Description of trial distribution in each block

Path: /Volumes/BL-PSY-gunderson_lab/Main/Studies/2023_manynumbers/materials/mn_psychopy_task/mn_amstask_blocks

  • 3 different spatial trial types resulting from combining equated and non equated dot size, surface area, and perimeter (e.g, perimeter_equated [1], surf_area_equated [2], and dot_size_equated [3]).

  • 2 convex hull (ch) conditions (equated and non equated)

  • 2 side conditions (left correct and right correct)

  • 4 numerical ratios

These results in 48 trials, 16 trials per block

It is not possible to have the 6 trial types resulting from combining 3 spatial conditions x 2 convex hull conditions for each numerical ratio within a block, as only 4 trials for each numerical ratio are presented in a block.

For each numerical ratio, we followed these 3 criteria:

  • 1 We decided to present at least the 3 spatial conditions + a repeated one (randomly selected).

  • 2 In each block, there should be not duplicated trials when considering convex hull. For example, a balanced block could have 1-non_ch, 1-equated_ch, 2-non_ch, 3-equated_ch, BUT not 1-non_ch, 1-non_ch, 2-equated_ch, and 3-equated_ch, as this block would repeat 1-non_ch twice.

  • 3 Blocks should be balanced by equated and non equated trials for convex hull and left correct and right correct:
    1 equated right, 1 equated left, 1 non equated right 1 non equated left

Three year old’s stimulus schedule

Pivot Table - Spatial Features

This pivot table shows that there are not duplicated trials (see criterion 2). There should not be 2s in any block, except for the total row

Pivot Table - Side Conditions

This pivot table shows that left and right are balanced by side within each ratio and within each block (criterion 3)

