ManyNumbers: W reliability

This file combines data from three sites: Indiana University, Lafayette University, and University College Dublin. The mean age of participants was 3.81 (SD = 0.75). Number of participants by age group:

	IU	laffayette	ucd
3	11	8	12
4	2	8	23
5	6	6	4

Note: There are 4 two-year-olds in the 3-year-old age group.
Participants completed the full battery: give-n task, highest count task, dot comparison task, and a visual memory task.

Eight participants were removed because of experimenter errors (age entered in AMS task did not match the age calculated using DOB or reported in months)

Accuracy

Participants saw different numerical ratios depending on their age:

Three-year-olds saw 3.0, 2.5, 2.0, 1.5
Four-year-olds saw 2.5, 2.0, 1.5, 1.25
Five-year-olds saw 2.0, 1.5, 1.25, 1.17

Accuracy across all trials was: 0.59 (0.13).

The number of participants with accuracy equal or above 0.6 is 6, 15, 14, for 3-, 4-, and 5-year-olds respectively. Typically, w can only be obtained for participants with accuracy above 0.6

Histograms

age	N	accuracy	sd	se	ci
3	31	0.5188172	0.1008291	0.0181094	0.0369844
4	33	0.5928030	0.1064962	0.0185386	0.0377619
5	16	0.7109375	0.1226339	0.0306585	0.0653470

Reliability

## 
##  Pearson's product-moment correlation
## 
## data:  ams_acc_reliability$accuracy_even and ams_acc_reliability$accuracy_odd
## t = 5.5204, df = 78, p-value = 4.276e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3512242 0.6715477
## sample estimates:
##       cor 
## 0.5300381

## $estimate
##               accuracy_even accuracy_odd       age
## accuracy_even     1.0000000    0.4016670 0.3974636
## accuracy_odd      0.4016670    1.0000000 0.1906663
## age               0.3974636    0.1906663 1.0000000
## 
## $p.value
##               accuracy_even accuracy_odd          age
## accuracy_even  0.0000000000 0.0002435198 0.0002866681
## accuracy_odd   0.0002435198 0.0000000000 0.0923467938
## age            0.0002866681 0.0923467938 0.0000000000
## 
## $statistic
##               accuracy_even accuracy_odd      age
## accuracy_even      0.000000     3.848732 3.800850
## accuracy_odd       3.848732     0.000000 1.704357
## age                3.800850     1.704357 0.000000
## 
## $n
## [1] 80
## 
## $gp
## [1] 1
## 
## $method
## [1] "pearson"

## 
##  Pearson's product-moment correlation
## 
## data:  .$accuracy_even and .$accuracy_odd
## t = 1.689, df = 29, p-value = 0.1019
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.0616009  0.5909455
## sample estimates:
##       cor 
## 0.2992716

## 
##  Pearson's product-moment correlation
## 
## data:  .$accuracy_even and .$accuracy_odd
## t = 2.881, df = 31, p-value = 0.007133
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1380293 0.6934617
## sample estimates:
##       cor 
## 0.4595612

## 
##  Pearson's product-moment correlation
## 
## data:  .$accuracy_even and .$accuracy_odd
## t = 2.0515, df = 14, p-value = 0.05941
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.01960455  0.78854976
## sample estimates:
##      cor 
## 0.480773

Accuracy - Overlapping Trials

To compare accuracy across age groups, we used the averaged accuracy on overlapping trials (2.0 and 1.5 ratio).

Histograms

age	N	accuracy_overlap	sd	se	ci
3	31	0.5107527	0.1212243	0.0217725	0.0444654
4	33	0.6010101	0.1126881	0.0196165	0.0399575
5	16	0.7812500	0.1649214	0.0412304	0.0878804

Reliability for DeWind Method - Full Model

The visual magnitudes were added to the Psychopy output files, and files for even and odd trials were created.
Code: /Volumes/BL-PSY-gunderson_lab/Main/Studies/2023_manynumbers/scripts/mn_weberfraction_firststep_082224.R
W fraction was calculated using code from DeWind et al. (2015) and considering the two continuous covariates (space [convex hull] and size [surface area]) for all the 48 trials.
Code: /Volumes/BL-PSY-gunderson_lab/Main/Studies/2023_manynumbers/scripts/mn_scripts/mn_dewind_weberfraction_042324.m
/Volumes/BL-PSY-gunderson_lab/Main/Studies/2023_manynumbers/2024_iu_pilot/scripts/mn_w_secondstep.m
W fraction was calculated for odd and even trials.
For the split-half reliability, only w greater than 0 and smaller or equal than 3 were considered.
Participants with w within the range (all trials):

