Weighting methods

Markbook 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:

• Weighted deviation
• z-scores
• Linear weighting

Weighted deviation

This method is the default weighting. The result of each student for each task is multiplied by a factor that is based on a sum of the maximums and standard deviations of each task.

The method is similar to using z-scores, but does not require a mean and standard deviation to be specified to convert the marks into the range between 0 and the maximum of the task storing the results of the weighting.

• This method is the default used by Markbook Online after installation. Unless you have a specific reason to use another method, this is recommended because it is easy to use and takes into account the standard deviation of the marks.

When this method is chosen, there is the option of turning off the standardisation and using the linear weighting method for any individual calculation by choosing the Options button in the Edit|Calculation command, and selecting the Linear weighting only option.

z-scores

This method first converts each task into a set of z-scores. Each task is then multiplied by the weight and added to give a total as a dimension less z-score. A z-score is not a mark between 0 and the task maximum, but is a positive or negative values above or below the mean. A student with a result equal to the mean gets zero.

• z-scores can be ranked, but are more difficult to understand and so should only be used if you are specifically required to.

If necessary, you can convert the z-scores into marks with the Convert z-scores calculation of the Edit|Calculation command.

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 command, and selecting the Linear weighting only option.

Linear weighting

This method is based on multiplying the result in each task by a linear factor based on the weight of each task.

With 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 results.

If before using Markbook Online, you previously weighted student results without ever requiring statistics such as the mean and standard deviation of each task, this is probably the method previously used.

Choosing the best method

None of these methods is the right method for all situations. Each method makes assumptions about what is the most accurate interpretation of a weighted set of results.

There is debate about what a measure such "standard deviation" means for a small sample of scores and how accurately the standard deviation can be calculated in those cases.

Using the z-scores method is the most statistically rigorous, for a course with large candidature.

Conversely, if the number of students is relatively small, or the distribution of results is unusual the Linear Weighting method can be a suitable method to use.

• Using the default weighted deviation method is a compromise between the two other methods, and if you have no reason to use either of them, you can use the default settings.

The way Markbook Online calculates results is affected by the Preferences method command. In the Calculation defaults, Methods item you can set the method used by Markbook Online. Set the fields as shown in the table below to change the weighting calculations.

Weighting method	Linear weighting	z-score weighting
Weighted Deviation	No	No
z-scores	No	Yes
Linear	Yes	No

 

SMPCS makes no claim as to which method of weighting should be used with your results. Markbook Online is a flexible mathematical tool that provides different calculation methods 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.

 

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