## Correlation Coefficient

#### The correlation coefficient is very useful in determining whether 2 or more
different data sets are related.

#### You might use this to determine relationships between data representing the
following :

#### a. pH and streamflow

#### b. water temperature and streamflow

#### c. water temperature and dissolved oxygen

#### d. pH and ammonia concentration

#### e. nitrate and ammonia concentrations

#### f. etc........

#### Definitions of Symbols:

#### Note that there is a differenc between lower case x and y and
the upper case X and Y.

### Calculating Correlation Coefficient using
Excel

#### 1. Copy & paste the data you wish to compare into an Excel
spreadsheet.

#### 2. Click the formula button and select the formula: CORREL
(Array1, Array 2)

#### Where, Array 1= the range of cells for the first set of values
(X) ......

#### and Array 2 = the range of cells for the second set of values
(Y).

#### 3. Find the level of significance of the result by

#### a. Count the number of sample pairs, N, you compared.

#### b. Compare the absolute value (number regardless of positive
or negative) for r with the values in the corresponding row for N.

#### c. To be significant, the value for r must be equal to or larger
than the value shown in the table.

#### [Levels of Significance Table]

#### What does the correlation coefficient, r, value mean? The value
for r is always between -1.00 and +1.00. For values that are positive there
is a positive correlation, meaning that the two variables vary in the same direction
(i.e. as X increases Y increases, or as x decreases Y decreases). For values
that are negative there is a negative correlation, meaning that the two values
vary in opposite directions (i.e., as X increases Y decreases, or as X decreases
Y increases). For example, as water temperature increases dissolved oxygen decreases.

#### The closer to 1.00 the value for r is, the greater the correlation.
So, at +1.00 there is a perfect positive correlation, and at -1.00 there is
a perfect negative correlation. At 0.00 there is no correlation between the
two variables. If the value is greater than 0.50 in either the positive or negative
direction, there is likely a significant correlation between the two variables.

#### The

*Slichter*