Var1	Freq
3	17
4	18
5	14

Participants with w within the range (intersection between even and odd trials):

Var1	Freq
3	11
4	13
5	12

Histograms

Reliablity

w_data_wfraction_reliability %>%
  subset(w_even<= thr & w_even > 0) %>%
  subset(w_odd <= thr & w_odd > 0) %>%
  ggplot(aes(x=w_even, y=w_odd)) +
  geom_smooth(method=lm, se=F, fullrange=F, alpha = .1, color = "black")+
  geom_smooth(method=lm, se=T, fullrange=F, alpha = .1, aes(color =as.factor(age)))+
  geom_point(aes(color =as.factor(age))) + 
  xlab("Weber Fraction\n(Even trials)")+
  ylab("Weber Fraction\n(Odd trials)")+
  #scale_shape_manual(values=c(3, 16, 17))+ 
  theme_bw()+
  #scale_color_manual(values = c("#0186C7","#E96A01","#FED602"))+
  scale_y_continuous(breaks=seq(0, 2., .5), limits=c(0,2))+
  scale_x_continuous(breaks=seq(0, 2., .5), limits=c(0,2))+
  theme(legend.position = c(.9, .85),
        axis.title.x=element_text(size=size_text),
        axis.text.x =  element_text(size=size_text),
        #axis.title.x =  element_text(size = size_text),
        panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_rect(fill = "white", colour = "grey50"),
        strip.background =element_rect(fill="#f0f0f0"),
        strip.text = element_text(size = size_text),
        axis.text.y =  element_text(size=size_text),
        axis.title.y =  element_text(size=size_text),
        legend.text=element_text(size=size_text))

w_data_wfraction_reliability %>%
  subset(w_even<= thr & w_even > 0) %>%
  subset(w_odd <= thr & w_odd > 0) %>%
  {cor.test(.$w_even, .$w_odd)}

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_even and .$w_odd
## t = -0.065477, df = 34, p-value = 0.9482
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3385154  0.3184822
## sample estimates:
##         cor 
## -0.01122844

w_data_wfraction_reliability %>%
  subset(w_even<= thr & w_even > 0) %>%
  subset(w_odd <= thr & w_odd > 0) %>%
  {pcor(dplyr::select(., w_odd, w_even, age))}

## $estimate
##              w_odd      w_even        age
## w_odd   1.00000000 -0.06785315 -0.1551190
## w_even -0.06785315  1.00000000 -0.3710207
## age    -0.15511896 -0.37102072  1.0000000
## 
## $p.value
##            w_odd     w_even        age
## w_odd  0.0000000 0.69853942 0.37358903
## w_even 0.6985394 0.00000000 0.02821668
## age    0.3735890 0.02821668 0.00000000
## 
## $statistic
##             w_odd     w_even        age
## w_odd   0.0000000 -0.3906871 -0.9020087
## w_even -0.3906871  0.0000000 -2.2951705
## age    -0.9020087 -2.2951705  0.0000000
## 
## $n
## [1] 36
## 
## $gp
## [1] 1
## 
## $method
## [1] "pearson"

# w_data_wfraction_reliability %>%
#   subset(w_all <= thr & w_all > 0) %>%
#   subset(w_odd <= thr & w_odd > 0) %>%
#   {cor.test(.$w_odd, .$w_all)}
# 
# w_data_wfraction_reliability %>%
#   subset(w_all <= thr & w_all > 0) %>%
#   subset(w_even <= thr & w_even > 0) %>%
#   {cor.test(.$w_even, .$w_all)}

