Basic Measurement for Education

Tests and Measurements

Mean

Median

Range

a) The standard deviation (SD) in 1.d. is large compared to the SD in 1.b. because the range of numbers is wider. That is to say that, given the outlier number 45, there is a long tail.

b) The mean is higher in 1.d. than in 1.b., because the sum of the numbers in 1.d. is greater than the sum of numbers in 1.b.

c) The median is relatively unaffected because it is based on the middle value in an odd-numbered set, which is 9 in both 1.b. And 1.d. If the set is even-numbered, the median is determined by taking the average of the two middle values.

d) The median is the best measure of central tendency for the set of scores in 1.d. because it is not skewed by the outlier number (45).

3.

Raw Score

z Score

T Score

Percentile

-3.0

20

99.865

62

11.507

35

6.6807

40

4.

a) Approximately 5% of the people taking the GRE score above 1300.

b) Approximately 85% of the people taking the GRE score above 800.

c) Approximately 85% of the people taking the GRE score below 1200.

d) Approximately 20% of the people taking the test score at 850.

e) Approximately 30% of the people taking the test score at 900.

5.

g) The correlation coefficient in the first instance is 0.831, and the results are not significant (the null hypothesis is rejected). When the lower scores of the Current Events test results (scores 15 points and lower) are used for the analysis, the correlation coefficient changes to 0.056, and the null hypothesis is rejected (p = .0837).

h) A non-truncated scatterplot shows a zero point at the Y-axis, where a truncated scatterplot can indicate the zero point at some other place, though it must be clearly marked. A truncated scatterplot may distort the data (or our perception of the data) due to the uncommon display.

i) It is likely that correlational relationship exists between the scores on the two tests, but it a causal relationship is not indicated. There is nothing in the test taking processes that would cause one test score to create the scores on the other test, thought it is reasonable to assume they move with the other due to study habits, content aptitude, and content overlap.