Read through the example of how to calculate the standard error and confidence limits and why we calculate them.

Now try calculating the standard error and 95% confidence limits for the exposed shore.

The standard deviation for the exposed shore (from the spreadsheet) is

The number of samples (observations) is

Calculate the standard error (to two decimal places)

The 95% confidence limits are

STANDARD ERROR

The data in the speadsheet comes from the the following project that was set on a field trip.

'Does the shape of limpet shells change with exposure to wave action? Many organisms show a change in morphology according to environmental conditions. For example are limpets exposed to wave action more or less flattened than those in more sheltered situations. This can be measured by working out the ratio between height and length. Samples can be taken from different areas of the shore and the ratios statistically compared'.

The student t-test shows that there is a significant difference between the means of the populations on the two shores (i.e. there is a less than 5% probability that the differences between the means is due to chance). The limpets on the two shores do differ in their shapes. However, not every limpet on the shore was measured so how accurate is our estimate of the means of the populations? By calculating the standard error we can set confidence limits within which the true mean of the whole population should fall.

Standard error (SE) =

N is the number of samples (observations).

So for the sheltered shore (the number of samples is in the table at the bottom right of the screen shot).

SE=

SE= 0.01

The 95% confidence limits can now be calculated. These give the range within which there is a 95% the mean of the whole population should fall.

95% confidence limits = SE x 1.96

So for this example 0.01 x 1.96 = 0.02

This is written down is this format

95% confidence limits of the mean =

The mean of the sample taken from the sheltered shore was 0.31, there is a 95% probability that the mean of the whole population is within 0.02 of this value.