Calculations
Weighting methods
SM-Marks Online has three different methods that can be used when weighting tasks. Each method may give a different set of results depending on the distribution of marks.
The methods are:
- Standardise
- Weighted Deviation
- Linear Weighting
Standardise
This method first standardises each task to the specified mean and standard deviation using the same formula used with the Standardise calculation.
Each task is then multiplied by the weight and added to give a total that is linearly scaled to the required maximum.
This method is the default used by SM-Marks Online, until otherwise changed. If before using SM-Marks Online, you previously weighted student results with a formula that first required the standard deviation of each task, this is probably the same method previously used.
When this method is chosen, there is the option of turning off the standardisation and using the linear weighting method for individual calculations by choosing the Options button in the Edit Calculation pop-up, and selecting the Linear weighting only option.
Weighted Deviation
This method produces similar, but different, results to the first method. The main difference is that each student result is not individually standardised.
Instead, the result for each task is multiplied by a factor that is based on a sum of the maximums and standard deviations of each task. This method is the same as the old Motorised Markbook.
Linear Weighting
This method is based on multiplying the result in each task by a linear factor based on the weight for each task.
Using this method the calculation of each weighted total is independent of the other students. There is no attempt to alter, or take into account, the distribution of students.
If before using SM-Marks Online, you previously weighted student results without ever requiring the statistics for each task, this is probably the method previously used.
Choosing the best method
None of these methods is the best method for all situations. Each method makes certain assumptions about what is the most accurate interpretation of a weighted set of results.
As a guide, the Standardise method is closest to what the NSW Board of Senior Studies has used when manipulating results for a course with large candidature.
Conversely, if the number of students in the calculation is not large, or the distribution of results does not follow the normal bell curve, both the Standardise and Weighted Deviation methods can distort the final results in unexpected ways.
For some situations, particularly those with a relatively small number of students, or certain distributions of results, the Linear Weighting method is a more suitable method to use. The way SM-Marks Online calculates results is affected by the Preferences method command. In the Calculation defaults, Methods item you can set the method used by SM-Marks Online. Set the fields as shown in the table below to change the weighting calculations.
| Weighting method | Linear weighting | Weighted deviation |
| Standardise | No | No |
| Linear weighting | Yes | No |
| Weighted Deviation | No | Yes |
SMPCS makes no claim as to which method of weighting should be used. SM-Marks Online is a flexible mathematical tool that provides different methods of calculating to satisfy the needs of different schools and teachers.
When weighting results, and in general when doing any calculations, due care should be exercised to ensure the results produced are those intended.