Cause & Effect (Correlation vs. Causality) MDM4U – Data Management

Learning Goals Distinguish between correlation and causality Identify different types of relationships between two variables

Cause & Effect The main reason for a correlational study is to find evidence of a cause-and-effect relationship Examples: A health researcher may wish to prove that mild exercise reduces the risk of heart disease A school board may want to know whether calculators improve student learning

What is Correlation? (Review) Strength and direction of the relationship between two variables Shows how closely data points on a scatter plot fit to a line of best fit An r value between -1 and 1 If r is negative, as the independent variable , the dependent variable  If r is positive, as the independent variable , the dependent variable also  The closer r vis to -1 or 1, the stronger the relationship is Two variables = dependent and independent Strength = strong, moderate, weak Direction = positive, negative

Correlation vs. causality Consider: A strong positive correlation is found between eating ice cream and drowning incidents. A news report claims that people who eat more ice cream are more likely to die by drowning. Does this seem reasonable? If analysis shows that two variables are strongly correlated, does that mean that change in the independent variable CAUSES changes in the dependent? Answer: NO… not necessarily Data analysis involves much more than fitting a line or a curve to a set of data points Correlation is just the first step in understanding the true nature of a relationship If a correlation exists, we must ask WHY it exists.

Causal Relationships – direct Cause & Effect A change in the independent variable directly causes a change in the dependent variable (X causes Y) Examples: As distance driven increases, amount of available fuel decreases As the speed of a production line increases, the number of items produced increases The more one prepares for a task, the better he/she is likely to do on that task Positive correlation between seat belt infractions and traffic fatalities Relationships are often clearly evident

Causal Relationships – Common Cause An external (third) variable causes two variables to change (Z causes X and Y) Examples: A strong positive correlation between ice-cream sales and drowning incidents A strong negative correlation between the # of robberies and automobile sales The number of fire stations is positively correlated with the number of parks Drowning vs ice cream sales = correlation unlikely Common cause = Good weather Auto sales vs robberies = correlation unlikely Common cause = Poor economic times (higher rates of unemployment) Fire stations vs parks = correlation unlikely Common cause = city population

Causal Relationships – Reverse Cause & Effect The independent and dependent variables are reversed in the process of establishing causality (Y causes X) Examples: A positive correlation between coffee consumption and anxiety levels Hypothesis: coffee causes nervousness. Conclusion: nervous people more likely to drink coffee A positive correlation between severe illness and depression Hypothesis: being severely ill causes depression. Conclusion: depressed people struggle to care for themselves Coffee vs anxiety Illness vs depression Depressed people struggle to care for themselves causing them to become severely ill

Causal Relationships – Accidental RelationshiP A correlation exists without any causal relationship between variables Examples: A correlation between local kitten birth rate and declining school enrolment A negative correlation between population of bumble-bees and student averages A positive correlation between the price of butter and the fish population Often easy to identify because the relationships do not make sense. Even if strong correlations exist, the relationships are purely coincidental

Causal Relationships – Presumed Relationship A relationship that makes sense, but no cause & effect or common cause is apparent Examples: A positive correlation between self esteem and vocabulary level A positive correlation between fitness level and the number of adventure movies watched Makes sense that someone with stronger language skills might have more confidence Logical that a fit person might prefer adventure movies BUT… in all three cases it is difficult to suggest causality or find a common cause factor

Your Turn – Examples The rate of a chemical reaction increases with temperature Direct Cause & Effect: Higher temperature cause faster reaction rates. Direct Cause & Effect Common Cause Accidental Relationship Presumed Relationship Reverse Cause & Effect

Your Turn – Examples Leadership ability has a positive correlation with academic achievement Presumed relationship: Seems logical, yet there is no apparent common-cause factor or cause & effect relationship Direct Cause & Effect Common Cause Accidental Relationship Presumed Relationship Reverse Cause & Effect

Your Turn – Examples The prices of butter and motorcycles have a strong positive correlation over many years Common cause factor: Inflation has caused parallel increases in the prices of many variables over time, including butter and motorcycles Direct Cause & Effect Common Cause Accidental Relationship Presumed Relationship Reverse Cause & Effect

Your Turn – Examples Cell phone sales have a strong negative correlation with ozone levels in the atmosphere over the past decade Accidental cause: The correlation is largely coincidental, but it could be possible that the chemicals and processes used to manufacture cell phones cause a small depletion of the ozone layer. Direct Cause & Effect Common Cause Accidental Relationship Presumed Relationship Reverse Cause & Effect

Your Turn – Examples Traffic congestion has a strong correlation with the number of urban expressways Cause & Effect: Originally expressways were built to relieve traffic congestion, so traffic congestion did lead to the construction of more expressways in urban areas, BUT… Reverse Cause & Effect: Numerous studies have shown that urban express has caused traffic congestion by encouraging more people to use cars Direct Cause & Effect Common Cause Accidental Relationship Presumed Relationship Reverse Cause & Effect