1. How early can we begin assessing g with Coloured progressive matrices?
Gregor Sočan
Tina Kavčič
Maja Zupančič
Department of Psychology
University of Ljubljana

2. Coloured progressive matrices (CPM)
Raven’s progressive matrices (RPM) and the g factor
CPM: children from about 5th year
Pre-analogical operations (no complex abstract rules)
Coefficient alpha (SLO): 0.85 – 0.92 (age 7-13)
3×12 items, increasing difficulty, 2-by-2 matrices

3. Illustrations of “rules”
Pattern completion

4. Illustrations of “rules”
Identity (repetition)

5. Illustrations of “rules”
Mirroring

6. Illustrations of “rules”
Change of colour/
pattern / form
Subtraction

7. Problem and method
“How useful are CPM for children below the age of seven?”
431 children, tested at the age of three (N = 302), four (N = 285) and six (N = 318) years.
Analyses performed:
Classical (unidimensionality, reliability etc.)
Rasch scaling

8. Unidimensionality
Is the hypothesis of perfect unidimensionality tenable?  Structural equation modelling (not used here).
Age 3: 14%
Age 4: 19%
Age 6: 28%
First factor clearly dominant at age 4 and 6.
Age 3: pattern completion vs. change in orientation and filling.
What % of common variance is attributable to the general factor?  Minimum rank factor analysis.

9. Reliability (lower bounds)
Age 3 4 6
Alpha
.41
.55
.75
Bias-corrected
greatest lower bound
.61
.68
.83

10. Rasch analysis Model fit:
Number of items (out of 36) with fit MSQ > 1.3
Age 3 4 6
Unweighted MSQ 5 7
Information weighted MSQ
Reasonable stability of item parameters over time:
r’s between .93 and .97.

11. Item & person distribution: age 3
CPM.2E12 |
CPM.2B11
| CPM.2B8
| CPM.2A11
| CPM.2A12 CPM.2AB6 CPM.2AB8 CPM.2B5
| CPM.2AB9
CPM.2B6 CPM.2B9
. | CPM.2B10 CPM.2B7
| CPM.2A9
# | CPM.2A10 CPM.2AB7 CPM.2A_B CPM.2A_C
# + CPM.2B3
. | CPM.2A7 CPM.2AB4
.# |
.## | CPM.2AB5 CPM.2A_A
###### + CPM.2B2 CPM.2B4
.######### | CPM.2AB3
########## |
######## + CPM.2A8 CPM.2AB2
.############ |
.######## | CPM.2A6
##### +
.#### |
# +
| CPM.2A5
# |
| CPM.2AB1
| CPM.2A4
. |
| CPM.2B1
CPM.2A1
| CPM.2A2
| CPM.2A3
Item & person distribution: age 3
person mean
Low ability High ability
Difficult
items
Easy
items

12. Item & person distribution: age 4
| CPM.3E12 |
| CPM.3B11
CPM.3B8
| CPM.3B9
| CPM.3A11
| CPM.3A12 CPM.3AB8
CPM.3B10
. |
. | CPM.3AB9 CPM.3B5
CPM.3AB6 CPM.3A_B CPM.3A_C CPM.3B7
.# |
.### | CPM.3AB7 CPM.3B6
#### + CPM.3A10 CPM.3A7 CPM.3A_A
###### | CPM.3A9
.###### | CPM.3AB4 CPM.3B3
0 ############# + CPM.3AB5 CPM.3B4
##### | CPM.3B2
###### | CPM.3A8
### + CPM.3AB2 CPM.3AB3
.## |
# +
. | CPM.3A6
CPM.3A5 CPM.3AB1
| CPM.3A1
CPM.3A4
| CPM.3A3 CPM.3B1
CPM.3A2
person mean
Low ability High ability
Difficult
items
Easy
items

13. Item & person distribution: age 6
CPM.4E12 |
. | CPM.4B11
| CPM.4B8
. | CPM.4A11
. | CPM.4B9
CPM.4B10
# | CPM.4A12
.## | CPM.4AB8 CPM.4A_C
## |
#### +
##### | CPM.4AB9
.##### | CPM.4A_B CPM.4B7
.######## | CPM.4A_A
.###### | CPM.4B5 CPM.4B6
##### + CPM.4AB6
.###### | CPM.4A7 CPM.4A9 CPM.4AB7
.########## | CPM.4A10 CPM.4A8
.### |
### + CPM.4AB4 CPM.4AB5
.#### |
.# | CPM.4B3 CPM.4B4
### |
| CPM.4B2
# +
. | CPM.4AB2 CPM.4AB3
| CPM.4A6
| CPM.4A5
| CPM.4AB1
| CPM.4A1 CPM.4A2 CPM.4A3
CPM.4A4 CPM.4B1
Item & person distribution: age 6
Low ability High ability
person mean
Difficult
items
Easy
items

14. Test information function

15. Some interesting issues in brief:
Time stability:
r34 = .32
r36 = .33 r46 = .43
True-score correlations (upper bounds):
r34 = .49
r36 = .46 r46 = .57
No (statistically or practically) significant sex differences, including DIF.

16. Conclusions Conventional measurement standards met at the age of 6.
In certain circumstances (gifted children, group-level analysis…): 4 years.
The validity question requires further investigation.
In general, CPM is a high-quality test; some items still too easy/difficult.