Scale score

An introduction to Progressive Achievement Tests in Mathematics (PATMaths) Fourth Edition

About the tests PATMaths Fourth Edition: • Consists of ten mathematics tests suitable for Years 1 to 10 • Can be used to track development of mathematics skills over time • Includes multiple-choice items covering number, algebra, geometry, measurement, statistics and probability • Provides group reports and individual reports showing performance by item and strand • Provides norm reference data based on an Australian student sample • Provides detailed information on students’ strengths and weaknesses to inform teaching and learning.

The Results All tests provide the following information: • • • • • •

Test score (total of correct responses) Scale score Percentile rank Stanine Mean and standard deviation of scale and test scores Diagnostic information to inform teaching.

What does all this mean?

Test Interpretation Scale Scores Scale scores enable results on tests of different levels of difficulty to be compared. Scale scores take into consideration both the level of difficulty of the test items and the level of ability of students and are used to measure progress. For example, a test score of 18 on PATMaths Test 1 is equal to a scale score of 102.5, whereas the same test score on PATMaths Test 2 is equal to a scale score of 110.3. In both cases the standard error of measurement is 3.9.

Test Interpretation Percentile Ranks Percentile ranks provide a simple means of indicating the rank order and position of the student’s result in relation to the reference sample. For example, a student with a percentile rank of 45 has a score that is higher than the score obtained by 45 per cent of the reference group students. A student with a percentile rank of 96 has a score that is higher than the score obtained by 96 per cent of the reference group.

Test Interpretation Stanines Stanines are derived from percentile ranks. Percentile ranks are divided into 9 categories – called stanines (short for ‘standard nine’), and the categories 1 to 9 are used. Stanines are particularly useful for grouping students. It is recommended that only differences of two or more stanines should be regarded as indicating a real difference in performance.

Relationship between Percentile Ranks and Stanines

Stanine

Descriptor

9

Very high

8

High

7

Above average

4, 5, 6

Average

3

Below average

2

Low

1

Very low

The normal distribution curve

Relationship between percentile ranks and stanines Description of Performance

Stanine

Corresponding percentile ranks

Percentage of cases

Very high

9

96 and above

4

High

8

89-96

7

Above average

7

77-89

12

6

60-77

17

5

40-60

20

4

23-40

17

Below average

3

11-23

12

Low

2

4-11

7

Very low

1

0-4

4

Average

Number of students in a class of 25

Interpretation of Scores Score Ranges Results as scale scores. It is also important to pay attention to the error margin, so that small differences in scale scores are not given more importance than they deserve. Error margins tend to be larger for very high and very low scores. For example, a student with a test score of 30 on PATMaths Test 5 would have a corresponding scale score of 142.2. The error margin for this score is 4.9. We can be confident that the student’s true score would be within the range 137.3 and 147.10. That is, 142.2 plus or minus 4.9.

What to do with the data?

Key pages in the PATMaths Fourth Edition Teacher Manual Information

Page Number

Administration instructions

Pages 9–18

Describing test content

Pages 1– 6

Sample reports

Page 23–28

Test items by level of difficulty by test

Page 48

Test items by strand

Page 52

Description of scale scores

Pages 29–32

Item descriptors and curriculum links

Pages 88–108

Definitions for percentiles and stanines

Page 68–70

Mean scale scores by year level

Page 62

Score conversion tables

Pages 77–87

Score key

Page 76

Scoring and reporting masters (also on USB or as a download)

Pages 75–108

Some suggestions

• Make analysing the results of the testing a priority – allocating time for teachers to do this process is essential • Provide professional development for staff in how to interpret the data • Use the manual information to get the most out of the results.

Further suggestions • Use stanines to identify students who would benefit from further diagnostic testing • Use group diagnostic reports to identify the types of questions students have had difficulty with to inform teaching • Use levels of achievement figures to identify the types of skills students should be working towards • Use direct instruction approaches to help students develop skills • Monitor progress during the year – informally and consider use of easier tests and/or an alternative assessment • Re-test on an annual basis to measure progress and the effectiveness of interventions.

Results used to