After loading the data…

Descriptive statistics

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.6000  1.0000  0.8083  1.0000  1.0000

Categorization accuracy by Modality
Modality	mean_accuracy	sd
Auditory-Linguistic	0.8227	0.2689
Auditory-Non-Linguistic	0.8138	0.2704
Visual-Spatial	0.8356	0.2709
Visual-Temporal	0.7614	0.3039

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

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

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

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

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

Regression Results

Categorization

The model includes random intercepts for participants and stimuli length, as well as a by-participant slope for the effect of modality. (Since the model with maximal random effect structure failed to converge, we had to removed the by-length random slope for the effect of modality, which gave a singular fit)

Significant difference between the visual temporal vs. spatial tasks: accuracy in the temporal task is significantly lower than in the spatial task
Significant difference between the visual temporal task and the two auditory tasks: accuracy in the visual-temporal task is significantly lower than in the linguistic and non-linguistic tasks
No significant difference between the two auditory tasks

Categorization Accuracy
	Estimate	Std.Error	df	t-value	p-value
(Intercept)	0.8082	0.0285	12.5174	28.3901	0.0000
Auditory non-linguistic vs. linguistic	0.0090	0.0090	117.9908	0.9994	0.3197
Visual Temporal vs. Spatial	-0.0743	0.0194	117.4287	-3.8255	0.0002
Visual Temporal vs. Auditory	-0.0565	0.0135	117.8031	-4.1764	0.0001

Production

Deviation from category mode

We included the category length (TrueValue) as a fixed effect rather than a random effect, since the DV (response deviation) is affected by the category (people do different things for short and long productions).

The model includes random intercepts for participants as well as a by-participant slope for the interaction between modality and true value (maximal structure)

Significant intercept - there is significant deviation from category mode overall
Significant difference between the auditory linguistic and non-linguistic tasks: more deviation from mode in the linguistic task compared to the non-linguistic task
Significant difference between the visual temporal and the two auditory tasks: less deviation from mode in the visual temporal task compared to both auditory tasks
Significant effect of TrueValue: less deviation in productions for short categories (=more deviation in the long productions)

Deviation of gap between categories

The model includes random intercepts for participants.(No random effect of category’s true length since our measure is calculated over the two lengths. Also no by-participant slopes since each participant only has 1 data point per modality)

Significant intercept - there is significant gap deviation between categories - people do exaggerate the difference between short and long
No Significant difference between tasks: the gap deviation between categories is similar across modalities

Productions’ Deviation from Mean
	Estimate	Std.Error	df	t-value	p-value
(Intercept)	142.1060	6.1376	118.5127	23.1533	0.0000
Auditory linguistic vs. non-linguistic	31.6594	10.3759	117.8627	3.0512	0.0028
Visual Temporal vs. Spatial	9.5803	8.1911	118.1146	1.1696	0.2445
Visual Temporal vs. Auditory	-233.0142	9.6852	115.7515	-24.0589	0.0000
Category value (Short vs. Long)	-54.4384	6.8726	115.2528	-7.9211	0.0000
Cateogry X Modality (auditory inguistic vs. non-linguistic)	-3.5337	11.8203	117.1834	-0.2990	0.7655
Cateogry X Modality (visual temporal vs. spatial)	-2.3035	11.6538	112.6084	-0.1977	0.8437
Cateogry X Modality (visual temporal vs. auditory)	5.5065	9.7115	111.7781	0.5670	0.5718

## NOTE: Modality is not a high-order term in the model

## NOTE: TrueValue is not a high-order term in the model

Gap Deviation from Mean
	Estimate	Std.Error	df	t-value	p-value
(Intercept)	54.1317	6.9427	112.5875	7.7969	0.0000
Auditory linguistic vs. non-linguistic	4.2370	11.2363	347.8548	0.3771	0.7063
Visual Temporal vs. Spatial	2.7476	11.2208	348.8867	0.2449	0.8067
Visual Temporal vs. Auditory	-5.1152	9.7130	349.2320	-0.5266	0.5988