Continuous Dimensions

Histograms

graph_w_size = w_data_wfraction_reliability %>%
  #subset(w_all<= thr & w_all > 0) %>%
  ggplot(aes(y=w_size, x =as.factor(age))) + 
  geom_boxplot(color="black", fill="white")+
  #ylab("Frequency")+  
  xlab("Weber Fraction\n(Size)")+
  #facet_grid(.~(age))+
  scale_y_continuous(breaks=seq(-350, 150, 50), limits=c(-350,150))
  # theme(legend.position="bottom",
  #       axis.title.x=element_text(size=size_text),
  #       axis.text.x =  element_text(size=size_text),
  #       #axis.title.x =  element_text(size = size_text),
  #       panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
  #       panel.background = element_rect(fill = "white", colour = "grey50"),
  #       strip.background =element_rect(fill="#f0f0f0"),
  #       strip.text = element_text(size = size_text),
  #       axis.text.y =  element_text(size=size_text),
  #       axis.title.y =  element_text(size=size_text),
  #       legend.text=element_text(size=size_text)) 
  #annotate("text", x=3, y=10, label= paste("n =", (n_w_all), sep = "")) 
#graph_w_size

graph_w_space = w_data_wfraction_reliability %>%
  #subset(w_all<= thr & w_all > 0) %>%
  ggplot(aes(y=w_space, x =as.factor(age))) + 
  geom_boxplot(color="black", fill="white")+
  #ylab("Frequency")+  
   xlab("Weber Fraction\n(Space)")+
  #facet_grid(.~(age))+
  scale_y_continuous(breaks=seq(-40, 60, 20), limits=c(-40,60))
  # theme(legend.position="bottom",
  #       axis.title.x=element_text(size=size_text),
  #       axis.text.x =  element_text(size=size_text),
  #       #axis.title.x =  element_text(size = size_text),
  #       panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
  #       panel.background = element_rect(fill = "white", colour = "grey50"),
  #       strip.background =element_rect(fill="#f0f0f0"),
  #       strip.text = element_text(size = size_text),
  #       axis.text.y =  element_text(size=size_text),
  #       axis.title.y =  element_text(size=size_text),
  #       legend.text=element_text(size=size_text)) 
  #annotate("text", x=3, y=10, label= paste("n =", (n_w_all), sep = "")) 
#graph_w_space
multiplot(graph_w_size,graph_w_space, cols =1)

Do participants with extreme numerical w’s have resonable w’s for continuous variables?

n_w_size = w_data_wfraction_reliability %>%
  subset(w_all> thr | w_all < 0) %>%
  subset(w_size <= thr & w_size > 0) %>%
  nrow()
n_w_size

## [1] 2

n_w_space = w_data_wfraction_reliability %>%
  subset(w_all> thr | w_all < 0) %>%
  subset(w_space <= thr & w_space > 0) %>%
  nrow()
n_w_space

## [1] 1

Relations with Number modulation

To examine te relations between size and space with number, we needed to use the beta values instead of the w’s, as to calculate w’s, the DeWind method transforms the betas using a 1/(x) function, which doesn’t allow to combine negative and positive values.

Scatter plots

In Starr et al. (2017), the relation between size and number was -.07 and -.16 for the four and the six-year-old group, respectively. The relation between space and number was .64 and .29, for the four and the six- year-old groups, respectively

 w_data_wfraction_reliability %>%
  #subset(w_space >= -15 & w_space<= 15) %>%
  subset(w_all<= thr & w_all > 0) %>%
  #subset(w_all> thr | w_all < 0) %>%
  {cor.test(.$num_all, .$size_all)}

## 
##  Pearson's product-moment correlation
## 
## data:  .$num_all and .$size_all
## t = -1.9712, df = 47, p-value = 0.05461
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.517329669  0.005275101
## sample estimates:
##        cor 
## -0.2763314

 w_data_wfraction_reliability %>%
  #subset(w_space >= -15 & w_space<= 15) %>%
  #subset(w_all> thr | w_all < 0) %>%
   subset(w_all<= thr & w_all > 0) %>%
{cor.test(.$num_all, .$space_all)}

## 
##  Pearson's product-moment correlation
## 
## data:  .$num_all and .$space_all
## t = 5.0291, df = 47, p-value = 7.623e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.372199 0.748236
## sample estimates:
##       cor 
## 0.5914896

