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Statistical formula for the net difference test
Formula for proportions
For any row, and any of the four columns being tested (i=1,2,3, and 4):
Notation
Description
W i
Sum of the weights (weighted base) for column i.
Q i
Sum of the squared weights for column i.
E i = (W i * W i) / Q i
Effective base for column i.
P i
Proportion in column i
For a table with overlap or a grid table, and any pair of columns from the four being tested (i and j=1,2,3, and 4):
Notation
Description
W ij
Sum of the weights (weighted base) for respondents in both columns.
Q ij
Sum of the squared weights for respondents in both columns.
E ij = (W ij * W ij) / Q ij
Effective base for respondents in both columns.
P ij
Proportion for respondents belonging in the row being tested for both columns.
The formula is: where
numer = (P 3 - P 4) - (P 1 - P 2)
and for a non-grid, non-overlap table For a table with overlap or a grid table where The degrees of freedom are: where, for a non-grid, non-overlap table and For a table with overlap or a grid table and Formula for means
For any row, and any of the four columns being tested (i=1,2,3, and 4):
Notation
Description
W i
Sum of the weighted base for column i.
Q i
Sum of the squared weights for column i.
E i = (W i * W i) / Q i
Effective base for column i.
X i
sum of values for column i
Y i
sum of squared values for column i
M i
mean for column i=X i/W i
The values can be either numeric values or factor values.
For a table with overlap or a grid table, and any pair of columns from the four being tested (i and j=1,2,3, and 4):
Notation
Description
W ij
Sum of the weighted base for respondents in both columns
Q ij
Sum of the squared weights for respondents in both columns
E ij = (W ij * W ij) / Q ij
Effective base for respondents in both columns
The intermediate term SX is: The tstat is where
numer = (M 3 - M 4) - (M 1 - M 2)
and for a grid, non-overlap table, For a table with overlap or a grid table where For a non-grid table with overlap, R ij reduces to 1.