Post on 08-Aug-2020
Relating your PIRA and PUMA test marks
to the national standard
We have carried out a detailed statistical analysis between the results from the PIRA and PUMA tests for Year 2
and Year 6 and the scaled scores of the 2016 national tests.
In doing this, the PIRA and PUMA test raw scores of 1,150 children for PiRA and over 1,400 children for PUMA
from 56 schools across the country have been linked to the scaled scores achieved by the same children in their
actual national tests*.
In order to describe the relationship between the Rising Stars PIRA and PUMA tests and the national test
scores, a statistical technique known as linear regression was used to model the relationship between the two
variables. Outputs of this analysis are provided below as tables and graphs to assist teachers in using the
findings to relate their own children’s PiRA and PUMA marks to the national test scaled scores.
*Please note that this will be indicative only. Other factors can influence a child’s performance on any given day.
How this analysis will help you
The results of this analysis provide teachers with a clear indication of the marks children are likely to need in
their PIRA and PUMA tests in order to achieve a scaled score of 100 or above when they sit their national tests.
The Relationship Tables show what PIRA and PUMA raw marks were achieved by children who went on to
achieve 100 or more in the national tests. Children achieving similar scores in the PIRA and PUMA tests in 2016-
2017 would therefore be operating at the national standard. The analysis correlates all PIRA and PUMA marks
to the full range of scaled scores from 85 to 115 at KS1 and 80 to 120 at KS2. This analysis should concentrate
efforts to help identify those currently on track to perform slightly below the 100 scaled score, so you can use
your PIRA and PUMA gap analysis to highlight the areas for development/intervention.
Relating your PIRA and PUMA test marks
to the national standard
Using the Relationship Tables
The Relationship Tables have been created to enable you to monitor the marks children are likely to need in their PIRA and PUMA tests in
order to achieve a scaled score of 100 or above when they sit their national tests
The middle column shows you the child’s Estimated Scaled Score. The numbers on either side of this are prediction and confidence intervals –
this simply means they show the lowest score the child is likely to achieve, and the highest. Because all children and all test experiences vary, it
is impossible to say that they will definitely achieve the number in the middle column – but you can be comfortable that there is a 95% chance
they will achieve a score between the lowest and highest listed in that row.
Using the Relationship Graphs
For each table there is a corresponding graph which has the PIRA or PUMA test marks plotted against the national test scores, for easy
reference. Either side of the central line are two lines directly above and below which show the upper and lower 95% confidence limits for the
estimated scaled score of all pupils in the population.
The outer lines show a prediction with 95% confidence for individual pupil’s scaled score from their PIRA or PUMA test mark.
PiRA 2 Autumn Test Relationship Table
National test scores
PIRA 2
Autumn Test
mark
Lower 95%
prediction
limit
Lower 95%
confidence limit
Estimated
Scaled Score
Upper 95%
confidence limit
Upper 95%
prediction limit
1 <85 90 91 92 102
2 <85 91 92 93 102
3 <85 92 93 93 103
4 <85 93 94 94 104
5 <85 94 94 95 105
6 85 95 95 96 106
7 86 96 96 97 107
8 86 96 97 98 108
9 87 97 98 98 108
10 88 98 99 99 109
11 89 99 100 100 110
12 90 100 100 101 111
13 91 101 101 102 112
14 92 102 102 102 113
15 92 103 103 103 114
16 93 104 104 104 114
17 94 104 105 105 115
18 95 105 106 106 >115 19 96 106 106 107 >115 20 97 107 107 108 >115 21 98 108 108 109 >115 22 98 109 109 110 >115 23 99 109 110 110 >115 24 100 110 111 111 >115 25 101 111 112 112 >115
PiRA 2 Autumn Test Relationship Graph
PiRA 2 Spring Test Relationship Table
National Test scores
PIRA 2 Spring
Test mark
Lower 95%
prediction
limit
Lower 95%
confidence limit
Estimated
Scaled Score
Upper 95%
confidence limit
Upper 95%
prediction limit
1 <85 <85 85 86 94
2 <85 85 86 87 96
3 <85 87 87 88 97
4 <85 88 88 89 98
5 <85 89 89 90 99
6 <85 90 91 91 100
7 <85 91 92 92 101
8 <85 92 93 93 102
9 85 93 94 94 103
10 86 94 95 95 104
11 87 95 96 96 105
12 88 96 97 97 106
13 89 98 98 98 107
14 90 99 99 99 108
15 91 100 100 100 109
16 92 101 101 101 110
17 93 102 102 102 111
18 94 103 103 103 112
19 95 104 104 105 113
20 96 105 105 106 114
21 97 106 106 107 >115
22 98 107 107 108 >115 23 99 108 108 109 >115 24 100 109 110 110 >115 25 101 110 111 111 >115
PiRA 2 Spring Test Relationship Graph
PiRA 2 Summer Test Relationship Table
National Test scores
PIRA 2 Summer
Test mark
Lower 95% prediction
limit
Lower 95%
confidence limit
Estimated
Scaled Score
Upper 95%
confidence limit
Upper 95%
prediction limit
1 <85 84 85 87 95
2 <85 85 86 88 96
3 <85 86 88 89 97
4 <85 88 89 90 98
5 <85 89 90 91 99
6 <85 90 91 92 100
7 <85 91 92 93 101
8 <85 92 93 94 102
9 <85 93 94 95 103
10 85 94 95 96 104
11 86 95 96 97 106
12 87 97 97 98 107
13 89 98 98 99 108
14 90 99 99 100 109
15 91 100 100 101 110
16 92 101 101 102 111
17 93 102 102 103 112
18 94 103 103 104 113
19 95 104 104 105 114
20 96 105 105 106 115
21 97 106 107 107 >115 22 98 107 108 108 >115 23 99 108 109 109 >115 24 100 109 110 110 >115 25 101 110 111 111 >115
PiRA 2 Summer Test Relationship Graph