# Introduction

## The nature of LASS 11-15 scores

LASS 11-15 results on each individual test are available in these forms:

Raw scores (progressive tests)

Pass rates (adaptive tests)

Centile scores

Z-scores (standard deviation units)

Age equivalent scores

Raw scores, pass rates and age equivalents are accessed via the on-screen *Data Tables* for every *LASS* test, which also show the means and standard deviations for the population norms of each test (for further explanation of this, see Section 2.4.3.2).

A *Summary Table* shows mean scores for all tests taken (see Section 2.4.3.1). Centile and standard deviation scores are shown in graphical form as bar charts on-screen and both these and the data pages can be printed out if desired. The *Graphical Profile* automatically charts the individual student’s performance against those of the norm referenced group, which is based on the student’s age in the following bands: 11:0–11:11; 12:0–12:11; 13:0–13:11; 14:0–14:11; 15:0–15:11 (see Section 2.4.2).

In the case of the progressive tests in *LASS*, raw scores represent the number of items correct in each test. In the case of the adaptive tests in the suite (i.e. * Sentence Reading*,

*, and*

**Spelling***) the*

**Reasoning***Pass Rate*is equivalent to a Raw Score. The Pass Rate is a measure of the difficulty of each item, i.e. it tells you how many students in that age band attempted that item successfully. Pass Rates are expressed as a decimal: 1.0 would mean that all students in the age band passed the item correctly, 0.0 would mean that no students in the age band passed the item correctly, and 0.5 would mean that 50% of the students in the age band passed the item correctly. The final Pass rate achieved by the student is referred to as the

*Adaptive Score*, and it is this that should be used if converting to an age equivalent score — see Section 4.5.

Raw scores are not corrected for age, but centile scores, z-scores, pass rates and adaptive scores all take account of the student’s age. Of the different types of scores, centile scores will generally be most useful for teachers, although educational and clinical psychologists may prefer to work with z-scores.

## Centile scores

*A centile score (sometimes referred to as a ‘percentile score’) should not be confused with percent correct*. It reflects a student’s ability on any given test on a scale of 1 to 99 in comparison with other students in the reference group (i.e. the norm group or the same age group). Hence the average student will obtain centile scores in the middle range (e.g. in the range 35–65), whilst an above-average student will have centile scores higher than this, and the below-average student will have centile scores lower than this. For example, a student with a centile score of 5 will be just inside the bottom 5% of students for that particular ability, and a student with a centile score of 95 will be just inside the top 5% of students for that particular ability.

## Z-scores

It is not essential for users to understand the statistical principles behind z-scores, and readers who do not have a particular interest in this may wish to skip this section. The following outline is necessarily brief: it is not intended to be a comprehensive tutorial on the subject. Readers who desire to find out more about these ideas are recommended to consult any standard textbook of statistics.

A z-score (also known as a standard deviation unit) is a statistic based on a normal distribution of scores. Most human characteristics are distributed in a normal (or approximately normal) fashion (i.e. a bell shaped curve), in which individuals cluster towards the mean (or average) and become less common as one approaches the extremes (or ‘tails’) of the distribution. The proportion of individuals that will fall in any given portion of a normal distribution can be calculated. For example, two-thirds (66%) of individuals will lie between + or – one standard deviation of the mean, while slightly less than 3% will fall below 2 standard deviations of the mean.

An advantage of z-scores is that they facilitate analysis of the *extremeness* of individual scores or of differences between scores, which are not apparent when using the centile score format. For example, consider the following results:

Centile scores |
Reasoning |
Sentence Reading |
Difference |

Student 1 |
60 | 40 | 20 |

Student 2 |
90 | 70 | 20 |

In both cases, the students’ sentence reading performance is 20 centile points below their reasoning scores. Which (if any) of these is a significant difference, i.e. one that we should take notice of when interpreting results? On centile score difference, both appear to be identical, so this format does not help us. The same results in equivalent z-score format reveal a different story:

z-scores |
Reasoning |
Sentence Reading |
Difference |

Student 1 |
0.25 | -0.25 | 0.5 |

Student 2 |
1.6 | 0.6 | 1.0 |

Now it is apparent that the difference between the two scores for Student 2 is *twice* the magnitude of the difference between the same scores for Student 1. In fact, the former would not be regarded as significant, but the latter certainly would (for explanation of how to calculate significance, see Section 4.3.3). In practice, scores at the tails of the distribution are much rarer than scores in the middle of the distribution, so differences between them will tend to assume greater significance. The z-score format allows us to determine that significance.

The term ‘normal’ here is being used in its statistical sense.

## Relationship between centile scores and z-scores

In a normal distribution of scores, centile scores and z-scores have a consistent relationship to each other and also to standard scores, (the latter, like IQ, being most usually expressed with a mean of 100 and a standard deviation of 15). This relationship is depicted in Table 5.

