To manage a large number of candidates, IBPS conducts the exam in multiple sessions or shifts. While this is a practical necessity, it also introduces a challenge: how to ensure fairness when different shifts may have slightly different question difficulties?
To address this, IBPS uses a well-recognized statistical technique called Equipercentile Equating for normalization of scores. This ensures that no candidate is unfairly advantaged or disadvantaged just because they appeared in a particular shift.
Why Is Normalization Needed in the IBPS PO Exam?
The IBPS PO exam is conducted in multiple shifts across various days. While the examiners take care to maintain consistency, slight variations in difficulty are natural. For example, the Quant section in the morning shift may turn out to be slightly tougher than that in the afternoon shift.
If candidates from different shifts are compared solely based on raw scores, those who faced a tougher paper may be unfairly penalized. Normalization helps adjust for these differences, creating a level playing field for all candidates.
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What is Equipercentile Equating?
Equipercentile equating is a statistical method used to adjust scores from different test forms (or shifts) so that they can be fairly compared. In simple terms, it means:
A score that places a candidate at a certain percentile in one shift will be converted to the score that corresponds to the same percentile in another shift.
This method ensures that candidates with similar relative performance across shifts receive equivalent normalized scores, even if the difficulty of their respective papers was different.
The IBPS Normalization Formula
The normalization process uses the following formula:
Yₑ = Fᵧ⁻¹(Fₓ(X))
Where:
- X = raw score in Test Form A (one shift)
- Yₑ = normalized (equivalent) score in Test Form B (another shift)
- Fₓ(X) = cumulative distribution function (CDF) of scores in Shift A
- Fᵧ⁻¹ = inverse of the cumulative distribution function of Shift B
This formula simply maps a candidate’s percentile rank from one shift to the equivalent score in another shift.
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How Does IBPS Implement This Process?
The actual process followed by IBPS includes several technical steps, but here is a simplified version:
- First, IBPS collects the raw scores of all candidates across different shifts. From these, it creates a score distribution for each shift.
- To avoid minor irregularities in the data, IBPS applies smoothing techniques (like log-linear models) to make the score distributions more stable and accurate for equating.
- One shift is selected as a base session—usually the one with the most reliable statistical properties.
- For each candidate score, IBPS calculates the percentile rank within their own shift.
- Finally, that percentile rank is mapped to the equivalent score in the base session, thus producing the normalized score.
Understanding Percentiles with an Example
Let’s understand how normalization works using a simple example:
Suppose the IBPS PO exam is held in two different shifts — Shift X and Shift Y.
- In Shift X, a candidate scores 45 marks, which places them at the 75th percentile. This means the candidate performed better than 75% of the candidates in that shift.
- In Shift Y, the paper was slightly tougher, so to reach the 75th percentile, a candidate only needs to score 43 marks.
Here’s where equipercentile equating comes in.
Since both candidates are at the same percentile rank (75th percentile) in their respective shifts, they are considered to have shown the same level of performance relative to others in their group.
So, IBPS normalizes the scores to ensure fairness. The candidate who scored 43 in Shift Y will receive a normalized score of 45, equal to the equivalent performance level in Shift X.
This way, even though the actual scores were different, the relative performance was the same — and the final scores reflect that fairly.
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