Relationship between Variables

Assessment Statement1.1.6 Explain that the existence of a

correlation does not establish that there is a causal relationship between two variables.(3).

Correlation

• Typically in IB Biology your experiment may involve a continuous quantitative independent variable and a continuous quanitative variable dependent variable. – e.g effect of enzyme concentration on the rate of

an enzyme catalysed reaction.• The statistical analysis would set out to test

the strength of the relationship (correlation).

EXAMPLES OF CORRELATION

CALCULATING CORRELATIONS ON EXCEL

• There are two tests for correlation:1. the Pearson correlation coefficient ( r ), used from

normal distribution data

2. and Spearman's rank-order correlation coefficient ( r s ) used from non-normal distribution data

• These both vary from – +1 (perfect correlation) through – 0 (no correlation) – to –1 (perfect negative correlation).

Correlations & Relationships between variable

Correlation does NOT mean Causation

Interpreting R - Values

• Exactly –1. A perfect downhill (negative) linear relationship

• –0.70. A strong downhill (negative) linear relationship• –0.50. A moderate downhill (negative) relationship• –0.30. A weak downhill (negative) linear relationship• 0. No linear relationship• +0.30. A weak uphill (positive) linear relationship• +0.50. A moderate uphill (positive) relationship• +0.70. A strong uphill (positive) linear relationship• Exactly +1. A perfect uphill (positive) linear relationship

Correlation does NOT mean Causation

• It is important to realize that if the statistical analysis of data indicates a correlation between the independent and dependent variable this does not prove any causation. Only further investigation will reveal the causal effect between the two variables.

• Correlation does NOT imply causation. Here are some unusual examples of correlation but not causation's !– Ice cream sales and the number of shark attacks on swimmers are correlated. – Skirt lengths and stock prices are highly correlated (as stock prices go up, skirt

lengths get shorter). – The number of cavities in elementary school children and vocabulary size have a

strong positive correlation. • Clearly there is no real interaction between the factors involved simply a

co-incidence of the data.• Once a correlation between two factors has been established from

experimental data it would be necessary to advance the research to determine what the causal relationship might be.