Applying statistical techniques

Applying statistical techniques

1. Why use statistical tests?

   • ~data about variation may provides a series of numbers ->a small difference between 2 figures may or may not be signifiant ->using the correct statistical test can help to determine whether the difference observed is a significant difference of simply natural variation

2. Standard deviation

   • ~is a measure of deviation, it measures the amount of variation or spread from the mean.
     • *a low sd indicates that the data have a narrow range & the point are closely grouped to the mean =indicates greater reliability
       • *a high sd indicates that the data points have a larger range & are less well grouped =indicated lower reliability
   • ~Calculating sd
     • use the formula:
       • • s= standard deviation, x =individual value, x =mean value, n =number of data points
           • ->then say that the spread of our data set is the mean + the standard deviation
             • ->if the 'leaves' show a normal distribution, then:
               • *68% of 'leaves' should like within the range _ to _
                 • *95% of 'leaves' should lie within the 2 sd from the mean
                   • *anything outside this range might be viewed as anomalous

3. Student's t-test

   • ~is used to compare 2 means ->test whether the difference between the 2 means is a significant difference. ->first state the NULL hypothesis =that there is no significant difference between the means of these 2 sets of data. -> t-test will then test whether we can reject this hypothesis or must accept it.
   • use the formula:
     • • x is the mean of the first data set, s is the sd of the first data set squared, & n is the number of data point in the first data set. -> x , s & n refer to the second data set
   • Is this significant
     • ~the degrees of freedom are defined as the number of values in a statistical calculation that are free to vary. ->usually calculated as the (sample size) - (the number of data sets). ->in the t-test there are 2 data sets =degrees of freedom for the t-test is (n + n ) -2 =18 in this case. ->the number of degrees of freedom must be taken into account when considering if out calculated t-value is significant
       • ~we always consider the 5% significance level ->if calculated value of t is greater than value at 5% = difference between the 2 sets of data is significant ->if lower than 5% =insignificant. ->if 2 sets of data aren't significantly diff = accept null

4. Correlation coefficient

   • ~is used to consider the relationships between 2 sets of the data. ->spearman rank correlation tells us whether 2 sets of data are correlated or not
     • use the formula:
       • • r is the rank coefficient, D =difference between the ranks & n is the number of pairs of values
           • once r has been calculated, we can use a table of critical values to assess whether this value or r indicates a correlation