APASO-III - Quotient Scores (Q-score) and Percentile Scores (P-score)

1. Q-score and P-score

In APASO-III, Quotient Scores (Q-score) and Percentile Scores (P-score) are adopted to replace the previous approach of using mean and effect size for expressing results and simplify the data comparison between different subscales.

The Q-score is similar to the intelligence quotient (IQ). In APASO-III, the mean and standard deviation of the Q-score for all schools in Hong Kong are set to 100 and 15 respectively. A Q-score of a school’s subscale above 100 indicates that the school’s average performance is higher than that of all schools in Hong Kong, and vice versa. Responses in the negatively phrased subscales would be recoded such that a high Q-score usually means more educationally desirable, making it easier for schools to compare the performance across subscales.

P-score puts schools in ranking order from 1 to 100. A P-score 50 and a Q-score 100 represent the average performance of all schools in Hong Kong and they are identical. Q-score and P-score have a one-to-one correspondence, meaning that the higher the Q-score, the higher the corresponding P-score and school’s ranking, and vice versa.

Q	P	Q	P
85	15.9	101	52.7
86	17.5	102	55.3
87	19.3	103	57.9
88	21.2	104	60.5
89	23.2	105	63.1
90	25.2	106	65.5
91	27.4	107	68.0
92	29.7	108	70.3
93	32.0	109	72.6
94	34.5	110	74.8
95	36.9	111	76.8
96	39.5	112	78.8
97	42.1	113	80.7
98	44.7	114	82.5
99	47.3	115	84.1
100	50.0	116	85.7

Schools should pay attention to the uniform difference between Q-scores, that is, the differences between Q-scores 90 to 100 and Q-scores 100 to 110 represent the same magnitude of change. This makes it easy for schools to conduct data analysis of different years. In contrast, P-score does not have this characteristic. The same difference in P-score does not represent the same magnitude of change in performance. From the table above, it can be seen that when the Q-score is close to 100, the change in P-score is about 2.5 for every 1-point change in Q-score, whereas the change in P-score is about 1.6 when the Q-score closes to 85 or 116. An increase in P-score from 60 to 65 does not represent the same level of improvement as an increase from P-score 70 to 75. Thus, it is recommended that schools mainly use Q-score for interpreting data.

2. The maximum and minimum value

PQ-value

The figure above shows the normal distribution of Q-score and P-score. Since the accuracy at the two extreme ends is less reliable, the maximum and minimum Q-score in the APASO-III report are set at 116 and 85 (corresponding to P-score 85.7 and 15.9) respectively. Schools with Q-score below 85 or above 116 will be reported as 85 and 116 respectively.

3. Data interpretation

Although the Q-score could facilitate users to quickly understand their school performance compared to other schools in Hong Kong, without comparing the raw mean of Hong Kong and their own schools, schools should pay attention to the comparisons of student performance among subscales or cross-year changes in the data. This does not mean encouraging schools to set an objective of surpassing the norm. Schools should also refer to other school-based information and teachers’ observation to comprehensively examine students’ affective and social performance.