The given domain includes two reading tests, and two math tests. For each of these tests, scores from 150 participants are provided.
I created two tables to interpret the data obtained on the Excel spreadsheet, one to compare the mean and the standard deviation of the two reading tests, and a second to compare the mean and the standard deviation of the two math tests. Table 1 compares the mean and the standard deviation of Reading Test 1 with the mean and the standard deviation of Reading Test 2.
Table 1: Reading Test Scores
| C1rscale
Reading Test 1 |
C2rscale
Reading Test 2 |
Reading Score
Difference |
|
| Mean | 21.461 | 29.198 | +7.737 |
| Standard Deviation | 8.75899288 | 11.0333586 | +2.27436572 |
An examination of the difference in the mean of Reading Test 1 and the mean of Reading Test 2 leads one to believe that participants scored higher on the second reading test, since the mean increased by 7.737 from Reading Test 1 to Reading Test 2. Since the mean is the average of all scores, it could be said that, overall, participants scored higher on Reading Test 2. The corresponding increase in standard deviation of 2.27436572 from Reading Test 1 to Reading Test 2 indicates more variance in scores on Reading Test 2. On Reading Test 2 more participants scored above and/or below the mean of the distribution (29.198) than participants on Reading Test 1 (mean 21.461).
147 participant scores increased from Reading Test 1 to Reading Test 2. Of the three participants whose scores decreased from Reading Test 1 to Reading Test 2 (participants 3, 63, and 72), only one, participant 63, decreased by more than 2 points; the other two, participants 3 and 72, decreased by less than 0.5 points (0.45 and 0.492 respectively). Overall, participants scored higher on Reading Test 1 than on Reading Test 2. If Reading Test 1 were a pre-test, and Reading Test 2 were a post-test, it could be argued that this data indicates that the instruction that took place after Reading Test 1 and before Reading Test 2 was effective.
Table 2: Math Test Score
| C1rscale
MathTest 1 |
C2rscale
Math Test 2 |
Math Score
Difference |
|
| Mean | 18.609 | 25.820 | +7.211 |
| Standard Deviation | 7.57306288 | 9.0494668 | +1.47640392 |
Table 2 compares the mean and the standard deviation of Math Test 1 with the mean and the standard deviation of Math Test 2. The mean increased by 7.211 points from Math Test 1 to Math Test 2, therefore one could conclude that participant performance improved on Math Test 2. The standard deviation also increased, up 1.47640392 from Math Test 1 to Math Test 2, indicating more variance in test scores. On Math Test 2 more participants scored above and/or below the mean of the distribution (25.820) than participants on Math Test 1 (mean 18.609).
A closer examination of Math Test 1 and Math Test 2 individual scores shows that the score of every participant increased from Math Test 1 to Math Test 2. As with the reading tests, if Math Test 1 were the pre-test and Math Test 2 were the post-test for a unit of instruction, then, this unit of instruction could be considered effective.
For both the reading and the math tests, there were a handful of students whose scores did not improve significantly from the first to the second test. The teacher could use this data along with knowledge of those students to determine whether re-teaching were necessary. Depending upon circumstances, retesting might be more appropriate than re-teaching, but that decision would best be made by the instructor.