*Table 5. Relationship between centile scores, z-scores and standard scores.*

centile score |
3 | 5 | 17 | 20 | 25 | 50 | 75 | 83 | 97 |

z-score |
-2.0 | -1.75 | -1.0 | -0.85 | -0.66 | 0 | +0.66 | +1.0 | +2.0 |

standard score |
70 | 76 | 85 | 87 | 90 | 100 | 110 | 115 | 130 |

## Interpreting LASS 11-15 scores

How low must a *LASS* individual test result be before the teacher should be concerned about the student’s performance? Put another way: what is the critical cut-off point or threshold that can be used when deciding whether or not a given student is ‘at risk’? Unfortunately, this is not a question that can be answered in a straightforward fashion, because much depends on other factors. These include: (a) the particular *LASS* test undertaken, (b) whether the results of other individual *LASS* tests confirm or disconfirm the result being examined, (c) the age of the student being tested, and (d) the school’s or L.E.A.’s own SEN criteria or thresholds.

Conventional SEN thresholds are: below 20th centile (i.e. the ‘1 student in 5’ category) and below the 5th centile (the ‘1 in 20’ category). At one time, it was maintained that Statements of Special Educational Needs under the 1981 *Education Act* would be appropriate for only about 2% of students. Experience has shown that this, in general, is far too restrictive and that concentrating just on the lowest 2% will result in many students with special educational needs being overlooked.

Any individual *LASS* module result which falls *below the 20th centile* (i.e. near or below *one* standard deviation below the mean) is by definition significantly below average and thus indicates an area of *weakness*. This is a fairly conventional cut-off point in identifying special needs or moderate educational weaknesses. A student who falls below this threshold should always be *considered* for intervention of some kind, depending on other factors (see below). Sometimes a weakness is identified which can be remedied by appropriate training. In some cases the problem is more pervasive and requires a differentiated approach to teaching in basic skills. Where there is strong confirmation (e.g. a *number of related tests* at or below the 20th centile) then the assessor can be convinced that concern is appropriate.

Where a student is scoring *below the 5th centile* on any particular module (near or below *two* standard deviations below the mean), this generally indicates a *serious difficulty* and should always be treated as diagnostically significant, and usually this will be a strong indication that a student requires intervention. Again, where there is strong confirmation (e.g. *a number of related tests* at or below the 5th centile) then the assessor can be even more confident about the diagnosis.

However, it should not be forgotten that *LASS* 11-15 is also a *profiling* system, so when making interpretations of results it is important to consider the student’s *overall profile*. For example, a centile score of 30 for reading or spelling would not normally give particular cause for concern because it does not fall below the 20th centile threshold. But if the student in question had a centile score of 85+ on the reasoning module, there would be a significant discrepancy between ability and attainment, which *would* give cause for concern. How this is calculated is described in Section 4.3.3).

It should also be noted that the* Single Word Reading *test is the only test in the

*LASS*suite for which scores are not distributed in a normal curve. In fact, there is a significant negative skew, indicating that most students will achieve a maximum or near-maximum performance (in statistical terms this is sometimes referred to as a ‘

*ceiling effect*’). The

*test does not have sufficient sensitivity to discriminate amongst students within the average range, and so it should be confined to use with students who are*

**Single Word Reading***significantly behind*in reading development, either to determine their attainment level or evaluate progress.

## Age equivalents

An age equivalent is defined as the chronological age range of students that would be expected to achieve a given raw score (or, in the case of adaptive tests, adaptive score). *LASS* provides age equivalent scores for each module – the can be found in the Summary Table (see Section 2.4.3.1) and in the Data Table for each module (see Section2.4.3.2). In addition, a table of age equivalents for *LASS* 11-15 scores has been provided in the Appendix (see Section 9.4).

For various statistical reasons, age equivalent scores cannot be as accurate as centile scores or standard scores (e.g. z scores), so teachers should use these with care. The particular value of age equivalent scores, however, is when the teacher needs to assess a student who is outside the specified age range for *LASS* 11-15 (11:0 to 15:11) and there is no other suitable test available. Although as a general rule, *LASS* 11-15 should not be used outside the age range for which it is normed, there are exceptional circumstances when it is permissible to do so. For example, in the case of a very bright or advanced nine-year-old or a student of sixteen or over with moderate or severe learning difficulties, or an adult who has limited educational skills. Here, the centile norms may not be particularly helpful because they would be comparing the student with (in the first example) eleven-year-olds, and (in the second example) fifteen-yearolds. In such cases, age equivalents can often provide the teacher with more useful information. In fact, some teachers in special education prefer to work with age equivalents rather than centile scores, because it enables them to conceptualise the ability level of the student they are teaching, and so pitch the work at the correct level.

Age equivalents are designed to be used only in exceptional circumstances such as those illustrated above and should not be used routinely in cases where centile norms are applicable, because age equivalents give only a very rough approximation of the student’s ability. Nor should *LASS* 11-15 be used routinely above the age of 15 years 11 months to identify dyslexia as there is a screening test designed specifically for this older age group called **LADS** [Lucid Adult Dyslexia Screening] (Singleton, Horne and Thomas, 2002).For further information about LADS visit the website www.lucid-research.com

For examples of using age equivalent scores see Section 4.5.