Free item analysis calculator under Classical Test Theory: paste your response matrix (one row per subject, one column per item) and it returns, per item, difficulty (p or mean), standard deviation, corrected item-total correlation, 27% extreme-group discrimination (Kelley, 1939) and alpha-if-deleted; and for the whole test, Cronbach's alpha (which with 0/1 items is exactly KR-20), mean, SD and the standard error of measurement. It auto-detects dichotomous (exam) versus polytomous (Likert) data, rates each item with the Ebel and Frisbie (1991) thresholds and drafts the APA 7 results sentence.
Worked example: in an 8-question exam taken by 25 students (mean 4.64, SD 1.63), overall reliability was KR-20 = .37. Question 5 looked normal by difficulty (p = .52), but its discrimination was negative (D = −.57: 2 of the 7 best students answered it correctly versus 6 of the 7 weakest) and its corrected item-total correlation was −.70. Removing it raises KR-20 from .37 to .69: the answer key was wrong or the stem was ambiguous.
Cronbach's alpha or KR-20? They are the same coefficient when items are scored 0/1: KR-20 is the dichotomous case of alpha. What to do with a negatively discriminating item? First check the answer key and any reverse-worded items left unrecoded; if the key is correct, void it (exam) or drop/rewrite it (scale).
Item difficulty, discrimination (27% extreme groups), corrected item-total correlation, alpha-if-deleted and KR-20 or Cronbach's alpha. Free, Word-ready table.