Descriptive stats

Values between blocks are roughly similar

Surface_Area threefeat_num block N ts_ratio sd se ci
0 perimeter_equated Block 1 6 0.4870017 0.1590036 0.0649130 0.1668641
0 perimeter_equated Block 2 5 0.4622875 0.1316163 0.0588606 0.1634233
0 perimeter_equated Block 3 5 0.4821948 0.1257707 0.0562464 0.1561649
0 dot_size_equated Block 1 6 2.2500000 0.5244044 0.2140872 0.5503287
0 dot_size_equated Block 2 5 2.1000000 0.6519202 0.2915476 0.8094659
0 dot_size_equated Block 3 5 2.4000000 0.6519202 0.2915476 0.8094659
equated surf_area_equated Block 1 4 1.0000000 0.0000000 0.0000000 0.0000000
equated surf_area_equated Block 2 6 1.0000000 0.0000000 0.0000000 0.0000000
equated surf_area_equated Block 3 6 1.0000000 0.0000000 0.0000000 0.0000000
Perimeter threefeat_num block N cont_ratio sd se ci
0 surf_area_equated Block 1 4 1.485558 0.2112315 0.1056157 0.3361164
0 surf_area_equated Block 2 6 1.519633 0.2043458 0.0834238 0.2144477
0 surf_area_equated Block 3 6 1.455395 0.2076125 0.0847574 0.2178760
0 dot_size_equated Block 1 6 2.245375 0.5163093 0.2107824 0.5418334
0 dot_size_equated Block 2 5 2.099710 0.6510987 0.2911802 0.8084458
0 dot_size_equated Block 3 5 2.394582 0.6487963 0.2901505 0.8055870
equated perimeter_equated Block 1 6 1.000000 0.0000000 0.0000000 0.0000000
equated perimeter_equated Block 2 5 1.000000 0.0000000 0.0000000 0.0000000
equated perimeter_equated Block 3 5 1.000000 0.0000000 0.0000000 0.0000000
Avg_Dot_Size threefeat_num block N diam_ratio sd se ci
0 perimeter_equated Block 1 6 0.4857957 0.1555287 0.0634943 0.1632174
0 perimeter_equated Block 2 5 0.4647109 0.1351699 0.0604498 0.1678356
0 perimeter_equated Block 3 5 0.4720571 0.1219075 0.0545187 0.1513681
0 surf_area_equated Block 1 4 0.6708575 0.0908683 0.0454341 0.1445917
0 surf_area_equated Block 2 6 0.6668499 0.0915880 0.0373906 0.0961157
0 surf_area_equated Block 3 6 0.6984359 0.0952658 0.0388921 0.0999753
equated dot_size_equated Block 1 6 1.0000000 0.0000000 0.0000000 0.0000000
equated dot_size_equated Block 2 5 1.0000000 0.0000000 0.0000000 0.0000000
equated dot_size_equated Block 3 5 1.0000000 0.0000000 0.0000000 0.0000000
Convex_Hull numRatio block N ch_ratio sd se ci
0 1.5 Block 1 2 1.0361673 0.0213754 0.0151147 0.1920506
0 1.5 Block 2 2 1.1218331 0.1491142 0.1054396 1.3397377
0 1.5 Block 3 2 1.1204861 0.1389661 0.0982639 1.2485611
0 2.0 Block 1 2 1.2134755 0.0763199 0.0539663 0.6857072
0 2.0 Block 2 2 1.0622519 0.1916971 0.1355503 1.7223300
0 2.0 Block 3 2 1.2507815 0.0433537 0.0306557 0.3895172
0 2.5 Block 1 2 1.0251208 0.0901817 0.0637681 0.8102507
0 2.5 Block 2 2 1.1052550 0.0959146 0.0678219 0.8617587
0 2.5 Block 3 2 1.1968560 0.2281876 0.1613530 2.0501842
0 3.0 Block 1 2 1.1762620 0.3324611 0.2350855 2.9870448
0 3.0 Block 2 2 1.0627040 0.0817103 0.0577779 0.7341379
0 3.0 Block 3 2 1.3605877 0.2080373 0.1471046 1.8691409
equated 1.5 Block 1 2 1.0000236 0.0002631 0.0001861 0.0023643
equated 1.5 Block 2 2 1.0002090 0.0002956 0.0002090 0.0026558
equated 1.5 Block 3 2 1.0000000 0.0000000 0.0000000 0.0000000
equated 2.0 Block 1 2 0.9966185 0.0044610 0.0031544 0.0400808
equated 2.0 Block 2 2 1.0000377 0.0000533 0.0000377 0.0004788
equated 2.0 Block 3 2 1.0003913 0.0005261 0.0003720 0.0047270
equated 2.5 Block 1 2 1.0000000 0.0000000 0.0000000 0.0000000
equated 2.5 Block 2 2 1.0002474 0.0005274 0.0003729 0.0047381
equated 2.5 Block 3 2 0.9998243 0.0001421 0.0001005 0.0012765
equated 3.0 Block 1 2 1.0000000 0.0000000 0.0000000 0.0000000
equated 3.0 Block 2 2 0.9995685 0.0000513 0.0000363 0.0004607
equated 3.0 Block 3 2 1.0000000 0.0000000 0.0000000 0.0000000 
## # A tibble: 2 × 6
##   Surface_Area ts_ratio_mean ts_ratio_sd ts_ratio_min ts_ratio_max
##   <chr>                <dbl>       <dbl>        <dbl>        <dbl>
## 1 0                     1.36       0.990        0.332            3
## 2 equated               1          0            1                1
## # ℹ 1 more variable: ts_ratio_median <dbl>
## # A tibble: 2 × 6
##   Perimeter cont_ratio_mean cont_ratio_sd cont_ratio_min cont_ratio_max
##   <chr>               <dbl>         <dbl>          <dbl>          <dbl>
## 1 0                    1.87         0.571           1.22           3.00
## 2 equated              1            0               1              1   
## # ℹ 1 more variable: cont_ratio_median <dbl>
## # A tibble: 2 × 6
##   Avg_Dot_Size diam_ratio_mean diam_ratio_sd diam_ratio_min diam_ratio_max
##   <chr>                  <dbl>         <dbl>          <dbl>          <dbl>
## 1 0                      0.577         0.151          0.327          0.824
## 2 equated                1             0              1              1    
## # ℹ 1 more variable: diam_ratio_median <dbl>
## # A tibble: 2 × 6
##   Convex_Hull ch_ratio_mean ch_ratio_sd ch_ratio_min ch_ratio_max
##   <chr>               <dbl>       <dbl>        <dbl>        <dbl>
## 1 0                    1.14     0.152          0.927         1.51
## 2 equated              1.00     0.00137        0.993         1.00
## # ℹ 1 more variable: ch_ratio_median <dbl>

