Chapter 4
Compare and contrast the two scales of measurement most commonly used in educational and psychological measurement.
Ordinal and equal intervals are the most commonly employed scales of measurement. These scales are more different than they are equal. The main similarity is that they are used to rank objects. On the one hand, ordinal scales offer a worse-to-better ranking of objects (Salvia, Ysseldyke & Bolt, 2013). On the other hand, when educators or psychology practitioners use equal interval scales, they wish to rank items from best to worst. The key difference between the two scales lies in the size of the difference between two values appearing next to one another. While the values in ordinal scales vary and are unknown, those in equal interval scales can be established with precision since they are known (Salvia, Ysseldyke & Bolt, 2013a). Furthermore, these values are equal in magnitude. A teacher would find ordinal and equal intervals to be useful. The ordinal values enable the teacher to gain the insights of his students regarding the quality of learning. For example, the teacher may use a scale of 1-10. On the other hand, the equal interval scale would be useful when the teacher wishes to rank the students in order of performance in a test.
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Explain the following terms: mean, median, mode, variance, skew, and correlation-coefficient.
Mean : This measure refers to the average score that is computed by dividing the total score by the number of subjects (Salvia, Ysseldyke & Bolt, 2013a). For a teacher, the mean may represent the average score that his students have scored. It offers an indication of how the entire class has performed in the test.
Median : Median refers to the value that represents the midpoint (Salvia, Ysseldyke & Bolt, 2013a). A teacher may use the median to determine the distribution of the scores of the best and poorest performers.
Mode : This figure represents the most common score (Salvia, Ysseldyke & Bolt, 2013a). It may be useful to a teacher who wishes to understand the score that most of his students obtained.
Variance : Variance is defined as a measure of the degree of deviation of score from the mean (Salvia, Ysseldyke & Bolt, 2013a). Using this measure, a teacher is able to find out how close or away from the mean score his students’ performance is.
Skew : This measure represents the level of symmetry of scores (Salvia, Ysseldyke & Bolt, 2013a). When most scores lean toward a particular side of the mean, the distribution of scores is considered skewed. Using this measure, a teacher can determine if a majority of the students registered scores that were above or below the average.
Correlation-coefficient : Is a value that depicts the relationship among various variables (Salvia, Ysseldyke & Bolt, 2013a). This value would be useful to a teacher who is keen on determining say, the degree by which a student’s attendance affected their score in a test.
Explain the statistical meaning of the following scores: percentile, z score, IQ, NCE, age equivalent, and grade equivalent.
Percentile: Is a value that captures the percentage of subjects whose scores fall below or are greater than the mean score (Salvia, Ysseldyke & Bolt, 2013a). This value would help a teacher that is interested in determining how individual students performed in relation to the rest of the class.
Z score: Z score refers to a value that is calculated using mean and standard deviation values that are set (Salvia, Ysseldyke & Bolt, 2013a). They are useful for standardizing scores. The Z score would benefit a teacher interested in establishing the degree by which the score of a particular student deviates from the mean.
IQ: This score is computed using set values. The mean is set at 100 while the standard deviation is 15 (Salvia, Ysseldyke & Bolt, 2013a). Its application is similar to that of the Z score. The IQ enables the teacher to establish the degree of a student’s score’s deviation from the mean of 100.
NCE: Normal curve equivalent (NCE) is similar to Z score and IQ. It also serves as a standard score but during computation, the mean is set at 50 and the standard deviation at 21.06 (Salvia, Ysseldyke & Bolt, 2013a).
Age equivalent: These are scores that compare the performance of a particular subject against the scores of those in the same age range (Salvia, Ysseldyke & Bolt, 2013a). This score would make it possible for a teacher to determine if students are performing as expected given their age.
Grade equivalent: Grade equivalent is somewhat similar to age equivalent. The key difference is that grade equivalent is a score which compares the score of a specific student to the performance of others in the same grade (Salvia, Ysseldyke & Bolt, 2013a). A teacher would use this score to find out if a student is lagging behind or performing at per with students in the same grade.
Why is the acculturation of the parents of students in normative samples important?
Acculturation is vital in student assessment. It essentially accounts for the cultural, social and historic background of students. Its importance lies in the fact that it makes it possible for the influence of culture, socioeconomic status and history of student scores to be established (Salvia, Ysseldyke & Bolt, 2013a).
Chapter 5
Explain evidence of validity based on relations or other measures.
Evidence of validity based on elations and other measures is intended to validate tests by comparing the results that they yield to the results obtained from some other sources (Salvia, Ysseldyke & Bolt, 2013b). This evidence is vital as it allows for the determination of whether a test actually and accurately measures the metric for which it was designed.
Explain evidence of validity based on test content.
Evidence of validity based on test content establishes the validity of a test by scrutinizing the specific contents of the test and the administration procedures followed (Salvia, Ysseldyke & Bolt, 2013b). To be considered valid, the contents and the procedures have to be such that they make it possible for the variables to be measured can actually be determined using the test.
Explain three factors that can affect a test’s validity.
Systematic bias, reliability and administration errors are some of the factors that influence the validity of a test (Salvia, Ysseldyke & Bolt, 2013b). When systematic bias exists, it becomes nearly impossible for students to exhibit the traits that a test is supposed to measure. For example, a test asking students to answer questions can only be valid when the students taking the test can write. Students who are unable to read would be disadvantaged and the test should be considered invalid. Reliability affects validity by determining how close and properly a test actually measures the variables and metrics for which it was intended. An unreliable test is likely to be equally invalid. Administration errors also affect validity. When one fails to follow the established procedures for administering a test, the risk of the test being invalid is high.
References
Salvia, J., Ysseldyke, J., & Bolt, S. (2013a). Test scores and how to use them. In Assessment: in special and inclusive education. Boston: Cengage Learning.
Salvia, J., Ysseldyke, J., & Bolt, S. (2013b). Technical adequacy. In Assessment: in special and inclusive education. Boston: Cengage Learning.
