On-line statistics

Pearson's Product Moment correlation

 the relationship should be linear (draw a scatter graph)

 data points within samples should be independent from each other

 interval scale data are most suitable for the PPM

 both data sets should follow a normal distribution

 all individuals must be selected at random from the population

 all individuals must have equal chance of being selected

 a significant correlation does not necessarily mean cause and effect

Correlation tests are used to assess whether there is a relationship between two or more variables. For instance, a tall Homo sapiens individual will have longer arms and legs when compared to a short Homo sapiens. The arms and legs will have some variation but generally longer arms will accompany longer legs, and vice versa. The evolutionary implications of the reverse (especially longer arms and shorter legs) are regressive. In a relationship where both variables (arm and leg length) increase the relationship is said to be positive. A negative relationship is where one of the variables decreases as the other increases. An example would be the growth of a plant species relative to altitude.

This latter example is a good one to discuss the lack of cause and effect. Just because the growth of a plant species declines with increasing altitude does not mean it is the fault of altitude. With altitude comes several other factors that could inhibit the growth of plants. Temperature, lack of oxygen, poor soil nutrients and a host of other potential variables which could all be found to correlate negatively with plant growth.

Excel can calculate the correlation coefficient r , using the CORREL function or the Correlation tool in the Analysis Toolpack. Data can be in rows or columns but as always in columns for the statistical packages.

(Degrees of freedom = pairs of observations - 2)

The output from Pearson's Product Moment is similar to that shown below:

You can check that the program has used the right data by making sure that the degrees of freedom (27) are correct. The values you then need to use in order to reject or accept your H_O, is the Pearson Correlation value (0.635) and the Probability value (1.07E-04 [0.000107]). The latter value shows the actual probability value rather than the one you selected (normally 0.05). If the P-value is less than 0.05 the H_O can be rejected. When using Excel, the only value given is the Correlation coefficient (0.635). Unfortunately, you will need to look up the critical value from the Pearson Product Moment tables and compare the two values. If the calculated value is greater than the critical value reject the H_O. In the above case the critical value at 0.05 confidence level and n - 2 degrees of freedom (29-2=27) is 0.367. Therefore the H_O must be rejected.

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Descriptive Stats

Diversity Indices

Comparisons

Correlations

Regression