Step 1. Give a hard test and grade it on the percent scale. Examine the data and get sick & tired and disgusted with the % scores.
Step 2. Use a grading curve spreadsheet to transform test data from hard and challenging tests. From above to below: Use TGGS, y = x^.65
Step 3. Does this do the job?? If not, try x^.5 or x^.8 and ponder; does this do the job?? Look at various statistics and compare.
Step 4. If not, customize the grading curve spreadsheet template by changing the svalue until the job is delivered to your satisfaction. How to calculate a new svalue:
A TGGS value, t, is determined when a % score, x, is raised to the s power, that is, t = x^s; and this implies that ln(t) = s(ln(x)) or s = ln(t) / ln(x). From the sample above, four statistics are used to calculate a new svalue(use a scientific calculator):
a) To change the hi score, 94, to 99, s = ln(.99)/ln(.94) = .16(or simply use column G, where s = .2).
b) To change the mean score, 69.5, to 82.5, s = ln(.825)/ln(.695) = .53(or simply use column C, where s = .5).
c) To change the median score, 71, to 78, s = ln(.78)/ln(.71) = .73(replace .65 with .73 in column H).
d) To change the low score, 36, to 55, s = ln(.55)/ln(.36) = .59(replace .65 with .59 in column H).
e) To change the minimum passing score from 60 to 80, s = ln(.60)/ln(.80) = 2.29 for competency or mastery testing, if you dare!
Step 5. Last, review and correct the test; this validates that student growth & improvement after the test merits the adjustment.
