In articles such as Mark Calculation, Guess Correction and Automatic Scoring it is explained how these features in Ans can be enabled and how the features work. In this article, multiple examples are provided on the mark calculations, taking different situations into account. In this article, both formula and table examples are described.

## Examples formula

The difference between applying and not applying the guess correction is explained by giving multiple examples.

In the first example, we want to achieve a linear distribution of the marks. The scores are evenly distributed over the marks. You can use the default Ans formula to achieve this result. An assignment with the following characteristics is used:

- 40 multiple choice questions
- 1 correct answer per question, which is worth 1 point

- Maximum score of the assignment: 40 points
- Guess score: 10
- Minimum mark: 1
- Maximum mark: 10
- Pass mark: 5.5
- Used formula: 1+9*points/total (default Ans formula)

To show the consequences for different cases, 6 participants with different scores are included in the table below:

Participants |
A |
B |
C |
D |
E |
F |

Score |
15 | 20 | 25 | 30 | 35 | 40 |

Corrected score |
6.67 | 13.3 | 20 | 26.7 | 33.3 | 40 |

Mark without guess correction |
4.375 | 5.5 | 6.625 | 7.75 | 8.875 | 10 |

Mark with guess correction |
2.5 | 4 | 5.5 | 7 | 8.5 | 10 |

Note: in the example above, the corrected score does not drop below 0, therefore the option 'limit guess correction to 0' is not shown.

In this example, an assignment with both multiple choice and open questions is explained. Also, the consequences of either or not using the option 'Guess correction' is shown. For this example, we use an assignment with the following characteristics:

- 40 multiple choice questions
- 1 correct answer per question, which is worth 1 point

- 6 open questions

- Maximum of 10 points per question

- Maximum score of the assignment: 100 points
- Guess score: 10
- Minimum mark: 1
- Maximum mark: 10
- Pass mark: 5.5
- Used formula: 1+9*points/total (default Ans formula)

To show the difference between the options two scores of participants have been given.

Participants |
A |
B |
C |
D |

Score multiple choice questions |
0 | 5 | 5 | 10 |

Score open questions |
45 | 45 | 50 | 50 |

Total score |
45 | 50 | 55 | 60 |

Total corrected score, limit to 0 off |
31,7 | 38,3 | 43,3 | 50 |

Total corrected score, limit to 0 on |
45 | 45 | 50 | 50 |

Mark without guess correction |
5,05 | 5,5 | 5,95 | 6,4 |

Mark with guess correction, without limit to 0 |
3,85 | 4,45 | 4,9 | 5,5 |

Mark with guess correction, with limit to 0 |
5,05 | 5,05 | 5,5 | 5,5 |

Sometimes, it's desired to have a non-linear distribution of the marks, for example when an exam has a higher cut-off score. The cut-off score is in this case the percentage of points that a participant needs to answer correctly in order to receive the pass mark. All these attributes can be built into the formula. For this example, take the same situation as in example two is used.

- 40 multiple choice questions
- 1 correct answer per question, which is worth 1 point

- 6 open questions

- Maximum of 10 points per question

- Maximum score of the assignment: 100 points
- Guess score: 10
- Minimum mark: 1
- Maximum mark: 10
- Pass mark: 5.5
- Cut-off: 60% of the score
- Formula used: IF(points<(total*0.6),(4.5*points)/(0.6*total)+1,4.5*(points-0.6*total)/(0.4*total)+5.5)

The formula consists of three parts. An IF statement, the calculation if it's true and the calculation if it's not true. The three parts are separated by commas.

- IF-statement: Ans checks if the amount of points of the participant is lower than the cut-off score (60% of the maximum score, which is total*0.6).
- Calculation if true: In this case, a participant will need to score 60% of the score to get a 5.5. In the second part of the formula, Ans will first divide the number of points (60% of the points of the total) over a total of 4.5 of the marks (from 1 until the pass mark 5.5). This is done to check how many mark(s) 1 point is worth. After that, this is multiplied by the number of points of the participant. Lastly, 1 mark is added to this total (as a participant will get a 1 in case 0 points are scored).
- Calculation if not true: If the participant has scored a higher amount of points than the 60% cut-off, Ans will check the third part of the formula. Here, Ans divides 4.5 marks (from pass mark 5.5 until 10) over 40% of the points.

