Source code for psychometrics.CTT

import pandas as pd
import numpy as np
import os
import statsmodels
import random

'''
This secion is built to implement many commonly used item analysis tools in Classical Test Theory. Included is a method to optain 
coefficient alpha, p-values for all items, discrimination (point biserials and biserals) values for all items and get examinee raw scores.
'''



def examinee_score(items):
    '''
    Returns examinee scores for an exam

    :param items: a pandas dataframe containing the correct (1) and incorrect (0) response patterns for each examinee on every item.
    :return: a vector containing raw scores for the exam.
    '''
    return items.sum(axis=1)

def get_p_values(data):
    '''
    returns p-values for every item in the dataframe

    :param data: a pandas dataframe where columns are items and rows are examinees.
    :return: a vector of p-values for each item in the assessment.
    '''
    p_values = pd.DataFrame(data.mean(axis=0))
    p_values.columns = ['P_Value']
    p_values['Item'] = p_values.index
    return p_values

def k_and_k(items):
    item_count = items.shape[1]
    if item_count > 1:
        return (item_count / float(item_count - 1))
    else:
        return 0


def alpha_without_item(items):
    alpha_without_items = pd.Series(index=items.columns, name='Alpha Without Item')
    for item in items.columns:
        use_items = items.drop(item, axis=1)
        alpha_without_items.ix[item] = k_and_k(use_items) * (1 - (item_var_sum(use_items) / total_var(use_items)))
    return alpha_without_items


def total_var(items):
    return float(items.sum(axis=1).var(ddof=1))


def item_var_sum(items):
    return float(items.var(axis=0, ddof=1).sum())


def calculate_alpha(items):
    '''
    Calculates coefficient alpha for the given exam.

    :param items: a pandas dataframe with columns for each item and rows for each examinee.
    :return: coefficient alpha
    '''
    return k_and_k(items) * (1 - (item_var_sum(items) / total_var(items)))


def discrimination_index(items):
    '''
    Calculates the point biserial and biserial for each item on the exam. Essentially these are item-total correlations where the item is not included in the total score (point-biserial) and is included int he total score (biserial).

    :param items: a pandas dataframe with columns for each item and rows for each examinee.
    :return: two dataframes. one containing the point-biserials and the other containing the biserials
    '''
    stat_without_item = pd.Series(index=items.columns, name='Point Biseral')
    for item in items.columns:
        total_deitemed = examinee_score(items) - items[item]
        stat_without_item.ix[item] = items[item].corr(total_deitemed)

    stat_with_item = pd.Series(index=items.columns, name='Biserial')
    for item in items.columns:
        total = examinee_score(items)
        stat_with_item.ix[item] = items[item].corr(total)
    return stat_without_item, stat_with_item