Spurious Relationship A correlation between two variables that have no causal relationship; both variables are caused by another variable

Scatterplot illustration of a spurious relationship All Fires Fire Damage Only small fires Fire Damage Only large fires Fire trucks Fire Damage Fire trucks Fire trucks

Scatterplot illustration of a spurious relationship All months Babies Only fall and winter months Babies Only spring and summer months Storks Babies Storks Storks

Example of correlation Reconciliation Truth

Solution Logic: deep concern about the logic of the causal mechanism

Does truth lead to reconciliation? I find it difficult to understand the customs and ways of [the opposite racial group]. It is hard to imagine ever being friends with a [the opposite racial group]. More than most groups, [the opposite racial group] are likely to engage in crime. [The opposite racial group] are untrustworthy. [The opposite racial group] are selfish, and only look after the interests of their group. I feel uncomfortable when I am around a group of [the opposite racial group]. I often don't believe what [the opposite racial group] say to me. South Africa would be a better place if there were no [the opposite racial group] in the country. I could never imagine being part of a political party made up mainly of [the opposite racial group].

Does truth lead to reconciliation? Apartheid was a crime against humanity. (True). There were certainly some abuses under the old apartheid system, but the ideas behind apartheid were basically good ones. (False) The struggle to preserve apartheid was just. (False) Both those struggling for and those struggling against the old apartheid system did unforgivable things to people. (True) The abuses under apartheid were largely committed by a few evil individuals, not by the state institutions themselves. (False)

An illustration with a causal model A and B are spuriously correlated if: A and B are NOT spuriously correlated if: Z Z A B A B

A test of whether A and B are spurious Look at the relationship between A and B, controlling for Z This means, that for all values of Z, you should look at the relationship between A and B.

Scatterplot illustration of a spurious relationship All South Africans Reconciliation Reconciliation Only racists Truth Only non- racists Reconciliation Truth Truth

Explaining Venn Diagrams Variance Reconciliation

Explaining Venn Diagrams Variance Truth

Explaining Venn Diagrams Variance Racism

Plot showing positive covariance Mean urban % Mean female literacy

Plot showing negative covariance Mean calorie intake Mean infant mortality

Plot showing no covariance Mean GDP Mean crop production

Venn diagram showing truth is only spuriously related to reconciliation Racism Reconciliation

Scatterplot illustration of a spurious relationship All South Africans Reconciliation Reconciliation Only racists Truth Only non- racists Reconciliation Truth Truth

Scatterplot illustration of a relationship that is {not necessarily} spurious All South Africans Reconciliation Reconciliation Only racists Truth Only non- racists Reconciliation Truth Truth

Venn diagram showing truth has an independent impact on reconciliation Racism Reconciliation