                                 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 s-value until the job is delivered to your satisfaction.  How to calculate a new s-value:

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 s-value(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.      