Relationship between Variables
Assessment Statement
1.1.6 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.