Arithmetic experiment

To make a program that can do the psychology experiment of arithmetic cognition on human subjects

Program dependency

1. Python 3.xx
2. Numpy
3. Pandas
4. Matplotlib

1. User data

Our user data saved in the directory user_data. In user_data/results, each file contains experiment data from a participant.

1.1. Participant information

1. Birth year (Age) : int
2. Gender = {'male', 'female'}
3. Math ability (answered by a participant) = {1:'very bad', 2:'below average', 3:'above average', 4:'very good'}

The name of the file means the datetime the experiment taken, birth year, gender(1: male, 2: female), and mathematical ability(1-4). For example, 2018-12-06_04_26_02_1999_1_3.result stands for "This experiment was taken at 04:26:02, Dec. 06, 2018 by a male born in 1999 who had 3-level, above average, mathematical ability."

1.2. Experiment data

In the file, its data are organized like below:

Carry dataset index	Corret	Solving time (sec.)	Answer	True ansewer	Operand digits	Operator	Carries
7	True	21.242	1001110	01001110	4	multiply	2

Each row is separated by '\n', and in each row, each column record is separated by '\t'. In the actual file, there is no header row.

Carry data index refers to the index with which the operation can be retrieved. For example, we can retrieve the operation like below:

from data_utils import *
operand_digits = 4 # operand_digits in [4, 6, 8]
operator = 'multiply' # operator in ['add', 'substract', 'multiply', 'divide', 'modulo']
carries = 2
index = 7
carry_datasets = import_carry_datasets(operand_digits, operator)
op_operands = carry_datasets[carries]['input'][index] # concatenated operands
op_result = carry_datasets[carries]['input'][index]
print(op_operands)
print(op_result)

2. Operation data

For subtraction, we only deal with the case that operand1 >= operand2 if operand1 - operand2. For division and modulo, we only deal with the case that operand2 != 0 if operand1 / operand2 or operand1 % operand2.

The number of total operations

2.1. Operation datasets

Operator	Operand digits	Input dim	Output dim	Total operations
add	4	8	5	256
add	6	12	7	4096
add	8	16	9	65536
subtract	4	8	4	136
subtract	6	12	6	2080
subtract	8	16	8	32896
multiply	4	8	8	256
multiply	6	12	12	4096
multiply	8	16	16	65536
divide	4	8	4	240
divide	6	12	6	4032
divide	8	16	8	65280
modulo	4	8	4	240
modulo	6	12	6	4032
modulo	8	16	8	65280

2.2. Carry datasets

The size of n-carry datasets for each (operator, operand_digits)

Reference this CSV file carry_dataset_statistics.csv.

The distribution of operations by carries

2.3. Access to the carry datasets

Import data structure

from data_utils import *
operand_digits = 4 # operand_digits in [4, 6, 8]
operator = 'add' # operator in ['add', 'substract', 'multiply', 'divide', 'modulo']
carry_datasets = import_carry_datasets(operand_digits, operator)

How to access the data of carry_datasets

How see what kinds of carries exist in the dataset.

carry_datasets.keys()

How to access the 2-carry dataset

carry_datasets[2]

How to access the input the 2-carry dataset

carry_datasets[2]['input']

carry_datasets[2]['input'].shape == (n_operations, 2 * operand_digits)

How to access the input the 2-carry dataset

carry_datasets[2]['output']

carry_datasets[2]['output'].shape == (n_operations, operand_digits)

How to access the i-th operation in the 2-carry dataset

carry_datasets[2]['input'][i,:]
carry_datasets[2]['output'][i,:]