Age differences in the influence of continuous magnitudes

age_num = w_data_wfraction_reliability %>%
  subset(w_all<= thr & w_all > 0) %>%
  ggplot(aes(x=as.factor(age), y=num_all)) + 
  geom_dotplot(binaxis='y', stackdir='center')+
  #scale_y_continuous(breaks=seq(0, 1, .1), limits=c(0,1.1),trans = shift_trans(0), expand = c(0,0))+
  ylab("Number\n(Beta)")+
  xlab("Age")+
stat_summary(fun.data=mean_sdl, fun.args = list(mult=1), 
                 geom="pointrange", color="red")+
  theme_bw()

age_size = w_data_wfraction_reliability %>%
  subset(w_all<= thr & w_all > 0) %>%
  ggplot(aes(x=as.factor(age), y=size_all)) + 
  geom_dotplot(binaxis='y', stackdir='center')+
  #scale_y_continuous(breaks=seq(0, 1, .1), limits=c(0,1.1),trans = shift_trans(0), expand = c(0,0))+
  ylab("Size\n(Beta)")+
  xlab("Age")+
stat_summary(fun.data=mean_sdl, fun.args = list(mult=1), 
                 geom="pointrange", color="red")+
  theme_bw()


age_space =w_data_wfraction_reliability %>%
  subset(w_all<= thr & w_all > 0) %>%
  ggplot(aes(x=as.factor(age), y=space_all)) + 
  geom_dotplot(binaxis='y', stackdir='center')+
  #scale_y_continuous(breaks=seq(0, 1, .1), limits=c(0,1.1),trans = shift_trans(0), expand = c(0,0))+
  ylab("Space\n(Beta)")+
  xlab("Age")+
stat_summary(fun.data=mean_sdl, fun.args = list(mult=1), 
                 geom="pointrange", color="red")+
  theme_bw()

multiplot(age_num,age_size, age_space, cols = 1)

These results resamble the ones reported by Starr et al. (2017):

Reliability for DeWind Method - Num Only Model

W scores were calculated for all trials, even and odd, but only entering the numerical information into the model.
Reliability was also only calculated for values above zero and below or equal 3
Participants with w within the range (all trials):

Var1	Freq
3	5
4	19
5	15

Participants with w within the range (intersection between even and odd trials):

Var1	Freq
3	3
4	14
5	13

Histograms

ScatterPlots

w_data_wfraction_reliability %>%
  subset(w_odd_numonly<= thr & w_odd_numonly > 0) %>%
  subset(w_even_numonly <= thr & w_even_numonly > 0) %>%
  #{cor.test(.$w_all_numonly, .$weber_fraction_all)}
ggplot(aes(x=w_odd_numonly, y=w_even_numonly)) +
  geom_smooth(method=lm, se=F, fullrange=F, alpha = .1, color = "black")+
  geom_smooth(method=lm, se=F, fullrange=F, alpha = .1, aes(color =as.factor(age)))+
  geom_point(aes(color =as.factor(age))) + 
  xlab("Weber Fraction\n(Even trials)")+
  ylab("Weber Fraction\n(Odd trials)")+
  #scale_shape_manual(values=c(3, 16, 17))+ 
  theme_bw()+
  #scale_color_manual(values = c("#0186C7","#E96A01","#FED602"))+
  #scale_y_continuous(breaks=seq(0, 1, .1), limits=c(0,1.01),trans = shift_trans(0), expand = c(0,0))+
  #scale_x_continuous(breaks=seq(0, 1, .1), limits=c(0,1.01),trans = shift_trans(0), expand = c(0,0))+
  theme(legend.position="bottom",
        axis.title.x=element_text(size=size_text),
        axis.text.x =  element_text(size=size_text),
        #axis.title.x =  element_text(size = size_text),
        panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_rect(fill = "white", colour = "grey50"),
        strip.background =element_rect(fill="#f0f0f0"),
        strip.text = element_text(size = size_text),
        axis.text.y =  element_text(size=size_text),
        axis.title.y =  element_text(size=size_text),
        legend.text=element_text(size=size_text))

w_data_wfraction_reliability %>%
  subset(w_odd_numonly<= thr & w_odd_numonly > 0) %>%
  subset(w_even_numonly <= thr & w_even_numonly > 0) %>%
  {cor.test(.$w_even_numonly, .$w_odd_numonly)}

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_even_numonly and .$w_odd_numonly
## t = 3.8501, df = 28, p-value = 0.0006272
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2894201 0.7827081
## sample estimates:
##       cor 
## 0.5883433

w_data_wfraction_reliability %>%
  subset(w_odd_numonly<= thr & w_odd_numonly > 0) %>%
  subset(w_even_numonly <= thr & w_even_numonly > 0) %>%
  {pcor(dplyr::select(., w_even_numonly, w_odd_numonly, age))}

