Edited by: George Kachergis, Stanford University, United States
Reviewed by: Robert Reeve, The University of Melbourne, Australia; Dawei Li, Duke University, United States
This article was submitted to Cognition, a section of the journal Frontiers in Psychology
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The hybrid model of number magnitude processing suggests that multi-digit numbers are simultaneously processed holistically (whole number magnitudes) and in a decomposed manner (digit magnitudes). Thus, individual tendencies and situational factors may affect which type of processing becomes dominant in a certain individual in a given situation. The unit-decade compatibility effect has been described as indicative of stronger decomposed number processing. This effect occurs during the comparison of two-digit numbers. Compatible items in which the larger number contains the larger unit digit are easier to solve than incompatible items in which the larger number contains the smaller unit digit. We have previously described women show a larger compatibility effect than men. Furthermore, the compatibility effect is modulated by situational factors like the vertical spacing of the presented numbers. However, it has not been addressed whether situational factors and sex affect the unit-decade compatibility effect interactively. We have also demonstrated that the unit-decade compatibility effects relates to global-local processing, which in turn also affects spatial processing strategies. However, a link between spatial processing strategies and the unit-decade compatibility effect has not yet been established. In the present study we investigate, whether sex differences in the unit-decade compatibility effect (i) depend on the vertical spacing between numbers, (ii) are mediated via sex hormone levels of participants, and (iii) relate to sex differences in spatial processing strategies. 42 men and 41 women completed a two-digit number comparison task as well as a spatial navigation task. The number comparison task modulates compatibility and vertical spacing in a 2 × 2 design. The results confirm a larger compatibility effect in women compared to men and with dense compared to sparse spacing. However, no interactive effect was observed, suggesting that these factors modulate number magnitude processing independently. The progesterone/testosterone ratio was related to the compatibility effect, but did not mediate the sex difference in the compatibility effect. Furthermore, spatial processing strategies were related to the compatibility effect and did mediate the sex difference in the compatibility effect. Participants with a stronger focus on landmarks in the spatial navigation task showed a larger compatibility effect.
Number magnitude processing has been extensively studied using various versions of number comparison tasks (for reviews see
There is accumulating evidence that spatial processing is influenced by basic visual attentional processes, like global-local processing (see e.g.,
These differences in global-local processing also influence spatial processing (
A more holistic processing style during spatial tasks has repeatedly been linked to global processing (
Like spatial stimuli, numerical stimuli are hierarchical with multi-digit numbers being composed of single digits. Accordingly, the question arises, whether global-local processing also transcends to cognitive processing in the numerical domain. Independent of the global-local processing literature, it has been discussed, whether number comparison occurs holistically, i.e., by comparing whole number magnitudes, or in a decomposed manner, i.e., by comparing units, decades, hundreds, etc. separately. The holistic model assumes a single logarithmically compressed mental number line along which whole number magnitudes are represented (
Evidence for the decomposed model comes from the so called
More recent models of multi-digit number processing (hybrid model) assume that holistic and decomposed number processing occur in parallel. Accordingly, a stronger unit-decade compatibility effect can be viewed as indicative of stronger decomposed number processing. This further outlines similarities between number magnitude processing and basic global-local processing of visual stimuli. Indeed we were recently able to link the unit-decade compatibility effect during number comparison to the global advantage effect in a global-local processing task (Pletzer et al., unpublished). The smaller the global advantage effect, the larger is the unit-decade compatibility effect. Accordingly, it has been established, that both spatial and numerical processing are influenced by basic visual attentional processes. It is therefore reasonable to assume that factors affecting global-local processing may transcend into the spatial and numerical domain.
Multiple studies have now demonstrated sex differences in the unit-decade compatibility effect (
In a more recent behavioral study however, we failed to replicate the sex difference in the compatibility effect when numbers where presented to the centre of the screen like in the previous fMRI study (
Indeed we were able to demonstrate in a sample of men that the size of the compatibility effect depends on presentation mode (
Accordingly, it has been established that like spatial processing and global-local processing, number magnitude processing is influenced by task characteristics and individual characteristics, like participant’s sex. However, so far sex differences and task characteristics have been addressed in separation and it has not been established whether they interactively modulate number processing. Furthermore, not all factors affecting global-local processing have also been investigated in the numerical domain. For instance no study has yet addressed whether sex hormones relate to the compatibility effect during number comparison. Finally, a pattern has emerged, suggesting that sex differences in basic global-local processing may transcend into the spatial and numerical domain, manifesting in sex differences in spatial and numerical processing styles. However, a link between spatial and numerical processing styles remains yet to be established.
