#### Developmental Quotient

A **developmental quotient** an estimate of the rate of development. If we know a student's developmental age and chronological age, it is possible to calculate a developmental quotient. For example, suppose a student's developmental age is 12 years (12 years

Developmental age 144 months / Chronological age 144 months X 100 = 100

144/144 X 100 = 100

1/1 X 100 = 100

But, suppose another student's chronological age is also 144 months and that the developmental age is 108 months. Using the formula, this student would have a developmental quotient of 75.

Developmental age 108 months/ Chronological age X 100 = 75

108/144 X 100 = 75

Developmental quotients have all of the drawbacks associated with age and grade equivalents. In addition, they may be misleading because developmental age may not keep pace with chronological age as the individual gets older. Consequently, the gap between developmental age and chronological age becomes larger as the student gets older.

#### Scores of Relative Standing

**Percentile Ranks** A percentile rank is the point in a distribution at or below which the scores of a given percentage of students fall. Percentiles provide information about the relative standing of students when compared with the standardization sample. Look at the following test scores and their corresponding percentile ranks.

Student | Score | Percentile Rank |

Delia | 96 | 84 |

Jana | 93 | 81 |

Pete | 90 | 79 |

Marcus | 86 | 75 |

Jana's score of 93 has a percentile rank of 81. This means that 81 percent of the students who took the test scored 93 or lower. Said another way, Jana scored as well as or better than 81 percent of the students who took the test.

A percentile rank of 50 represents average performance. In a normal distribution, both the mean and the median fall at the 50th percentile. Half the students fall above the 50th percentile and half fall below. Percentiles can be divided into quartiles. A quartile contains 25 percentiles or 25 percent of the scores in a distribution. The 25th and the 75th percentiles are the first and the third quartiles. In addition, percentiles can be divided into groups of 10 known as deciles. A decile contains 10 percentiles. Beginning at the bottom of a group of students, the first 10 percent are known as the first decile, the second 10 percent are known as the second decile, and so on.

The position of percentiles in a normal curve is shown in Figure 4.5. Despite their ease of interpretation, percentiles have several problems. First, the intervals they represent are unequal, especially at the lower and upper ends of the distribution. A difference of a few percentile points at the extreme ends of the distribution is more serious than a difference of a few points in the middle of the distribution. Second, percentiles do not apply to mathematical calculations (Gronlund & Linn, 1990). Last, percentile scores are reported in one-hundredths. But, because of errors associated with measurement, they are only accurate to the nearest 0.06 (six one-hundredths) (Rudner, Conoley, & Plake, 1989). These limitations require the use of caution when interpreting percentile ranks. Confidence intervals, which are discussed later in this chapter, are useful when interpreting percentile scores.

**Standard Scores** Another type of derived score is a **standard score**. Standard score is the name given to a group or category of scores. Each specific type of standard score within this group has the same mean and the same standard deviation. Because each type of standard score has the same mean and the same standard deviation, standard scores are an excellent way of representing a child's performance. Standard scores allow us to compare a child's performance on several tests and to compare one child's performance to the performance of other students. Unlike percentile scores, standard scores function in mathematical operations. For instance, standard scores can be averaged. In the Snapshot, teachers Lincoln Bates and Sari Andrews discuss test scores. As is apparent, standard scores are equal interval scores. The different types of standard scores, some of which we discuss in the following subsections, are:

- z-scores: have a mean of 0 and a standard deviation of 1.
- T-scores: have a mean of 50 and a standard deviation of 10.
- Deviation IQ scores: have a mean of 100 and a standard deviation of 15 or 16.
- Normal curve equivalents: have a mean of 50 and a standard deviation of 21.06.
- Stanines: standard score bands divide a distribution of scores into nine parts.
- Percentile ranks: point in a distribution at or below which the scores of a given percentage of students fall.

**Deviation IQ Scores Deviation** **Deviation IQ** scores are frequently used to report the performance of students on norm-referenced standardized tests. The deviation scores of the *Wechsler Intelligence Scale for Children–III *and the *Wechsler Individual Achievement Test–II *have a mean of 100 and a standard deviation of 15, while the *Stanford-Binet Intelligence Scale–IV* has a mean of 100 and a standard deviation of 16. Many test manuals provide tables that allow conversion of raw scores to deviation IQ scores.

**Normal Curve Equivalents **Normal** **curve equivalents (NCEs) a type of standard score with a mean of 50 and a standard deviation of 21.06. When the baseline of the normal curve is divided into 99 equal units, the percentile ranks of 1, 50, and 99 are the same as NCE units (Lyman, 1986). One test that does report NCEs is the Developmental Inventory-2.However, NCEs are not reported for some tests.

**Stanines** Stanines are bands of standard scores that have a mean of 5 and a standard deviation of 2. Stanines range from 1 to 9. Despite their relative ease of interpretation, stanines have several disadvantages. A change in just a few raw score points can move a student from one stanine to another. Also, because stanines are a general way of interpreting test performance, caution is necessary when making classification and placement decisions. As an aid in interpreting stanines, evaluators can assign descriptors to each of the 9 values:

9—very superior

8—superior

7—very good

6—good

5—average

4—below average

3—considerably below average

2—poor

1—very poor

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