Derived scores –make meaning of a raw score by converting it into a derived score. Will need to be converted or compared against some criterion. Three types of derived scores: 106
comparison with scores obtained.by other individuals (norm-referenced),
comparison with an absolute score established by an authority (criterion-referenced),
comparison with other scores obtained by the same individual (self-referenced).
Organizing raw score data visually allows counselors to garner information beyond simply scanning a list of raw scores. There are several ways to visually organize raw data (106)
frequency distribution tabulates the number of observations (or number of individuals) per distinct response for a particular variable.
Row and column format
Values first column, frequencies second colum, percentages third,
histogram is a graph of bars that presents the data from a frequency distribution in a more visual format
frequency polygon is a line graph of a frequency distribution
a bar graph visually depicts nominal data.
Measures of Central Tendency Measures of central tendency refer to typical score indicators or the average score for a distribution of scores.
The mean or arithmetic average, has algebraic properties that make it the most frequently used measure of central tendency. (108)
median is the middle score below which one half, or 50%, of the scores will fall and above which the other half will fall. (108)
mode is the score that appears the most frequently in a set scores. The mode for the assessment score distribution is 87. (108)
Measures of Variability Measures of variability indicate the extent of individual differences around a measure of central tendency.
RANGE – distance between the lowest and the highest scores (109)
interquartile range may be a more useful as it removes potential outliers and focuses on the range around the median (109).
The standard deviation is the most frequently reported measure of variability and represents a standardized number of units from a measure of central tendency. (109).
it is the basis for standard scores
It yields a method of presenting the reliability of an individual test score
It is used in reach studies for statistical significance.
Characteristics of data distributions –
Normal curve – (109)
data evenly distrusted around a measure of central tendency…
34% one standard deviation above and below
14% one standard deviation above and below
When data are not equally distributed around central tendency…
Skewness: large numbers of individual scores at one end of the distribution…
Kurtosis – refers to the peakedness or height or distribution…
Less variation leptokurtosis
Greater distribution platykurtosis
Norms and Ranks – Standardized tests by nature are norm referenced. Norms are established by administering the instrument to a standardization group and then referencing an individual’s score to the distribution of scores obtained in the standardization sample…can compare individual score to norms (111)
Developmental Norms – There are two types of developmental norms, or comparison of an individual’s score
The individual’s grade level or age group. Grade equivalents are often used on educational achievement tests to in comparisons.
Age comparisons, of second type of developmental norms, refer to an individual being compared with others in his or her age group. (112)
Rank – A person’s rank or standing within a group is the simplest norm-referenced statistic with s interpretation based on the size and composition of the group. It is used extensively for grades
Percentile rank is more often used because it is not dependent on the size of the comparison group. Percentile scores are expressed in terms of the percentage of people in the comparison group who fall below them when the scores are placed in rank order.
Standard Scores are defined as a score expressed as a distance, in standard deviation units, between a raw score nd the mean. There are several common types of standard scores, including z scores, T scores, CEEB scores, Deviation IQs, and stanines. (113)
Z SCORE – basic standard score is the z score, a score that allows us to estimate where a raw score would fall on a normal curve. (113)
Z score results from subtracting the raw score from the mean and dividing by the standard deviation of the distribution. (114)
Says how many SD’s above or below the mean a score is…
T SCORE – is used on a number of the most widely used educational and psychological tests.
By definition, the T score has an arbitrary mean of 50 and standard deviation of 10 & rounded to the nearest whole number…(114)
Displayed on a table that gives t score, percentile rank and interpretation.
CEEB SCORES: “College Enterance Examination Board” – Are reported in standard scores that use a mean of 500 and a standard deviation of 100. All scores are reported in increments of 10. The result is a scale that recognizable for these instruments, although the scores may be thought of simply as T scores with an additional zero added…(115)
Deviation IQ scores: Deviation IQ standard scores have since been developed to replace ratio IQs. Current results still report the mean at 100, but they report a standard score based on standard deviation units. Therefore, tests such as the Wechsler scales and foe Stanford-Binet established mean of 100 and a standard deviation of 15 or 16….(116)…
A stanine (based on the term standard nine) is a type of standard score that divides a data distribution into nine parts.
Each stanine, with the exception of Stanines 1 and 9, divide standard deviation unit on a normal curve in half….
Stanines have a mean of five and SD of 2
Rarely used, hard to translate meaning….
Standard Error of Measurement – yields the same type of information as does the reliability coefficient but is specifically applicable to the interpretation of individual scores. represents the theoretical distribution that would be obtained if an individual were repeatedly tested with a large number of exactly equivalent forms of the same test.