Correlations

There are weak correlations between numerical ratio and convex hull and surface area, but moderate between perimeter (cont_ratio) and dot size (diam_ratio)

## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$ch_ratio
## t = 0.76104, df = 46, p-value = 0.4505
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1782742  0.3834931
## sample estimates:
##       cor 
## 0.1115088
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$ts_ratio
## t = 1.2251, df = 46, p-value = 0.2268
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1120413  0.4396805
## sample estimates:
##       cor 
## 0.1777521
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$cont_ratio
## t = 2.9892, df = 46, p-value = 0.004479
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1345886 0.6167597
## sample estimates:
##       cor 
## 0.4033006
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$diam_ratio
## t = -2.0989, df = 46, p-value = 0.04135
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.53483794 -0.01254809
## sample estimates:
##        cor 
## -0.2956288
## Warning: A numeric `legend.position` argument in `theme()` was deprecated in ggplot2
## 3.5.0.
## ℹ Please use the `legend.position.inside` argument of `theme()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Four year old’s stimulus schedule

Pivot Table - Spatial Features

This pivot table shows that there are not duplicated trials (see criterion 2). There should not be 2s in any block, except for the total row

Pivot Table - Side Conditions

This pivot table shows that left and right are balanced by side within each ratio and within each block (criterion 3)