## $estimate
##                w_even_numonly w_odd_numonly        age
## w_even_numonly      1.0000000     0.2769199 -0.5173151
## w_odd_numonly       0.2769199     1.0000000 -0.3692227
## age                -0.5173151    -0.3692227  1.0000000
## 
## $p.value
##                w_even_numonly w_odd_numonly         age
## w_even_numonly    0.000000000    0.14586891 0.004055285
## w_odd_numonly     0.145868913    0.00000000 0.048707572
## age               0.004055285    0.04870757 0.000000000
## 
## $statistic
##                w_even_numonly w_odd_numonly       age
## w_even_numonly       0.000000      1.497480 -3.140995
## w_odd_numonly        1.497480      0.000000 -2.064406
## age                 -3.140995     -2.064406  0.000000
## 
## $n
## [1] 30
## 
## $gp
## [1] 1
## 
## $method
## [1] "pearson"

# w_data_wfraction_reliability %>%
#   subset(w_all_numonly <= thr & w_all_numonly > 0) %>%
#   subset(w_odd_numonly <= thr & w_odd_numonly > 0) %>%
#   {cor.test(.$w_odd_numonly, .$w_all_numonly)}
# 
# w_data_wfraction_reliability %>%
#   subset(w_all_numonly <= thr & w_all_numonly > 0) %>%
#   subset(w_even_numonly <= thr & w_even_numonly > 0) %>%
#   {cor.test(.$w_even_numonly, .$w_all_numonly)}

Reliability for Panamath Method - Full Model

W scores were calculated for all trials, even and odd.
Code: /Volumes/BL-PSY-gunderson_lab/Main/Studies/2023_manynumbers/2024_coretasks_reliability/Panamath Weber Fraction Calculation.Rmd
Reliability was also only calculated for values above zero and below or equal 3
Participants with w within the range (all trials):

Var1	Freq
3	8
4	21
5	15

Participants with w within the range (intersection between even and odd trials):

Var1	Freq
3	5
4	14
5	13

Histograms

ScatterPlots

w_data_wfraction_reliability %>%
  subset(weber_fraction_odd<= thr & weber_fraction_odd > 0) %>%
  subset(weber_fraction_even <= thr & weber_fraction_even > 0) %>%
  #{cor.test(.$w_all_numonly, .$weber_fraction_all)}
ggplot(aes(x=weber_fraction_odd, y=weber_fraction_even,color =as.factor(age))) +
  geom_smooth(method=lm, se=F, fullrange=F, alpha = .1, color = "black")+
  geom_smooth(method=lm, se=F, fullrange=F, alpha = .1, aes(color =as.factor(age)))+
  geom_point(aes(color =as.factor(age))) + 
  ylab("Weber Fraction\n(Even trials)")+
  xlab("Weber Fraction\n(Odd trials)")+
  #scale_shape_manual(values=c(3, 16, 17))+ 
  theme_bw()+
  #scale_color_manual(values = c("#0186C7","#E96A01","#FED602"))+
  #scale_y_continuous(breaks=seq(0, 1, .1), limits=c(0,1.01),trans = shift_trans(0), expand = c(0,0))+
  #scale_x_continuous(breaks=seq(0, 1, .1), limits=c(0,1.01),trans = shift_trans(0), expand = c(0,0))+
  theme(legend.position="bottom",
        axis.title.x=element_text(size=size_text),
        axis.text.x =  element_text(size=size_text),
        #axis.title.x =  element_text(size = size_text),
        panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_rect(fill = "white", colour = "grey50"),
        strip.background =element_rect(fill="#f0f0f0"),
        strip.text = element_text(size = size_text),
        axis.text.y =  element_text(size=size_text),
        axis.title.y =  element_text(size=size_text),
        legend.text=element_text(size=size_text))

w_data_wfraction_reliability %>%
  subset(weber_fraction_odd<= thr & weber_fraction_odd > 0) %>%
  subset(weber_fraction_even <= thr & weber_fraction_even > 0) %>%
  {cor.test(.$weber_fraction_even, .$weber_fraction_odd)}

## 
##  Pearson's product-moment correlation
## 
## data:  .$weber_fraction_even and .$weber_fraction_odd
## t = 6.1395, df = 30, p-value = 9.447e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.5373248 0.8688330
## sample estimates:
##       cor 
## 0.7462078

w_data_wfraction_reliability %>%
  subset(weber_fraction_odd<= thr & weber_fraction_odd > 0) %>%
  subset(weber_fraction_even <= thr & weber_fraction_even > 0) %>%
{pcor(dplyr::select(., weber_fraction_odd, weber_fraction_even, age))}

