Chi Square Test of Independence

Conceptual

Questions of Independence

Questions of independence are actually the flip side of questions of relationship. If a variable is independent of another variable, then functions in one will not be accompanied by functions in the other.

Like the higher the temperature the stronger people are.

Like the higher the temperature the stronger people are.

Questions of Independence are often posed as questions of bias.

For example, the question, “Are admissions decisions at a local community college fair?” can reasonably be interpreted as a question of independence (or bias).

If fairness is taken to mean that there is proportional representation of minority and majority students that mirrors the local proportions, then a test of independence can estimate whether admissions are “fair”.

The question becomes “Are admissions decisions independent of majority/minority status?”

Assuming that majority students are similar in their preparation and motivation as minority students and they apply to the community college in proportionally similar notes as minority students, then a fair admissions process should be independent of majority status and render proportions of admissions that are similar to proportions of majority and minority students in the local populations

INDEPENDENT EXAMPLE: If you are a minority you are neither more likely nor less likely to be admitted

Failure to be independent would indicate bias.

BIAS EXAMPLE: If you are a minority you are more likely to be admitted

BIAS EXAMPLE: If you are a minority you less likely to be admitted

Failure to be independent would indicate bias.

BIAS EXAMPLE: If you are a minority you are more likely to be admitted

BIAS EXAMPLE: If you are a minority you less likely to be admitted

You will use certain statistical methods (like the chi square test of independence) to determine if independence is significant or not.