Descriptive stats

Values between blocks are roughly similar

Surface_Area threefeat_num block N ts_ratio sd se ci
0 perimeter_equated Block 1 4 0.5915147 0.1748875 0.0874437 0.2782850
0 perimeter_equated Block 2 5 0.5732915 0.1545943 0.0691367 0.1919542
0 perimeter_equated Block 3 7 0.6063682 0.1733434 0.0655176 0.1603159
0 dot_size_equated Block 1 6 1.6666667 0.4915960 0.2006932 0.5158984
0 dot_size_equated Block 2 5 1.9500000 0.5700877 0.2549510 0.7078574
0 dot_size_equated Block 3 5 1.8500000 0.4873397 0.2179449 0.6051122
equated surf_area_equated Block 1 6 1.0000000 0.0000000 0.0000000 0.0000000
equated surf_area_equated Block 2 6 1.0000000 0.0000000 0.0000000 0.0000000
equated surf_area_equated Block 3 4 1.0000000 0.0000000 0.0000000 0.0000000
Perimeter threefeat_num block N cont_ratio sd se ci
0 surf_area_equated Block 1 6 1.386794 0.1879951 0.0767487 0.1972887
0 surf_area_equated Block 2 6 1.281919 0.1839883 0.0751129 0.1930839
0 surf_area_equated Block 3 4 1.335546 0.2005059 0.1002530 0.3190497
0 dot_size_equated Block 1 6 1.665770 0.4915435 0.2006718 0.5158433
0 dot_size_equated Block 2 5 1.947637 0.5665855 0.2533848 0.7035088
0 dot_size_equated Block 3 5 1.851074 0.4903520 0.2192921 0.6088524
equated perimeter_equated Block 1 4 1.000000 0.0000000 0.0000000 0.0000000
equated perimeter_equated Block 2 5 1.000000 0.0000000 0.0000000 0.0000000
equated perimeter_equated Block 3 7 1.000000 0.0000000 0.0000000 0.0000000
Avg_Dot_Size threefeat_num block N diam_ratio sd se ci
0 perimeter_equated Block 1 4 0.5965074 0.1880116 0.0940058 0.2991684
0 perimeter_equated Block 2 5 0.5774547 0.1619330 0.0724186 0.2010663
0 perimeter_equated Block 3 7 0.6009113 0.1740842 0.0657976 0.1610010
0 surf_area_equated Block 1 6 0.7302612 0.1212461 0.0494985 0.1272400
0 surf_area_equated Block 2 6 0.7949973 0.1002257 0.0409170 0.1051805
0 surf_area_equated Block 3 4 0.7488566 0.1225625 0.0612812 0.1950243
equated dot_size_equated Block 1 6 1.0000000 0.0000000 0.0000000 0.0000000
equated dot_size_equated Block 2 5 1.0000000 0.0000000 0.0000000 0.0000000
equated dot_size_equated Block 3 5 1.0000000 0.0000000 0.0000000 0.0000000
Convex_Hull numRatio block N ch_ratio sd se ci
0 1.25 Block 1 2 1.0080985 0.1010412 0.0714469 0.9078194
0 1.25 Block 2 2 1.1080679 0.0425023 0.0300537 0.3818682
0 1.25 Block 3 2 1.1033307 0.1386093 0.0980116 1.2453550
0 1.50 Block 1 2 1.0386760 0.0937090 0.0662622 0.8419416
0 1.50 Block 2 2 0.8106436 0.0857630 0.0606436 0.7705495
0 1.50 Block 3 2 0.9698836 0.0216914 0.0153381 0.1948892
0 2.00 Block 1 2 1.0785958 0.0920403 0.0650823 0.8269493
0 2.00 Block 2 2 1.1083766 0.1956941 0.1383766 1.7582417
0 2.00 Block 3 2 1.0225569 0.2833160 0.2003347 2.5454934
0 2.50 Block 1 2 1.4153646 0.1749353 0.1236979 1.5717311
0 2.50 Block 2 2 1.1736598 0.1361589 0.0962788 1.2233388
0 2.50 Block 3 2 1.2298851 0.1462980 0.1034483 1.3144350
equated 1.25 Block 1 2 0.9999331 0.0006157 0.0004354 0.0055318
equated 1.25 Block 2 2 1.0002404 0.0005157 0.0003647 0.0046335
equated 1.25 Block 3 2 1.0000898 0.0001270 0.0000898 0.0011413
equated 1.50 Block 1 2 1.0000235 0.0000333 0.0000235 0.0002988
equated 1.50 Block 2 2 1.0000248 0.0000351 0.0000248 0.0003155
equated 1.50 Block 3 2 0.9997887 0.0002988 0.0002113 0.0026842
equated 2.00 Block 1 2 1.0000355 0.0000502 0.0000355 0.0004510
equated 2.00 Block 2 2 0.9995051 0.0000314 0.0000222 0.0002824
equated 2.00 Block 3 2 1.0003577 0.0005058 0.0003577 0.0045446
equated 2.50 Block 1 2 1.0001601 0.0002264 0.0001601 0.0020342
equated 2.50 Block 2 2 1.0001016 0.0001436 0.0001016 0.0012903
equated 2.50 Block 3 2 0.9997024 0.0004209 0.0002976 0.0037813 
## # A tibble: 2 × 6
##   Surface_Area ts_ratio_mean ts_ratio_sd ts_ratio_min ts_ratio_max
##   <chr>                <dbl>       <dbl>        <dbl>        <dbl>
## 1 0                     1.20       0.718        0.397          2.5
## 2 equated               1          0            1              1  
## # ℹ 1 more variable: ts_ratio_median <dbl>
## # A tibble: 2 × 6
##   Perimeter cont_ratio_mean cont_ratio_sd cont_ratio_min cont_ratio_max
##   <chr>               <dbl>         <dbl>          <dbl>          <dbl>
## 1 0                    1.57         0.440           1.11           2.51
## 2 equated              1            0               1              1   
## # ℹ 1 more variable: cont_ratio_median <dbl>
## # A tibble: 2 × 6
##   Avg_Dot_Size diam_ratio_mean diam_ratio_sd diam_ratio_min diam_ratio_max
##   <chr>                  <dbl>         <dbl>          <dbl>          <dbl>
## 1 0                      0.676         0.161          0.393          0.938
## 2 equated                1             0              1              1    
## # ℹ 1 more variable: diam_ratio_median <dbl>
## # A tibble: 2 × 6
##   Convex_Hull ch_ratio_mean ch_ratio_sd ch_ratio_min ch_ratio_max
##   <chr>               <dbl>       <dbl>        <dbl>        <dbl>
## 1 0                    1.09    0.178           0.75          1.54
## 2 equated              1.00    0.000329        0.999         1.00
## # ℹ 1 more variable: ch_ratio_median <dbl>