Relationship between Production and categorization

The model includes random intercepts for participants and true category length, as well as a by-participant random slope for the effect of modality. (Since the model with maximal random effect structure failed to converge, we had to removed the by-length random slope for the effect of modality, which gave a singular fit)

No significant effect of accuracy - participants’ production deviations are not predicted by their categorization accuracy
Significant difference between the visual temporal and the two auditory tasks: less deviation from mode in the visual temporal task compared to both auditory tasks [SAME AS THE PRODUCTION MODEL]

–> No support for either account (rule learning nor exemplar models)

## NOTE: Modality is not a high-order term in the model

## NOTE: Total_ACC is not a high-order term in the model

Relation between categorizatin accuracy and production deviation
	Estimate	Std.Error	df	t-value	p-value
(Intercept)	110.492787	35.25411	20.54376	3.1341822	0.005105266
Categorization Accuracy	4.830345	35.59260	248.21929	0.1357121	0.892158901
Auditory linguistic vs. non-linguistic	-49.158010	91.65236	135.67805	-0.5363529	0.592592980
Visual Temporal vs. Spatial	19.390243	29.04372	213.74264	0.6676225	0.505094752
Visual Temporal vs. Auditory	-202.088930	59.36338	241.11154	-3.4042692	0.000776829
Accuracy X Modality (auditory inguistic vs. non-linguistic)	95.684617	111.07695	136.07433	0.8614264	0.390518653
Accuracy X Modality (visual temporal vs. spatial)	-14.581673	36.40230	205.19209	-0.4005701	0.689153399
Cateogry X Accuracy (visual temporal vs. auditory)	-35.027705	72.51396	246.95414	-0.4830478	0.629489779

Correlation between modalities

categorization

Significant correlations between:

The two auditory tasks (linguistic and non-linguistic) - this is the highest correlation
The visual temporal task and the two auditory tasks - similar r between the visual temporal task and the linguistic/non-linguistic tasks
The visual spatial task and the non-linguistic task (this is a bit odd)

Non significant correlations between:

The two visual tasks (temporal and spatial) - really no connection whatsoever
The visual spatial task and the linguistic task

Summary:

Seems like the three temporal tasks and very much correlated, with the two auditory tasks more correlated with each other compared to the visual one (to be expected)
No correlation between the visual tasks (temp vs. spatial)
Odd result with respect to the correlation between spatial and non-linguistic

–> Suggests that distributional learning is more domain-general and unitary than sequential SL (or at least stimuli-type general in the sense of temporal stimuli being more similar)

Correlation Matrix - Categorization Accuracy Across Modalities
	Auditory Linguistic	Auditory Non-Linguistic	Visual Temporal	Visual Spatial
Auditory Linguistic	1.00000	0.51688	0.26814	0.14010
Auditory Non-Linguistic	0.51688	1.00000	0.24017	0.30125
Visual Temporal	0.26814	0.24017	1.00000	-0.00942
Visual Spatial	0.14010	0.30125	-0.00942	1.00000

## 
##  Pearson's product-moment correlation
## 
## data:  acc_mean$`Auditory Non-Linguistic` and acc_mean$`Auditory Linguistic`
## t = 6.503, df = 116, p-value = 0.000000002071
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3707599 0.6380269
## sample estimates:
##       cor 
## 0.5168789

## 
##  Pearson's product-moment correlation
## 
## data:  acc_mean$`Auditory Linguistic` and acc_mean$`Visual Temporal`
## t = 2.9978, df = 116, p-value = 0.003328
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.09183351 0.42814912
## sample estimates:
##       cor 
## 0.2681418

## 
##  Pearson's product-moment correlation
## 
## data:  acc_mean$`Auditory Non-Linguistic` and acc_mean$`Visual Temporal`
## t = 2.6647, df = 116, p-value = 0.008804
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.06210556 0.40341476
## sample estimates:
##       cor 
## 0.2401687

