SL Statistical Analysis

Error bars are a graphical representation of the variability of data. Error bars can be used to show either the range of the data or the standard deviation.

Mean: add all the values together and divide by the number of values.
Standard deviation:
1. STAT
2. Edit...
3. Enter data
4. STAT
5. CALC
6. 1-var
7. 2ND L1

The term standard deviation is used to summarize the spread of values around the mean, and that 68% of the values fall within one standard deviation of the mean. About 95% fall within 2 standard deviations.

The standard deviation shows how the values are spread above and below the mean. A small standard deviation means that the values/data are closely grouped around the mean. A large standard deviation indicates that the values are more widely spread.
We can use the standard deviation to decide whether the differences between two means are significant. If the difference between the two means is larger than that of the standard deviations then the difference between the two means is significant. If the difference between the two means is smaller than that of the standard deviation then the differences between the two means are insignificant.

The t-test is used to deduce the significance of the difference between two sets of data, other than that caused by chance. It measures the overlap of two sets of data. The data must have a normal distribution and a sample size of at least 10. The value for t will be given. The next step to calculate the degrees of freedom by adding the number of values in each data set together and subtracting 2. then find the critical value for t. Look on the table of critical values along the row for the degrees of freedom and find the value corresponding to a probability value of 5% or 0.05. Finally use the values to determine the significance. If the calculated t value is greater than the critical value the probability is low that the difference is due to chance. It can then be concluded that there is significant difference.

It often looks as though two variables may be linked. There may be no correlation, a positive one or a negative one. However, the existence of a correlation does not establish that there is a casual relationship between the two variables.
An example is looking at light intensity and vegetation density; water temperature and limpet movement. Two sets of data can be collected and a scatter graph drawn along with a line of best fit. In the first example a positive correlation would seem reasonable, since there is more light for photosynthesis. However, in the second example, even if we found a correlation, we could not be sure that the limpet movement was linked to the water temperature as this could have changed some other factor which in turn altered the limpet movement.