To investigate these questions we employed the two-digit number comparison task in a sample of healthy young men and women, while varying the vertical spacing between the two numbers as in
Forty-three healthy young men and 44 healthy young women between the ages of 18 and 35 years participated in this study. According to self-reports, all participants were right-handed, had no psychological, endocrinological, or neurological disorder and were free of medication. In order to adequately assess hormonal influences on the number comparison task, only women who did not take hormonal contraceptives, and had a regular menstrual cycle between 21 and 35 days of length were allowed to participate. Furthermore, all women were tested in their mid-luteal cycle phase, 3–11 days after ovulation, i.e., 11–3 days before the onset of next menses. Ovulation was confirmed by commercial ovulation tests and onset of next menses was evaluated in follow-up. Furthermore, cycle phase was confirmed by hormone analyses as described below. Three women were excluded due to low progesterone as a result of early onset of their next menses. The remaining women had a mean cycle length of 29.29 days (
All participants gave their informed written consent to participate in the study. All methods conform to the Code of Ethics of the World Medical Association (Declaration of Helsinki). According to §163 (1) of the institutional guidelines of the University of Salzburg
Participants completed (i) an attention task (not described in this manuscript), (ii) a two-digit number comparison task, and (iii) a spatial navigation task. This manuscript focuses on the results of the two-digit number comparison task and it’s relation to the spatial navigation task. Sex differences in the spatial navigation task are described elsewhere (Harris et al., unpublished). Upon arrival at the lab, participants were asked to rinse their mouth to remove particles before saliva sampling. They then completed the written consent form, as well as a general screening questionnaire to ensure they fulfilled all inclusion criteria. Tasks were performed in the order described. The first saliva sample was taken before the first task, the second saliva sample after the number comparison task and the third sample after the spatial navigation task. The IQ screening was performed as last measure of the study. The total session lasted for 1.5 h.
As part of a larger study, participants completed a two-digit number comparison task as described in
In order to address, whether sex differences in the unit-decade compatibility effect relate to sex differences in spatial processing strategies.
The spatial navigation task was described in detail in Harris et al. (unpublished). In short, 20 3D navigation items were created using Unreal Engine 4 Version 8.1. The task builds upon a previous 2D-version employed by
After the test session, saliva samples were immediately frozen at −20°C until further analysis. Before analysis they were centrifuged at 3000 rpm for 15 and 10 min, respectively to remove solid particles. Prior to analysis the three samples were pooled to assess an average hormone value across the whole test session. Estradiol, progesterone and testosterone were analyzed from the pooled samples using DeMediTec salivary ELISA kits. For each sample, duplicate values were assessed and the average of the duplicate values was accepted if the coefficient of variation between duplicate values was below 25%. In 4 participants (1 woman, 3 men) hormone values could not be assessed due to visible blood contamination of the samples or insufficient sample volume.
Statistical analyses were performed in R 3.4.0. As a preparatory step, the compatibility effect was calculated for the number comparison task as mean difference between the RT/ER of incompatible and compatible items. Furthermore, for the navigation task, the strategy effect was calculated as the mean difference between landmark trials and Euclidian trials. Accordingly, a smaller strategy effect represents better performance with landmark trials. The compatibility effects in RT and ER were then analyzed in the context of linear mixed effects models using the
If a significant sex difference was identified, the second step was to address whether sex hormones, particularly progesterone, and testosterone related to the compatibility effect. Thus, hormone values were entered as independent variables in the linear mixed model. Since we hypothesized a positive association to progesterone, but negative association to testosterone, the progesterone/testosterone ratio was also considered as predictor of interest. For hormones that emerged as significant predictors, we assessed whether their influence mediated sex differences in the compatibility effect. Mediation analyses were performed using the
The third step was to address whether the compatibility effect was related to navigation strategies. Accordingly, the strategy effect in navigation as well as it’s interaction with sex were entered as predictors in the linear mixed model including also sex and it’s interaction with strategy.
In all models, non-significant interactions were backward eliminated using the
For both, RT and ER, linear mixed models were performed including participant number as a random factor and spacing (dense vs. sparse), as well as sex (men vs. women) and their interactions as fixed effects. Age and IQ were entered as covariates. Neither age nor IQ had a significant effect on RT or ER. These variables were thus removed from the models.