In this situation, points scored above the cut-off score are worth more marks than points scored below the cut-off score. When the distribution is visualized, it will show a non-linear distribution. For this reason, this method is called the non-linear cut-off method. All numbers can be adjusted accordingly to your desired cut-off. In the example above, the numbers 0.6 and 0.4 align and should always add up to 1. In case you have a cut-off percentage of 70% for example, 0.6 needs to be changed in 0.7 and 0.4 needs to be changed to 0.3.

In different situations, the following mark calculations apply. Two additional participants have been added to the example, as the cut-off is higher.

The three methods are:

- Points needed when not using the guess correction
- Points needed when guess correction in lowest points (= 2.5)
- Points needed when guess correction in cut-off score (=70%)

Mark |
No guess correction |
Lowest score |
Cut-off score |

1 | 0 | 2.5 | 0 |

2 | 1.5 | 3.5 | 1.56 |

3 | 3 | 4.5 | 3.11 |

4 | 4.5 | 5.5 | 4.67 |

5 | 6 | 6.5 | 6.22 |

6 | 6.8 | 7.33 | 7.33 |

7 | 7.6 | 8 | 8 |

8 | 8.4 | 8.67 | 8.67 |

9 | 9.2 | 9.33 | 9.33 |

10 | 10 | 10 | 10 |

It is possible to round the formula or force a roundup or round down for (a part of) the formula. We will use the same situation as in the first example. In this example, we would like the formula to round to the nearest decimal (1 decimal), except for when rounding just below the pass mark. The pass mark is a threshold and marks below the threshold should never be rounded up to the pass mark. If rounding to the nearest decimal is used, all participants with grades between 5.45 and 5.49 will receive a 5.5 as well. By making use of an IF statement, combined with the rounding options for formulas, you can make an exception for these marks.

- 40 multiple choice questions
- 1 correct answer per question, which is worth 1 point

- Maximum score of the assignment: 40 points
- Guess score: 10
- Minimum mark: 1
- Maximum mark: 10
- Pass mark: 5.5
- All grades between 5.45 and 5.49 need to be rounded down.
- Used formula: IF(AND(1+9*points/total>5.44,1+9*points/total<5.5),ROUNDDOWN(1+9*points/total,1),1+9*points/total

The formula consists of three parts:

- IF-statement combined with an AND-statement: Ans checks if the calculated mark lies between 5.44 and 5.5.
- Calculation if true: If the mark lies between these boundaries, Ans will force a round down with the same formula, rounded to 1 decimal.
- Calculation if not true: If the mark lies outside these boundaries (either below or above), the regular formula with normal rounding is used.

To show the consequences for different cases, 5 participants with different scores are included in the table below. We have excluded guess correction in this example. With guess correction, the same rounding rules apply.

Participants |
A |
B |
C |
D |
E |

Score |
19 | 19,3 | 19,4 | 19,8 | 20 |

Mark |
5.275 = 5.3 | 5.3425 = 5.3 | 5.365 = 5.4 | 5.455 = 5.4 | 5.5 = 5.5 |

Please note, we strongly recommend aligning any rounding decimals in your formula with the overall rounding that can be selected above the formula in the dropdown menu. In the example above, it might be possible that for very specific cases the result is different than desired. For example, if a participant has received a score of 19,9 points, this must not result in a 5.5 mark according to the formula used above. If the two rounding options are not aligned, this could be the case:

- The overall rounding of the mark calculation (the dropdown menu) is set to 1 decimal
- The ROUNDDOWN in the formula rounds to 2 decimals (the digit after the comma is 2)

In the specific case that a participant has received 19,9 points, the ROUNDDOWN part of the formula will make sure the participant's score is 5.47. However, the overall rounding of the formula is set to 1 decimal. As 5.47 will be rounded to 5.5, the participant will still receive a 5.5. This can be prevented if both rounding options are equal. If the rounding is set to 1 decimal, the participant will receive a 5.4, if the rounding is set to 2 decimals, the participant will receive a 5.47.

