The most effective way of showing and analysing results is either by scatter graphs or Spearman’s rank correlation.
Scatter graphs present the relationship between two sets of variables, while also showing whether the results have a positive or negative correlation.
Spearman’s rank correlation portrays data in the correct order, as well as displaying the strength and reliability of the order. It gives a value, between 1 and 1, which describes the correlation between two sets of data.
Hypothesis 1
‘The depth of the river will increase downstream’
Spearman’s rank correlation coefficient:

Rs = 1(6 Sigma d2 / n3n).

Sigma d2 = 202 therefore 6 Sigma d2= 1212

n = 12 therefore n3n = 1716
 Rs = 1(1212/1716)
 Rs = 1 0.7062937
 Rs = 0.29(to2dp)
Analysis
This hypothesis was rejected. There is very little correlation between the results after calculating the Spearman’s rank correlation. The graph [fig.2] also shows very little correlation with some huge anomalies at depths of 20.3 upstream and 2.7 downstream, where opposites to these results would be expected. The main reason for this random data would be the fact that rain hadn’t fallen in the area for months before hand, which wouldn’t reflect fairly the true flow & depth of the river. Usually in October a lot of rainfall would be expected & the river should be in peak flow. Also the section of the River Lyd investigated [fig.1] was only in the middle course & therefore wouldn’t follow the general geographical theory. Reasons for the anomalies may have been a large area of deposition or a pool created from fast flowing water.
Hypothesis 2
‘The velocity of the river will increase as width of the river increases’.
Spearman’s rank correlation coefficient:

Rs = 1(6 Sigma d2 / n3n).

Sigma d2 = 195 therefore 6 Sigma d2= 1170

n = 12 therefore n3n = 1716
 Rs = 1(1170/1716)
 Rs = 1 0.6818182
 Rs = 0.32(to2dp)
Analysis
This hypothesis was rejected. The spearman’s rank correlation result of 0.32 shows little correlation between the increasing velocity & increasing width along the course of the River Lyd. The graph [fig.3] backs up the findings by also showing that there is almost no correlation. From the graph it can be seen that no two sets of results are related to each other, though does have a positive gradient. A reason why the results would have been affected would be the fact that the orange did not always flow in the fastest part of the river, shown in fig.6
Velocity of a river [fig.4]
 Less fast on surface due to air(wind) resistance
 Greatest velocity is where friction is least – i.e. away from banks, bed & air
 Slowest flow resulting from friction caused by contact with bed & banks
 speed(m/s)
Hypothesis 3
‘The amount of discharge increases as depth increases.’
Spearman’s rank correlation coefficient:

Rs = 1(6 Sigma d2 / n3n).

Sigma d2 = 64 therefore 6 Sigma d2= 384

n = 12 therefore n3n = 1716
 Rs = 1(384/1716)
 Rs = 1 0.223776223
 Rs = 0.78(to2dp)
Analysis This hypothesis was rejected. Although the Spearman’s rank results show that there is a high correlation between the two factors, discharge & depth; pairing this data with the graph [fig.6] actually illustrates the fact that the correlation is in fact negative. This would have been because of the large range in C.S.A which doesn’t fit into the geographical theory of which rivers become wider nearer the mouth.
Problems with the experiment
A number of problems were encountered in the process of collecting data. The most obvious was that of accessibility to the site. At times there were obstructions, such as steep river cliffs or fallen trees which made it hard to reach the chosen site in the river. Also it was hard to make the decision of where to locate the site, the distance chosen between them and the fact that 12 sites wasn’t enough to collect sufficient data needed to calculate & portray the rivers flow.
Another major problem was the fact that there had been little to no rain in the area for months before hand, owing to the extremely hot summer, which meant the flow was smaller & the results may not have reflected the real data.
Changes
Given the chance to repeat this experiment, certain aspects of the investigation would need to be altered or changed. Choosing a larger river would be a main point, as this could give more typical, expected results. It would also have to be done in a season when the rain would have more effect on the river or in two seasons, summer & winter to compare the two, and see if this has effect on the velocity / hydraulic radius.
More sites should be included and cover a larger stretch [nearer / further from the source] as this would produce a wider set of results and knowledge in which to accept or reject the hypothesis.
Conclusion
This study was designed to investigate how characteristics of the River Lyd changed downstream. The three hypotheses tested were rejected & therefore this section of river does not fit the studied models and geographical theories.