The Processing Of Two-digit Integers And Two-digit Decimals In The Numerical Magnitude Comparison Task

Currently most studies focused on the processing of the two-digit integers to explore the multi-digit numbers in the field of numerical cognition. Researchers put forward three processing models for integers:（1） Holistic model:According to this model, people represent the decade and the unit of two-digit integers on a mental number line as an integrated entity. The indicator reflected holistic model is the distance effect which means that speed and accuracy increases with numerical distance between the to-be-compared numbers.（2） Compositional model:This model based on the place-value structure of Arabic numbers with the value of the digits being determined by their position within the digit string. The strong evidence comes from the unit-decade compatibility effect that compatible pairs （e.g., for52₇8, both5<7and2<8） are responded faster and more accurately than incompatible pairs （e.g., for57₈3,5<8but7>3）. There are two modes of processing for compositional model. Parallel processing which is reflected by the positive compatibility effect assumes that each digit is represented separately and similarly. Sequential processing which is reflected by the negative compatibility effect refers to that integers are compared digit by digit sequentially from left to right.（3） Hybrid model:Only one model is too simple to embody the complex two-digit integers. It needs to synthesize several models or discuss the specific processing model under different paradigms or conditions. Although many studies explored the processing of two-digit integers, it is still debatable on the processing model. In addition, a few studies investigated how two-digit decimals are processed in adults since there were studies indicated that the processing of decimals is different from integers.The present study used the magnitude comparison task without fixed standards and changed the stimuli-presenting mode （simultaneously and successively） and number materials characteristics （whether there were same leftmost digit or not） to explore the processing of the two-digit integers （e.g.,54）, two-digit pure decimals （decimals between0and1with two decimal places, e.g.,0.54） and two-digit mixed decimals （decimals larger than1with one integer place and one decimal place, e.g.,5.4） with different leftmost digits.The first study asked participants to compare two numbers which were simultaneously presented on the left and right sides of the screen center. The number materials of Experiment1,2and3were the two-digit integers, two-digit pure decimals and two-digit mixed decimals with different leftmost digits, separately. Though analyzing the distance effect and the compatibility effect, the results showed that:（1） Experiment1found the unit distance and compatibility effects in two-digit integers, suggesting that two-digit integers are processed compositionally in a parallel fashion.（2） Experiment2found the hundredth distance effect but did not the compatibility effect in two-digit pure decimals, revealing the compositional processing. There is no evidence indicated the parallel or sequential processing.（3） In Experiment3, neither the tenth distance nor the compatibility effect was observed in two-digit mixed decimals, which did not show any evidence of compositional processing. It might be the holistic model or the processing with only focusing unit digit for two-digit mixed decimals.The second study made the two to-be-compared numbers successively presented. After one number disappeared on the center of the screen, the other number presented. Participants needed to make the decision when the second number was presented. The materials of the three experiments and analyze methods were similar with the first study. The results found that the negative compatibility effect was appeared in all the three experiments. It indicated that two-digit integers, pure decimals and mixed decimals were all processed compositionally in a sequential fashion.The third study further explored the processing of two-digit pure decimals and two-digit mixed decimals. Based on the Experiment2and3of the first study, decimals pairs with the same leftmost digits （e.g.,0.52₀.58,5.2₅.8） were joined in the decimals materials. And the three percentages of same leftmost digits decimals in all the numbers （as the between-participant variable） increased the relevance of the rightmost digit processing. Under this circumstance, participants were forced to concern the rightmost digits to some extent. By analyzing the distance and the compatibility effect, the results showed that both pure and mixed decimals produced the compatibility effect, the overall and leftmost digit distance effect. These suggested that the processing of pure and mixed decimals was hybrid. It includes both holistic processing and compositional processing with a parallel fashion. In addition, the size of compatibility effect increases monotonically with the percentage of same leftmost digits decimals.To sum up the results, two-digit integers and two-digit decimals have different processing models under different conditions （e.g., presenting mode, stimuli characteristic）. Moreover, the processing of decimals was different from that of integers. Limited to the experiments in the present study, the processing of two-digit integers and decimals was affected by the different presentation. Their processing was different when the to-be-compared numbers were simultaneously presented. In contrast, their processing was same when the numbers were successively presented. Besides, the decimals’ processing was also sensitive to the relevance of the rightmost digit processing when the to-be-compared numbers were simultaneously presented. With no relevance of the rightmost digit processing, the processing of pure and mixed decimals were different. However, it was the same with some relevance of the rightmost digit processing.