## Examples table

The table functionality is explained with two examples. The first example is using the button 'Determine cut-off score', which allows you to automatically generate a table based on input on certain variables. The second example is to manually create a table with multiple layers. This can be used when you are using a 'scale' such as insufficient - sufficient - good.

When you are in the mark calculation menu, you can click on **Determine cut-off score** when the table has been selected as the mark calculation method. For this example, the following assessment characteristics apply:

- 10 multiple choice questions
- 1 correct answer per question, which is worth 1 point
- Maximum score of the assignment: 10 points
- Minimum score of the assignment: 0 points
- Guess score: 2.5
- Minimum mark: 1
- Maximum mark: 10
- Pass mark: 5
- Cut-off score: 60%
- Rounding: halve marks

With these characteristics, a non-linear distribution of the marks will be created. It is possible to incorporate the guess correction in the mark calculation. The guess score can be applied either within the lowest amount of points or in the cut-off percentage:

- To incorporate the guess correction in the
**lowest amount of points**, equal the lowest amount of points to the guess score - To incorporate the guess score in the
**cut-off percentage**, increase the cut-off score. You can use the formula:

Corrected cut-off percentage = (GS + COP * (MS - GS)) / MS

In this formula:- GS = Guess score
- COP = Cut-off percentage
- MS = Maximum score of the assignment

The result of the mark calculation for the three different methods is shown below. The three methods are:

- Points needed when not using the guess correction
- Points needed when guess correction in lowest points (= 2.5)
- Points needed when guess correction in cut-off score (=70%)

Mark |
No guess score |
Lowest score |
Cut-off score |

1 | 0 | 2.5 | 0 |

2 | 1.5 | 3.5 | 1.56 |

3 | 3 | 4.5 | 3.11 |

4 | 4.5 | 5.5 | 4.67 |

5 | 6 | 6.5 | 6.22 |

6 | 6.8 | 7.33 | 7.33 |

7 | 7.6 | 8 | 8 |

8 | 8.4 | 8.67 | 8.67 |

9 | 9.2 | 9.33 | 9.33 |

10 | 10 | 10 | 10 |

The second option to create a table is to insert rows manually. This can be used in case scores need to be translated into letter grades. An example of a letter grade scale can be insufficient - sufficient - good. As explained in the mark calculation article, the table always rounds down in case the amount of points of a certain row is not met. For a three-point scale such as insufficient - sufficient - good, this means three rows are enough to establish the whole mark calculation table.

For an assignment with the same characteristics as in the other table example, the following situation can be applied:

Mark |
Points |
Letter grade |

1 | 0 | Insufficient |

5 | 6.8 | Sufficient |

8 | 8.4 | Good |

With this table, all participants that score lower than 6.8 points will receive a 1 and an 'insufficient' as a letter grade. All participants that score 6.8 points or higher, but lower than 8.4 points receive a 5 and 'sufficient'. Finally, all participants that score higher than 8.4 points will receive an 8 and a 'good'.

Of course, the mapping can be done accordingly to your own assignment. Also, it is possible to add additional rows if you want to differentiate for different marks. A letter grade can be applicable for multiple rows. Another outcome could be:

Mark |
Points |
Letter grade |

1 | 0 | Insufficient |

2 | 1.5 | Insufficient |

3 | 3 | Insufficient |

4 | 4.5 | Insufficient |

5 | 6 | Sufficient |

6 | 6.8 | Sufficient |

7 | 7.6 | Sufficient |

8 | 8.4 | Good |

9 | 9.2 | Good |

10 | 10 | Good |

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