Skills 5

Standard deviation What is it used for? This statistical test is used for measuring the degree of dispersion. It is another way of examining the spread of data but by using the mean instead of the median value. It shows use the reliability of the data. Because two sets of data could have the same mean but a very different spread of data standard deviation is used. It allows us to see the extend of reliability the mean has within the data set. A low standard deviation indicates that the mean is reliable as the data points are close to the mean. A high standard deviation indicates that there is a large variety within the data set and the mean is not reliable.

Step by step 1. Add up all your values 2. Work out the mean ( total of all values ÷ number of data sets) 3. Subtract the mean from each value 4. Square each value (that you got from step 3) 5. Add up all the values and divide by number of values( data sets) 6. Find the square root of value (from number 5) This value will be your standard deviation.

Advantages and disadvantages. Advantages Useful when used to compare the dispersion of two data sets. - Describes the average amount by which the values in a data set vary from the mean for that set. -Indicates the amount of clustering around the mean Disadvantages - Assumes that the data was distributed normally.

Chi-squared Usefulness A2 skill Usefulness It is used to investigate spatial distributions. It looks at distribution (or frequencies) of data that you can place into categories. This test is a comparative test. This means that it compares actual data collected against theoretical random distribution of the data. The data collected is called the observed data The theoretical random distribution is called the expected data What do you need to be able to use this test? Data has to be in categories The data cannot be in the form of percentages and must be in the form of frequencies Observed data must exceed a total of 20 The expected data for each category must exceed 4

Step by step 1. Assume null hypothesis 2. Place raw data into Observed column (O) . (the raw data is the frequency of that category) 3. Calculate expected frequencies by adding up the observed data and dividing it by the number of categories. Place into expected column (E) 4. Subtract O values from E values. (place in another column O-E) 5. Square each of the values ( Place values in another column O-E2) 6. Divide the figures in column O-E2 by the expected value (E) and place in another column ( (O-E)2 ÷E). 7. Total the values (O-E)2 ÷E column to give you your chi squared result (X2). 8. Work out the degrees of freedom using the following formula (n-1) where n is number of categories. 9. Compare your value to that of a critical values table (this is different to the spearman’s rank critical values table) if vaule is higher than the 0.05 significant level that you accept if low reject null hypothesis)

Advantages and disadvantages - Gives objective data. Makes no assumptions about the distribution of the data. Allows you to test the significance of the data as well as testing the distribution. Disadvantages -Human error is possible when completing the test. -Does not explain why there is or is not a pattern. It will need to be investigated further. -Frequencies of data must be put into categories. -Data cannot be in the form of percentages. -Total amount of observed data must exceed 20. -Expected data for each category must exceed 4.