## 
##  Pearson's product-moment correlation
## 
## data:  acc_mean$`Auditory Linguistic` and acc_mean$`Visual Spatial`
## t = 1.524, df = 116, p-value = 0.1302
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.04171115  0.31293867
## sample estimates:
##       cor 
## 0.1401045

## 
##  Pearson's product-moment correlation
## 
## data:  acc_mean$`Auditory Non-Linguistic` and acc_mean$`Visual Spatial`
## t = 3.4026, df = 116, p-value = 0.0009168
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1274255 0.4571142
## sample estimates:
##       cor 
## 0.3012461

## 
##  Pearson's product-moment correlation
## 
## data:  acc_mean$`Visual Spatial` and acc_mean$`Visual Temporal`
## t = -0.10141, df = 116, p-value = 0.9194
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1898517  0.1716360
## sample estimates:
##          cor 
## -0.009415419

Production

Significant correlations between:

The two auditory tasks (linguistic and non-linguistic) - this is the highest correlation
The visual temporal task and linguistic task
The two visual tasks (spatial and temporal) - but it’s kinda weak

Non significant correlations between:

The visual temporal task and non-linguistic task
The visual spatial task and the two auditory tasks (linguistic and non-linguistic) - really no connection whatsoever

Summary:

Seems like the three temporal tasks and again quite correlated, with the two auditory tasks more correlated with each other compared to the visual one (to be expected)
the two visual tasks are correlated in production deviation (but not in categorization accuracy)

Correlation Matrix - Production Deviation Across Modalities
	Auditory Linguistic	Auditory Non-Linguistic	Visual Temporal	Visual Spatial
Auditory Linguistic	1.00000	0.44072	0.31121	0.05585
Auditory Non-Linguistic	0.44072	1.00000	0.12706	-0.06335
Visual Temporal	0.31121	0.12706	1.00000	0.18303
Visual Spatial	0.05585	-0.06335	0.18303	1.00000

## 
##  Pearson's product-moment correlation
## 
## data:  diff_mean$`Auditory Non-Linguistic` and diff_mean$`Auditory Linguistic`
## t = 5.288, df = 116, p-value = 0.0000005896
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2824650 0.5756243
## sample estimates:
##       cor 
## 0.4407219

## 
##  Pearson's product-moment correlation
## 
## data:  diff_mean$`Auditory Linguistic` and diff_mean$`Visual Temporal`
## t = 3.5269, df = 116, p-value = 0.0006032
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1382221 0.4657645
## sample estimates:
##      cor 
## 0.311206

## 
##  Pearson's product-moment correlation
## 
## data:  diff_mean$`Auditory Non-Linguistic` and diff_mean$`Visual Temporal`
## t = 1.3797, df = 116, p-value = 0.1703
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.0549615  0.3009085
## sample estimates:
##       cor 
## 0.1270602

## 
##  Pearson's product-moment correlation
## 
## data:  diff_mean$`Auditory Linguistic` and diff_mean$`Visual Spatial`
## t = 0.60242, df = 116, p-value = 0.5481
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1261872  0.2342407
## sample estimates:
##        cor 
## 0.05584593

## 
##  Pearson's product-moment correlation
## 
## data:  diff_mean$`Auditory Non-Linguistic` and diff_mean$`Visual Spatial`
## t = -0.68364, df = 116, p-value = 0.4956
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2413429  0.1187723
## sample estimates:
##         cor 
## -0.06334706

## 
##  Pearson's product-moment correlation
## 
## data:  diff_mean$`Visual Spatial` and diff_mean$`Visual Temporal`
## t = 2.0052, df = 116, p-value = 0.04727
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.002348864 0.352139516
## sample estimates:
##       cor 
## 0.1830305

Modality-based differences in Distributional Statistical Learning

Limor Raviv

August 2021

After loading the data…

Descriptive statistics

Regression Results

Categorization

Production

Deviation from category mode

Deviation of gap between categories

Relationship between Production and categorization

Correlation between modalities

categorization

Production