'y ~ x'

## `summarise()` regrouping output by 'id' (override with `.groups` argument)
## `geom_smooth()` using formula 'y ~ x'

## 
## Error: id
##                              Df Sum Sq Mean Sq F value  Pr(>F)    
## same                          1   0.13    0.13    6.07 0.01611 *  
## set_current                   1   0.19    0.19    8.34 0.00510 ** 
## first_acc_z                   1   3.78    3.78  169.87 < 2e-16 ***
## same:set_current              1   0.35    0.35   15.75 0.00017 ***
## same:first_acc_z              1   0.01    0.01    0.44 0.51087    
## set_current:first_acc_z       1   0.01    0.01    0.59 0.44639    
## same:set_current:first_acc_z  1   0.26    0.26   11.88 0.00095 ***
## Residuals                    73   1.62    0.02                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Error: id:block
##                                     Df Sum Sq Mean Sq F value Pr(>F)   
## block                                3  0.095  0.0315    2.59 0.0540 . 
## same:block                           3  0.150  0.0501    4.11 0.0073 **
## set_current:block                    3  0.062  0.0207    1.70 0.1681   
## block:first_acc_z                    3  0.024  0.0080    0.66 0.5792   
## same:set_current:block               3  0.031  0.0102    0.84 0.4747   
## same:block:first_acc_z               3  0.024  0.0079    0.65 0.5858   
## set_current:block:first_acc_z        3  0.017  0.0057    0.47 0.7049   
## same:set_current:block:first_acc_z   3  0.022  0.0075    0.61 0.6072   
## Residuals                          219  2.670  0.0122                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Note: re-fitting model with sum-to-zero contrasts

Mauchly Tests for Sphericity
Test statistic Sig. (\(p\))
block 0.917 0.289
same:block 0.917 0.289
set_current:block 0.917 0.289
first_acc_z:block 0.917 0.289
same:set_current:block 0.917 0.289
same:first_acc_z:block 0.917 0.289
set_current:first_acc_z:block 0.917 0.289
same:set_current:first_acc_z:block 0.917 0.289
Sphericity adjustments
Greenhouse–Geisser (GG), Huynh–Feldt (HF)
GG eps Sig. (\(p\)) GG HF eps Sig. (\(p\)) HF
block 0.951 0.057 0.994 0.054
same:block 0.951 0.008 0.994 0.007
set_current:block 0.951 0.173 0.994 0.170
first_acc_z:block 0.951 0.572 0.994 0.579
same:set_current:block 0.951 0.490 0.994 0.494
same:first_acc_z:block 0.951 0.546 0.994 0.552
set_current:first_acc_z:block 0.951 0.695 0.994 0.704
same:set_current:first_acc_z:block 0.951 0.599 0.994 0.606

11.3 Linear mixed effects model

## Registered S3 methods overwritten by 'lme4':
##   method                          from
##   cooks.distance.influence.merMod car 
##   influence.merMod                car 
##   dfbeta.influence.merMod         car 
##   dfbetas.influence.merMod        car
## Contrasts set to contr.sum for the following variables: same, set_current, block, id
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]

11.4 MANOVA

Term d.f. Pillai's trace \(F\) Num. d.f. Denom. d.f. Sig. \(p\)
same 1 0.194 4.201 4 70 0.004
set_current 1 0.139 2.832 4 70 0.031
first_acc_z 1 0.709 42.723 4 70 0.000
same:set_current 1 0.205 4.512 4 70 0.003
same:first_acc_z 1 0.026 0.461 4 70 0.764
set_current:first_acc_z 1 0.029 0.514 4 70 0.725
same:set_current:first_acc_z 1 0.164 3.424 4 70 0.013
Residuals 73