VB 2010 - Rank The Data - Divide The Data - Find The Median

There are few steps to find out the half slopes of the graph.

Step 1: Rank the data The independent variable is required to rank it from the lowest to the highest.

Step 2: Divide the data Divide the sample size into 3 roughly equal parts, which is the lowest, middle and the highest parts. If n/3 has remainder of 1, +1 into the middle part. If n/3 has remainder of 2, +1 into the lower part.

Step 3: Find the median The size of each part = n, find the ((n+1)/2)^th value for both dependent and independent variables. If the ((n+1)/2)^th is not an integer, sum up the 〖n/2〗^th value and ((n+2)/2)^th value and divide the total by 2 to make it as median. The median, m1 for independent variable in lower part indicate as XL , middle part median, m2 as XM and the highest part median m3 as XH. For the dependent variable the median is indicate as YL, middle part as YM and the highest part as YH . Figure 3.2 Example of median m1, m2 and m3

Step 4: Find the half slope Find the half slope for the lower half, b_L=(Y_M-Y_L)/(X_M-X_L ) and for the upper half, b_H=(Y_H-Y_M)/(X_H-X_M ) .

Step 5: Find the half slope ratio, b_0=b_L/b_H . If the ratio is negative, the dependent variable need to add with a constant, c in order to make the slope same direction.

Step 6: Identify transformation. Depend on the graph pattern pick one type of transformation which is nearest to the original of the variable.

Step 7: New half slope Find out the new half slope ratio, b1 by repeat step 4 and 5 with the transformed variable.

Step 8: Repeats steps Repeat step 6 and 7 with choose the transformation which is nearest to previous transformation and find the new half slope ratio, b2, b3,�, bn. Repeating this step until |1-b_i |≤|1-b_j |, for i<j, i and j = 1,2,3,

Step 9: Result bi is chosen. The data transformation used in bi is the most closest to be normality.

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