Zero-order correlation table.
meanRT | meanER | Comp_effect_RT | Comp_effect_ER | |
---|---|---|---|---|
Age | 0.02 | −0.21 | −0.17 | −0.12 |
IQ | −0.13 | −0.17 | −0.07 | −0.17 |
Estradiol | 0.17 | 0.10 | 0.00 | 0.01 |
Progesterone | 0.23∗ | 0.23∗ | 0.07 | 0.18 |
Testosterone | −0.11 | −0.10 | −0.06 | −0.16 |
Progesterone/Testosterone | 0.19 | 0.21 | 0.02 | 0.26∗ |
In the analysis of RT, only spacing remained a significant effect in the model [
Reaction times
In the analysis of ER, only sex remained a significant effect in the model [
For both, the compatibility effect in RT and ER, linear mixed models were performed including participant number as a random factor and spacing (dense vs. sparse), as well as sex (men vs. women) and their interactions as fixed effects. Age and IQ were entered as covariates. Neither age nor IQ had a significant effect on the compatibility effect in RT or ER. These variables were thus removed from the models.
In the analysis of RT, only spacing remained a significant effect in the model [
In the analysis of ER, only sex remained a significant effect in the model [
Mean hormone values are displayed in
Sex hormone levels in men and women.
Men [Mean ± SD] | Women [Mean ± SD] | |
---|---|---|
Testosterone [pg/ml] | 117.99 ± 47.35 | 62.93 ± 24.09 |
Estradiol [pg/ml] | 2.83 ± 1.64 | 3.60 ± 1.88 |
Progesterone [pg/ml] | 84.54 ± 57.89 | 190.90 ± 107.38 |
To evaluate whether sex hormones mediated the sex differences in the compatibility effect in ER, mediation analyses were performed using estradiol, progesterone and testosterone as well as the progesterone/testosterone ratio as potential mediators. In a first step, hormone values were entered as predictors in linear mixed models including participant number as a random factor and the compatibility effect in ER as dependent variable. Neither estradiol nor progesterone nor testosterone showed a significant influence on the compatibility effect in ER [estradiol:
However, the progesterone/testosterone ratio was a significant positive predictor for the compatibility effect in RT [
In order to test the hypothesis that participants with a stronger focus on landmarks show a higher compatibility effect, we performed a linear mixed effects model on the compatibility effect in ER using participant number as a random factor and sex, the strategy effect in navigation time as well as their interaction as independent variables. The final model included the strategy effect as a significant negative predictor [
This study set out to investigate whether sex differences in the compatibility effect during number comparison (i) depend on situational aspects like the vertical spacing between the two numbers to be compared, (ii) are mediated via sex hormone levels, and (iii) relate to sex differences in spatial navigation strategies. We expected to replicate a larger compatibility effect in women compared to men and with dense vertical spacing compared to sparse vertical spacing. Regarding the first question, we hypothesized a significant interaction between sex and vertical spacing in such a way that the sex difference in the compatibility effect is larger with larger vertical spacing between the numbers. Regarding the second question, we hypothesized the compatibility effect to relate positively to progesterone and negatively to testosterone. Regarding the third question, we expected the compatibility effect during number comparison to relate to landmark-based strategies during spatial navigation.
Regarding the first hypothesis, we were able to confirm a larger compatibility effect in women compared to men for ER, while the sex difference in the compatibility effect in RT did not reach significance. This is in line with previous results from a large scale online study (
Indeed, we were able to confirm a larger compatibility effect in RT for dense as compared to sparse vertical spacing in both women and men, as we had previously demonstrated for men (
For instance, no sex differences in overall performance were observed in the neuroimaging study (
Since a significant sex difference was only observed on the compatibility effect in ER, the following discussion refers to the compatibility effect in ER.
Regarding the second hypothesis, absolute sex hormone levels were not related to the compatibility effect. However, the progesterone/testosterone ratio related positively to the compatibility effect, which is in line with the assumption that participants with higher progesterone, but lower testosterone levels show a larger compatibility effect. While the effect was rather small, it is in line with previous observations that progesterone relates to local and testosterone to global processing (
Regarding the third hypothesis, the strategy effect in spatial navigation was indeed related to the compatibility effect during number comparison. The better participants performed with landmark-based instructions in the navigation task, the larger was their compatibility effect. We were previously able to demonstrate better performance with landmark-based instructions in women compared to men (Harris et al., unpublished). Unlike the progesterone/testosterone ratio, navigation strategy did explain the sex difference in the compatibility effect in a mediation analysis. While both spatial and numerical processing strategies have previously been related to global-local processing (
In summary the present study corroborates previous findings that both sex and stimulus characteristics influence the compatibility effect during number magnitude processing. However, our data suggest that these factors contribute separately, but not interactively to the tendency of processing multi-digit numbers in a holistic or decomposed manner. Furthermore, our data suggest that sex differences in the compatibility effect cannot be explained by sex hormone levels, but by spatial processing strategies. This is the first report linking sex differences in number magnitude processing to sex differences in spatial processing.
BP designed the study, performed the analyses and wrote the manuscript. TH and AS assisted in data collection.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We thank the students of BP for their help with data acquisition and acknowledge all participants for their time and willingness to contribute to this study.