Correlations

There are weak correlations between numerical ratio and convex hull and surface area, but moderate between perimeter (cont_ratio) and dot size (diam_ratio)

## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$ch_ratio
## t = 2.579, df = 46, p-value = 0.01317
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.07929453 0.58089317
## sample estimates:
##       cor 
## 0.3554215
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$ts_ratio
## t = 1.3015, df = 46, p-value = 0.1996
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1010902  0.4485724
## sample estimates:
##       cor 
## 0.1884576
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$cont_ratio
## t = 3.827, df = 46, p-value = 0.0003898
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2409308 0.6805353
## sample estimates:
##       cor 
## 0.4914242
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$diam_ratio
## t = -3.2162, df = 46, p-value = 0.00238
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6352613 -0.1643361
## sample estimates:
##        cor 
## -0.4284643
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Five year old’s stimulus schedule

Pivot Table - Spatial Features

This pivot table shows that there are not duplicated trials (see criterion 2). There should not be 2s in any block, except for the total row

Pivot Table - Side Conditions

This pivot table shows that left and right are balanced by side within each ratio and within each block (criterion 3)

Descriptive stats

Values between blocks are roughly similar

Surface_Area threefeat_num block N ts_ratio sd se ci
0 perimeter_equated Block 1 5 0.6960457 0.1364216 0.0610096 0.1693898
0 perimeter_equated Block 2 6 0.6879983 0.1585332 0.0647209 0.1663704
0 perimeter_equated Block 3 5 0.7291996 0.1514249 0.0677193 0.1880189
0 dot_size_equated Block 1 4 1.4791667 0.3750000 0.1875000 0.5967087
0 dot_size_equated Block 2 6 1.4321800 0.3165587 0.1292345 0.3322080
0 dot_size_equated Block 3 6 1.5294118 0.3806523 0.1554007 0.3994701
equated surf_area_equated Block 1 7 1.0000000 0.0000000 0.0000000 0.0000000
equated surf_area_equated Block 2 4 1.0000000 0.0000000 0.0000000 0.0000000
equated surf_area_equated Block 3 5 1.0000000 0.0000000 0.0000000 0.0000000
Perimeter threefeat_num block N cont_ratio sd se ci
0 surf_area_equated Block 1 7 1.210772 0.1462943 0.0552940 0.1352996
0 surf_area_equated Block 2 4 1.210699 0.1538857 0.0769429 0.2448665
0 surf_area_equated Block 3 5 1.209676 0.1280824 0.0572802 0.1590353
0 dot_size_equated Block 1 4 1.481770 0.3792876 0.1896438 0.6035312
0 dot_size_equated Block 2 6 1.432343 0.3134727 0.1279747 0.3289694
0 dot_size_equated Block 3 6 1.527121 0.3838672 0.1567131 0.4028439
equated perimeter_equated Block 1 5 1.000000 0.0000000 0.0000000 0.0000000
equated perimeter_equated Block 2 6 1.000000 0.0000000 0.0000000 0.0000000
equated perimeter_equated Block 3 5 1.000000 0.0000000 0.0000000 0.0000000
Avg_Dot_Size threefeat_num block N diam_ratio sd se ci
0 perimeter_equated Block 1 5 0.6961677 0.1207576 0.0540044 0.1499404
0 perimeter_equated Block 2 6 0.6881884 0.1626055 0.0663834 0.1706440
0 perimeter_equated Block 3 5 0.7360039 0.1482116 0.0662822 0.1840290
0 surf_area_equated Block 1 7 0.8491564 0.1071139 0.0404853 0.0990638