## $estimate
##                     weber_fraction_odd weber_fraction_even        age
## weber_fraction_odd           1.0000000           0.5155411 -0.2248067
## weber_fraction_even          0.5155411           1.0000000 -0.5027071
## age                         -0.2248067          -0.5027071  1.0000000
## 
## $p.value
##                     weber_fraction_odd weber_fraction_even         age
## weber_fraction_odd         0.000000000         0.002995181 0.224033790
## weber_fraction_even        0.002995181         0.000000000 0.003949085
## age                        0.224033790         0.003949085 0.000000000
## 
## $statistic
##                     weber_fraction_odd weber_fraction_even       age
## weber_fraction_odd            0.000000            3.240037 -1.242423
## weber_fraction_even           3.240037            0.000000 -3.131632
## age                          -1.242423           -3.131632  0.000000
## 
## $n
## [1] 32
## 
## $gp
## [1] 1
## 
## $method
## [1] "pearson"

# w_data_wfraction_reliability %>%
#   subset(w_all_numonly <= thr & w_all_numonly > 0) %>%
#   subset(w_odd_numonly <= thr & w_odd_numonly > 0) %>%
#   {cor.test(.$w_odd_numonly, .$w_all_numonly)}
# 
# w_data_wfraction_reliability %>%
#   subset(w_all_numonly <= thr & w_all_numonly > 0) %>%
#   subset(w_even_numonly <= thr & w_even_numonly > 0) %>%
#   {cor.test(.$w_even_numonly, .$w_all_numonly)}

Relations Between W Measures

## 
##  Pearson's product-moment correlation
## 
## data:  .$weber_fraction_all and .$w_all
## t = 1.6014, df = 34, p-value = 0.1185
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.06977444  0.54587320
## sample estimates:
##       cor 
## 0.2648322

## 
##  Pearson's product-moment correlation
## 
## data:  .$weber_fraction_all and .$w_all_numonly
## t = 24.116, df = 37, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9424413 0.9840832
## sample estimates:
##       cor 
## 0.9696321

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all and .$w_all_numonly
## t = 2.0719, df = 31, p-value = 0.04668
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.00619809 0.61806989
## sample estimates:
##      cor 
## 0.348765

Relations With Accuracy (All Trials)

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all and .$accuracy
## t = -2.5144, df = 47, p-value = 0.0154
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.57031114 -0.06990778
## sample estimates:
##        cor 
## -0.3443355

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all_numonly and .$accuracy
## t = -8.0594, df = 37, p-value = 1.156e-09
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.8896488 -0.6451336
## sample estimates:
##        cor 
## -0.7981805

## 
##  Pearson's product-moment correlation
## 
## data:  .$weber_fraction_all and .$accuracy
## t = -8.9879, df = 42, p-value = 2.455e-11
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.8929751 -0.6773665
## sample estimates:
##       cor 
## -0.811131

Relations With Cognitive Measures

Accuracy (All Trials and Overlapping Trials)

## 
##  Pearson's product-moment correlation
## 
## data:  .$accuracy_overlap and .$accuracy
## t = 21.566, df = 78, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8857935 0.9516295
## sample estimates:
##       cor 
## 0.9254046

Age

##   age  N age_months       sd        se       ci
## 1   3 31   40.77419 4.128839 0.7415614 1.514470
## 2   4 33   53.57576 3.699918 0.6440731 1.311934
## 3   5 16   64.06250 3.872445 0.9681113 2.063480

Figures

Analyses

## 
##  Pearson's product-moment correlation
## 
## data:  .$accuracy_overlap and .$age_months
## t = 7.3979, df = 78, p-value = 1.366e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.4918031 0.7552880
## sample estimates:
##       cor 
## 0.6421327

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all and .$age_months
## t = -3.6377, df = 47, p-value = 0.0006816
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6625854 -0.2159905
## sample estimates:
##        cor 
## -0.4687191

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all_numonly and .$age_months
## t = -5.3327, df = 37, p-value = 5.027e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.8069078 -0.4339728
## sample estimates:
##        cor 
## -0.6592249

