## Grade calculation in Cirrus

In Cirrus, to assign grades to test scores, you choose an assessment scale. For example 1-10 (55%) – rounded off to grades with decimals – with grades between 5 and 6 *(1-10 (55%) – TIENDE cijfers - mét cijfers tussen 5 en 6)*. In this assessment scale, the percentage (here: 55%) is used to determine the cut-off score (fail/pass boundary). The grades are determined based on the cut-off score: grades 1-5.4 below the cut-off score and grades 5.5-10 from the cut-off score.

The default grade sequence set in Cirrus runs from 0-10. The various assessment scales in Cirrus use '1-10' because grades below 1 are not used. The grades 0-1 have been converted to 1.

**Example:**

• Assessment scale: 1-10 (55%) – rounded off to grades with decimals – with grades between 5 and 6

• 40 multiple choice questions with 4 alternatives

• Maximum possible score: 40

• Cut-off score: 40*0.55= 22

The 5.5 (= lowest pass) is based on a percentage (here: 55%) of the maximum possible score (here: 40). The remaining grades are distributed upwards and downwards at equal intervals from the cut-off point.

• With test score 22, the student receives a grade 5.5

• If the test score is < 4.2, the student will receive a grade 1

The 40 score points are divided over 100 points (because of rounding off to 1 decimal: 0.1;0.2;0.3…9.9;10).

The number of score points divided over 55 grade steps below 5.5 (from 0 to 5.49) is 22 (22 - 0). The number of score points above the cut-off mark that is divided over 45 grade steps (from 5.5 to 10) is 18 (40-22). This gives the following score distribution.

In this distribution, the series actually starts with test score 0 = grade 0. Score 3.8 - 4.19 = grade 1. However, students with test scores below 4.20 all receive a grade 1.

## Grade calculation in Cirrus when applying chance score correction

When constructed response questions are used in Cirrus, the option is given to apply chance score correction to determine the cut-off score. This is based on the chosen assessment scale. The formula used to calculate the cut-off score is:

*((maximum possible score - chance score)* cut-off percentage) + chance score*

The formula that Cirrus applies is a common formula for **calculating the cut-off score** with chance score correction. Note that this is not the same as calculating grades with a formula. Only the cut-off score is calculated with this formula. The grades above and below 5.5 are distributed in the same way as for the 'original' assessment scale from the cut-off point with equal intervals upwards and downwards. After the test has been administered and scored, the test scores are linked to the grades.

**Example:**

• Assessment scale: 1-10 (55%) 1-10 (55%) – rounded off to grades with decimals – with grades between 5 and 6

• 40 mc questions with 4 alternatives

• Maximum possible score: 40

• Chance score: 40*0.25= 10

• Cut-off score: ((40-10)*0.55) + 10= 26.5

• With a score of 26.5, the student receives a grade 5.5

• If the score is < 13.15, the student will receive a grade 1

The 30 score points (40-10) are divided over 100 grade points (because of rounding to 1 decimal: 0.1;0.2;0.3….9.9;10). The number of score points divided over 55 grade steps below 5.5 (from 0 to 5.49) is 16.5 (26.5 - 10) and the number of score points above the cut-off point that is divided over 45 grade steps (from 5.5 to 10) is 13.5 (40-26.5). This gives the following score-grade distribution.

In this distribution, the series actually starts with test score 10 = grade 0. Score 12.85 to 13.14 = grade 1. However, students with test scores below 13.15 all receive a grade 1.

## Grade calculation in Cirrus after changing the cut-off percentage

When setting the assessment scale in Cirrus, you can change the default cut-off percentage of '55%'. The cut-off score (pass/pass boundary) is then calculated based on the percentage entered. The other grades are based on the cut-off score: grades 1-5.4 below the cut-off score and grades 5.5-10 from the cut-off score.

After changing the cut-off percentage, the series of grades changes from 0-10 (where 0-1 = 1) to 1-10.

**Example:**

• Assessment scale: 1-10 (55%) 1-10 (55%) – rounded off to grades with decimals – with grades between 5 and 6

• 40 mc questions with 4 alternatives

• Maximum possible score: 40

• Cut-off score: 40*0.65= 26

• With test score 26, the student receives a grade 5.5

• If the test score is 0, the student will receive a grade 1

The 40 score points are divided over 90 grade points (grades from 1-10 and rounding of 1 decimal: 1.1;1.2;1.3…9.9;10).

The number of score points distributed over 45 grade steps below 5.5 (from 1 to 5.49) is 26 (26 - 0) and the number of score points above the cut-off point that is divided over 45 grade steps (from 5.5 to 10) is 14 (40-26). This gives the following score-grade distribution.

Because more score points are distributed under the cut-off score, the steps are larger than above the cut-off score. This gives a distribution with a kink at 5.5.

In this distribution, the series starts with test score 0 = grade 1.

If you want to use a cut-off percentage other than 55% in combination with grades from 0-10 (where 0-1 = 1), you have to export the test scores from Cirrus and calculate the grades outside Cirrus. You can use a specially developed conversion file (Excel). See How do I modify the Cirrus results outside Cirrus and transfer them to Osiris? for more information. Please ask for help from your faculty’s digital assessment coordinator.