0 surf_area_equated Block 2 4 0.8276720 0.0895263 0.0447631 0.1424562
0 surf_area_equated Block 3 5 0.8390951 0.0945888 0.0423014 0.1174475
equated dot_size_equated Block 1 4 1.0000000 0.0000000 0.0000000 0.0000000
equated dot_size_equated Block 2 6 1.0000000 0.0000000 0.0000000 0.0000000
equated dot_size_equated Block 3 6 1.0000000 0.0000000 0.0000000 0.0000000
Convex_Hull numRatio block N ch_ratio sd se ci
0 1.17 Block 1 2 1.1458028 0.1022110 0.0722741 0.9183291
0 1.17 Block 2 2 1.0411961 0.0552888 0.0390951 0.4967499
0 1.17 Block 3 2 1.1344989 0.0321832 0.0227569 0.2891542
0 1.25 Block 1 2 0.9353226 0.0948770 0.0670882 0.8524364
0 1.25 Block 2 2 0.9614341 0.0584632 0.0413397 0.5252707
0 1.25 Block 3 2 1.1053120 0.2533626 0.1791544 2.2763726
0 1.50 Block 1 2 1.2020843 0.0575542 0.0406969 0.5171037
0 1.50 Block 2 2 0.9477903 0.0223520 0.0158052 0.2008243
0 1.50 Block 3 2 1.1044432 0.1324961 0.0936889 1.1904299
0 2.00 Block 1 2 1.0594021 0.0474557 0.0335563 0.4263726
0 2.00 Block 2 2 0.9858172 0.1273336 0.0900385 1.1440470
0 2.00 Block 3 2 1.5845542 0.5777303 0.4085170 5.1907009
equated 1.17 Block 1 2 0.9997531 0.0000958 0.0000678 0.0008610
equated 1.17 Block 2 2 1.0001517 0.0005421 0.0003833 0.0048709
equated 1.17 Block 3 2 1.0003244 0.0004588 0.0003244 0.0041219
equated 1.25 Block 1 2 0.9996477 0.0004605 0.0003256 0.0041374
equated 1.25 Block 2 2 1.0001167 0.0002686 0.0001900 0.0024136
equated 1.25 Block 3 2 1.0002204 0.0004195 0.0002966 0.0037690
equated 1.50 Block 1 2 0.9999812 0.0006313 0.0004464 0.0056723
equated 1.50 Block 2 2 0.9996234 0.0000019 0.0000013 0.0000170
equated 1.50 Block 3 2 0.9998978 0.0003207 0.0002268 0.0028812
equated 2.00 Block 1 2 0.9997917 0.0000628 0.0000444 0.0005644
equated 2.00 Block 2 2 0.9999457 0.0004340 0.0003069 0.0038996
equated 2.00 Block 3 2 0.9999023 0.0002217 0.0001568 0.0019922 
## # A tibble: 2 × 6
##   Surface_Area ts_ratio_mean ts_ratio_sd ts_ratio_min ts_ratio_max
##   <chr>                <dbl>       <dbl>        <dbl>        <dbl>
## 1 0                     1.09       0.468        0.498            2
## 2 equated               1          0            1                1
## # ℹ 1 more variable: ts_ratio_median <dbl>
## # A tibble: 2 × 6
##   Perimeter cont_ratio_mean cont_ratio_sd cont_ratio_min cont_ratio_max
##   <chr>               <dbl>         <dbl>          <dbl>          <dbl>
## 1 0                    1.35         0.286           1.08           2.01
## 2 equated              1            0               1              1   
## # ℹ 1 more variable: cont_ratio_median <dbl>
## # A tibble: 2 × 6
##   Avg_Dot_Size diam_ratio_mean diam_ratio_sd diam_ratio_min diam_ratio_max
##   <chr>                  <dbl>         <dbl>          <dbl>          <dbl>
## 1 0                      0.773         0.135            0.5          0.947
## 2 equated                1             0                1            1    
## # ℹ 1 more variable: diam_ratio_median <dbl>
## # A tibble: 2 × 6
##   Convex_Hull ch_ratio_mean ch_ratio_sd ch_ratio_min ch_ratio_max
##   <chr>               <dbl>       <dbl>        <dbl>        <dbl>
## 1 0                    1.10    0.222           0.868         1.99
## 2 equated              1.00    0.000350        0.999         1.00
## # ℹ 1 more variable: ch_ratio_median <dbl>