## 
##  Pearson's product-moment correlation
## 
## data:  .$weber_fraction_all and .$age_months
## t = -5.2134, df = 42, p-value = 5.311e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7787675 -0.4053556
## sample estimates:
##        cor 
## -0.6268049

Give-N task

Figures - Accuracy

Analyses - Accuracy

## 
##  Pearson's product-moment correlation
## 
## data:  .$accuracy_overlap and .$given_accuracy
## t = 5.7999, df = 78, p-value = 1.349e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3743605 0.6859160
## sample estimates:
##       cor 
## 0.5489264

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all and .$given_accuracy
## t = -3.7973, df = 47, p-value = 0.0004188
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6739121 -0.2354146
## sample estimates:
##       cor 
## -0.484536

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all_numonly and .$given_accuracy
## t = -4.7165, df = 37, p-value = 3.375e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7778876 -0.3684923
## sample estimates:
##        cor 
## -0.6127658

## 
##  Pearson's product-moment correlation
## 
## data:  .$weber_fraction_all and .$given_accuracy
## t = -4.1656, df = 42, p-value = 0.0001512
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7217281 -0.2904454
## sample estimates:
##        cor 
## -0.5407023

Figures - Knower Levels

Highest Count task

Figures

Analyses

## 
##  Pearson's product-moment correlation
## 
## data:  .$accuracy_overlap and log(.$highestcount_score)
## t = 4.5934, df = 68, p-value = 1.942e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2841489 0.6475600
## sample estimates:
##       cor 
## 0.4866317

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all and log(.$highestcount_score)
## t = -3.0036, df = 43, p-value = 0.004435
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6326391 -0.1400202
## sample estimates:
##        cor 
## -0.4164382

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all_numonly and log(.$highestcount_score)
## t = -2.8377, df = 35, p-value = 0.007511
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6635183 -0.1261356
## sample estimates:
##       cor 
## -0.432479

## 
##  Pearson's product-moment correlation
## 
## data:  .$weber_fraction_all and log(.$highestcount_score)
## t = -3.1775, df = 39, p-value = 0.002905
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6679420 -0.1694708
## sample estimates:
##        cor 
## -0.4534779

Visual Memory task

Accuracy was calculated using the script below:
/Volumes/BL-PSY-gunderson_lab/Main/Studies/2023_manynumbers/2024_iu_pilot/scripts/mn_visualmemory_analyses_spring24.Rmd

Figures

Analyses

## 
##  Pearson's product-moment correlation
## 
## data:  .$accuracy_overlap and .$VisualMemoryTask
## t = 4.1078, df = 78, p-value = 9.775e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2226462 0.5870520
## sample estimates:
##       cor 
## 0.4217323

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all and .$VisualMemoryTask
## t = -2.9983, df = 47, p-value = 0.004329
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6128456 -0.1346807
## sample estimates:
##       cor 
## -0.400702

## 
##  Pearson's product-moment correlation
## 
## data:  .$w_all_numonly and .$VisualMemoryTask
## t = -4.4271, df = 37, p-value = 8.146e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7624147 -0.3351648
## sample estimates:
##        cor 
## -0.5884528

## 
##  Pearson's product-moment correlation
## 
## data:  .$weber_fraction_all and .$VisualMemoryTask
## t = -4.0641, df = 42, p-value = 0.0002067
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7153336 -0.2782946
## sample estimates:
##        cor 
## -0.5312804

ManyNumbers: W reliability

RAM

2024-09-15

Accuracy

Histograms

Reliability

Accuracy - Overlapping Trials

Histograms

Reliability for DeWind Method - Full Model

Histograms

Reliablity

Continuous Dimensions

Histograms

Do participants with extreme numerical w’s have resonable w’s for continuous variables?

Relations with Number modulation

Scatter plots

Age differences in the influence of continuous magnitudes

Reliability for DeWind Method - Num Only Model

Histograms

ScatterPlots

Reliability for Panamath Method - Full Model

Histograms

ScatterPlots

Relations Between W Measures

Relations With Accuracy (All Trials)

Relations With Cognitive Measures

Accuracy (All Trials and Overlapping Trials)

Age

Figures

Analyses

Give-N task

Figures - Accuracy

Analyses - Accuracy

Figures - Knower Levels

Highest Count task

Figures

Analyses

Visual Memory task

Figures

Analyses