Testing and Assessment
Describe the basic characteristics of a standardized test and norms.
Standardized tests are administered and scored in a consistent manner. When standardized tests are given, conditions are held consistent and conducted in a predetermined way that is considered the standard for the test. Some of the variables that are held constant include, such as the test questions, the conditions for administering the tests, the scoring procedures and interpretations of the answers. Norms are generated by using a single test score to relate it to the test scores of other students, or by the same students at different times. Norms are generally established on a nation-wide basis on standardized tests rather than classroom tests that are made by teachers.
A test measuring basic math skills in adults is normally distributed, with mean = 20 and standard deviation = 7.
Calculate the z score and T score for each of the following test scores:
The formula for computing z-scores is:
Raw Scores
Z Scores
11
-1.29
Score is less than the mean by more than1 standard deviation
18
-0.29
Score is less than the mean by about 1/4 standard deviation
24
0.57
Score is more than the mean, by about 1/2 standard deviation
32
1.71
Score is more than the mean by more than1 standard deviation
This means the formula for computing standard scores is:
Or this more complex formula: t = [ x - ? ] / [ s / sqrt ( n ) ]
Raw Scores
Z Scores
T Scores
11
-1.29
-1.46
18
-0.29
-0.46
24
0.57
0.39
32
1.71
1.54
What is the usefulness of transforming raw scores to z scores or T scores? What do these numbers tell us?
Converting individual raw scores into a standardized form provides a more meaningful description of the individual scores that make up the distribution. Z scores are a conversion of individual raw scores into a standardized form that relies on the population mean and standard deviation. T scores -- also known as standardized scores -- are a conversion of individual raw scores into a standard form, and the transformation is made without knowledge of the population's mean and standard deviation. Because the population parameters are not know, the statistician must estimate them by using...
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