Correlations

There are weak correlations between numerical ratio and convex hull and surface area, but moderate between perimeter (cont_ratio) and dot size (diam_ratio)

## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$ch_ratio
## t = 1.2724, df = 46, p-value = 0.2096
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1052593  0.4452001
## sample estimates:
##       cor 
## 0.1843901
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$ts_ratio
## t = 1.1427, df = 46, p-value = 0.2591
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1238455  0.4299732
## sample estimates:
##       cor 
## 0.1661353
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$cont_ratio
## t = 4.3119, df = 46, p-value = 8.468e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2977620 0.7120897
## sample estimates:
##       cor 
## 0.5365059
## 
##  Pearson's product-moment correlation
## 
## data:  trials$numRatio and trials$diam_ratio
## t = -3.7201, df = 46, p-value = 0.0005404
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6730701 -0.2279126
## sample estimates:
##        cor 
## -0.4809049
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Differences between Ages

To check whether there were differences in the strength of the relationship between numerical ratio and the perceptual features, I ran a linear model with the perceptual feature ratio as the dependent variable and age and numerical ratio, and their interaction as predictors. If there are differences in the strength between ages, we should observe an interaction between numerical ratio and age. There were no main effects of age or interactions, suggesting that the strength is similar across the three stimulus schedules.

## 
## Call:
## lm(formula = ch_ratio ~ numRatio * age, data = trials)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.28744 -0.07594 -0.03074  0.02124  0.90023 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.05454    0.22444   4.698  6.2e-06 ***
## numRatio     -0.03060    0.11399  -0.268    0.789    
## age          -0.03091    0.05543  -0.558    0.578    
## numRatio:age  0.02540    0.03039   0.836    0.405    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1398 on 140 degrees of freedom
## Multiple R-squared:  0.05075,    Adjusted R-squared:  0.03041 
## F-statistic: 2.495 on 3 and 140 DF,  p-value: 0.06243
## 
## Call:
## lm(formula = ts_ratio ~ numRatio * age, data = trials)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1053 -0.3867 -0.1035  0.2939  1.5632 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)   0.52055    0.99067   0.525    0.600
## numRatio      0.33940    0.50316   0.675    0.501
## age           0.04899    0.24468   0.200    0.842
## numRatio:age -0.02766    0.13412  -0.206    0.837
## 
## Residual standard error: 0.6171 on 140 degrees of freedom
## Multiple R-squared:  0.04606,    Adjusted R-squared:  0.02562 
## F-statistic: 2.253 on 3 and 140 DF,  p-value: 0.08485
## 
## Call:
## lm(formula = cont_ratio ~ numRatio * age, data = trials)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.91060 -0.20383 -0.03662  0.15825  1.09390 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)   0.63050    0.67972   0.928    0.355
## numRatio      0.41374    0.34522   1.198    0.233
## age          -0.01786    0.16788  -0.106    0.915
## numRatio:age  0.01027    0.09202   0.112    0.911
## 
## Residual standard error: 0.4234 on 140 degrees of freedom
## Multiple R-squared:  0.2694, Adjusted R-squared:  0.2537 
## F-statistic: 17.21 on 3 and 140 DF,  p-value: 1.441e-09
## 
## Call:
## lm(formula = diam_ratio ~ numRatio * age, data = trials)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.30005 -0.12387 -0.03257  0.13099  0.37551 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.760791   0.297454   2.558   0.0116 *
## numRatio      0.008551   0.151075   0.057   0.9549  
## age           0.083457   0.073467   1.136   0.2579  
## numRatio:age -0.045813   0.040271  -1.138   0.2572  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1853 on 140 degrees of freedom
## Multiple R-squared:  0.2055, Adjusted R-squared:  0.1884 
## F-statistic: 12.07 on 3 and 140 DF,  p-value: 4.496e-07
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'