How can I compare and contrast The Crucible and Macbeth?

Arthur Miller's The Crucible and Shakespeare's Macbeth share similar themes and are loosely based on historical events and figures. Arthur Miller's play is based on the Salem witch trials, which took place in seventeenth century New England. Shakespeare's Macbeth is named after the historical King of the Scots, who defeated Duncan I and reigned from 1040–1057 A.D. While both playwrights were greatly influenced by historical figures and events, they used artistic license to distort facts in order make their works more entertaining and dramatic. Both playwrights also incorporate supernatural elements and witchcraft into their plays. Arthur Miller's The Crucible focuses on the hysteria throughout the town of Salem concerning the fear of witchcraft while Macbeth is influenced into making fatal decisions based on the prophecies of the Three Witches. Both John Proctor and Macbeth are also considered tragic heroes, whose inherent character flaws lead to their demise.
Despite the many similarities between both plays, Arthur Miller's The Crucible allegorically represents Senator McCarthy's "witchhunt" for communist sympathizers in the 1950s. In addition to the fact that Macbeth is not an allegorical play, the settings, plot, and motivation of each character are completely different in The Crucible and Macbeth.