# Types of scores

All raw scores on Lucid Recall are saved automatically to a single data file on completion of each test. The data saved also includes the date and time the test was completed, as well as the registered details of the student. If a test has been abandoned before completion, then no results will be saved for that test. Reports are calculated in real time (at the moment of access or viewing) so that if ever any information has changed it will be incorporated in the current displays. This is important, for example, where errors have been made in entering the student’s date of birth, in which case the wrong norms may have been used by the program. Therefore if any mistakes of this nature were made then it is important to recalculate the results by generating new reports after any corrections have been made.

The program then refers to the standardised norms in order to convert raw scores to the following three types of score.

- Standard scores (and Confidence band)
- Centile scores
- Age equivalents

The first of these is shown in graphical (bar chart) format as well as numerical format, while the remaining two are shown only in numerical format. These different types of score formats are explained in the following sections.

**Figure 5. Example Single Assessment Report.**

**Figure 6. Example (Page 1) Historical Assessment Report.**

**Figure 7. Example (Page 2) Historical Assessment Report.**

## Standard scores

Standard scores are provided in 6-month age bands from 7:0 to 16:11. Standard scores have a mean (average) 100 and a standard deviation of 15. 4 They are distributed in a normal (bell shaped) curve as shown in Figure 8. Approximately two-thirds of the population will have scores that fall between plus or minus one standard deviation of the mean (i.e. score range 85 – 115, which is the area shaded blue on the graph in Figure 8). In some scoring systems the range 85 – 115 is regarded as the ‘normal’ or ‘average’ range, while other systems treat 90 – 110 as the ‘normal’ or ‘average’ range; in the latter case, 50% of the population will fall into the average band. The more extreme the score the fewer individuals are found in that category, so that only about 2% of the population have very low scores (less than 70) and about 2% have very high scores (130+). This distribution of scores is a characteristic of all human attributes (height, weight, strength, sociability, etc.), i.e. most people tend to cluster around a central point and as one approaches the extremes (known as the ‘tails’ of the distribution) fewer people are found.

**Figure 8. Distribution of Lucid Recall scores on a normal curve (the figures along the bottom of the diagram correspond to standard scores)**

4 The standard deviation is a statistical measure of the average variability of scores in a distribution.

## Confidence intervals

When reporting a standard score, it is good practice also to report the *confidence band* (or *interval*) associated with that score. The reason for this is that all psychological and educational tests scores give only *estimates* of ability, based on a sample of behaviour at a given point in time. If you were to assess a student on several occasions you would not expect them to obtain exactly the same score each time – there would be a spread of scores and somewhere within that spread we would expect the (hypothetical) *true score* to lie. The amount of spread or variation of actual scores obtained by an individual is dependent on the *reliability* of the test. The confidence interval is the zone around the standard score in which we are reasonably confident the *true score* lies. Different confidence intervals may be set: for Lucid Recall we have set a confidence level of 90%, which means that there is a 90% probability that the true standard score lies within the stated confidence interval. Put another way, if the student was retested 100 times, on 90 out of 100 occasions the score would lie within the stated confidence interval.

Confidence intervals are calculated on the basis of the* Standard Error of Measurement* (SEM) of a test which, in turn, is determined by the reliability of the test and the standard deviation of test scores (see Section 1.5).

## Centile scores

Centile scores are provided in 6-month age bands from 7:0 to 16:11. Centile scores (sometimes referred to as ‘percentile’ scores) represent the student’s performance in comparison with the population norms in centile units which range (roughly) from 1 to 99. A centile score of 63, for example, means that the students’ score lay at the point where 63% of the population scored less, and 37% scored more. A centile score of 50 indicates that the student’s score lay exactly on the median (middle point) of the distribution, with half the age group scoring higher and half lower. As will be obvious from Figure 8, centile scores have a strict relationship with standard scores as shown in Table 7.

**Table 7. Relationship between standard scores and centile scores.**

## Age equivalents

Age equivalents are provided for the age range 5:0 to 16:5 or 16:11, depending on the test (over this age, age equivalents become meaningless). Age equivalents may be defined as the average chronological age of students who would be expected to achieve a given raw score on the test. Age equivalents are another way of expressing how a given student is performing in relation to his or her peers. The most common type of age equivalent in educational testing is the ‘reading age’. For example, to say that a student has a reading age of 14 means that they read like an average 14-year-old, regardless of their chronological age.

Note that because of the way that age equivalents are calculated they are not as precise as standard scores or centile scores; age equivalents should be regarded as approximations and hence are often given in bands. Age equivalents should be used with caution and only in cases where standard scores or centile scores would be inappropriate or unhelpful. It is embarrassing and demotivating for a teenager or adult to be told (for example) that they are performing at the age of a 7-year-old! However, some teachers working in special education prefer to use age equivalents rather than centile scores, because age equivalents enable them to conceptualise the ability level of the student they are teaching, and so pitch the work at the correct level. Also, when circumstances dictate the use of Lucid Recall for assessing a student younger than 7:0 or older than 16:11, age equivalents can prove useful (see Section 2.3 for further information on this).

## Raw scores

Raw score are the actual scores obtained by the student on each test. For all except Working Memory Processing Speed the raw scores represent the number of correct items on the test (for Working Memory Composite scores have been weighted to reflect the different numbers of items in each test). For Working Memory Processing Speed the raw score represents the average time in seconds per item counted. For most purposes, raw scores are not particularly useful or interesting, but they may be relevant for some researchers. Note that two students can obtain the same raw score on a test but have different standard or centile scores if their chronological ages are different.