# What you need to know:  What is a correlation?  How do we know if the correlation between two variables is statistically significant?  How do we calculate.

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What you need to know:  What is a correlation?  How do we know if the correlation between two variables is statistically significant?  How do we calculate Spearman’s Rank Correlation coefficient? Data presentation and analysis

Aim: TO INVESTIGATE DOWNSTREAM CHANGE IN THE RIVER HARBOURBE, SPECIFICALLY THAT AFFECTING DISCHARGE, IN LIGHT OF BRADSHAW’S MODEL FOR DOWNSTREAM CHANGE Hypothesis: As the distance increases downstream cross sectional area and velocity will increase. Null Hypothesis: There is no relationship between cross sectional area and velocity. Does cross sectional are affect velocity? Is there a statistically significant correlation between these two sets of results?

VelocityCSA 1.Scatter graph to show velocity against CSA (how does one affect the other?) a)In excel extract the data from our results table. b)Create a scatter graph c)Add titles, axis labels etc d)Describe the results (state anomolies etc) e)Evaluate effectiveness of scattergraphs/ evaluate alternatives/ assess usefulness/ how did the aim or results influence 2. Spearmans rank on the variables a)Complete the spearman's rank sheet b)Do you accept or reject the null hypothesis? c)What conclusions can you draw in relation to the overall investigation. With the CSA you can do a graph to show discharge against distance downstream. d) State how & why useful for geog understanding/ appropriateness for data & aim/ justify use. Distance Downstream Discharge

Spearman’s Rank Correlation Coefficient: r s r s = 1 - 6∑di26∑di2 n 3 - n Where: n = the number of individuals in the sample d i = difference in the rank of the two measurements made on an individual r s will be a number between – 1 and +1 A negative value for r s implies a negative correlation A positive value for r s implies a positive correlation

8. Data Presentation (Scatter Graph) Potential questions: evaluate effectiveness/ evaluate alternatives/ assess usefulness/ how did the aim or results influence Clear visual representation of relationship between 2 variables Esp. with distance on x axis: illustrative representation of downstream change in R. Harbourne– useful & effective for drawing conclusions to aim Data continuous – needed scatter graph The need to see relationship for these 2 variables to meet aim influenced choice Allows for line of best fit – could see needed statistical test as line hard to draw Effective at communicating main info necessary to reach conclusion for aim Anomalies easily identifiable - useful Useful for easy data extraction Could only compare the 2 variables Not statistically verifying – may see correlation, but need statistical test to confirm For better effectiveness, could be located to give precise conclusions for aim Could have compared 2 variables with another e.g. depth/width/velocity on a triangular graph Negatives of method Positives of method

Interpretation – Spearman’s Rank Potential questions: how & why useful for geog understanding/ appropriateness for data & aim/ justify use Appropriate: Uses 10-30 data sets Had 2 variables which we wanted to statistically verify a correlation for Continuous data with a relationship Helped to achieve our aim: assess relationship between discharge & distance statistically Fact that it confirmed null hypothesis = helped to develop geog understanding as then had to return to data/maps/previous data/data from other rivers to understand why we achieved this result  turned out to be rocky outcrops – helped further understanding of external influences on river processes Justifiable: 10 data sets, continuous data, 2 corresponding variables, gave us the results needed to conclude our investigation & develop our conclusions to understand why

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