Addition is a combining of values. The most important thing to remember about addition is that values can be added in any order, i.e., that addition is commutative and associative.

commutative property: 7 + 8 + 3 = 7 + 3 + 8 = 8 + 3 + 7
associative property: (7 + 8) + 3 = 7 + (8 + 3)

Addition of a negative number is the same as subtraction.

7 + (-3) = 7 - 3 = 4
a + (-b) = a - b
a - (-b) = a + b
Note! I don't care how they taught you to do it in high school. Never write a + (-b) or a - (-b) in this class! It will be marked wrong. Use the correct sign.

The summation sign, Σ, tells you to sum the quantities represented by its arguments. If you don't remember how it works, then be sure to review this in the textbook or at the Internet links!!

ΣX = X₁ + X₂ + X₃ + X₄ + ...
Σ(X + Y) = ΣX + ΣY
Σ(kX) = kΣX (where k is a constant)
ΣX² = X₁² + X₂² + ...
(ΣX)² = (X₁ + X₂ + ...)²

An additive effect of a treatment is one that changes every subject's pretreated value by the same amount (plus or minus a little random error). That is, an additive effect adds a constant amount to what the subject's score would have been without (or before) treatment.

Fred's pretreatment score = 20, post-treatment score = 25, change = +5
Barb's pretreatment score = 28, post-treatment score = 33, change = +5
Jeff's pretreatment score = 12, post-treatment score = 17, change = +5
Greg's pretreatment score = 52, post-treatment score = 57, change = +5
Toni's pretreatment score = 45, post-treatment score = 50, change = +5

In the example above, the treatment added 5 to everyone's score. This is an additive effect of the treatment. We have conveniently ignored the messy effect of random error in this example. A nonadditive effect would occur if the treatment changed everyone's score by a constant percentage, say 20%.

Fred's pretreatment score = 20, post-treatment score = 24, change = +20% or +4
Barb's pretreatment score = 28, post-treatment score = 33.6, change = +20% or +5.6
Jeff's pretreatment score = 12, post-treatment score = 14.4, change = +20% or +2.4
Greg's pretreatment score = 52, post-treatment score = 62.4, change = +20% or +10.4
Toni's pretreatment score = 45, post-treatment score = 54, change = +20% or + 9

In the example of a nonadditive effect (again ignoring random error), how much the subject changed depended upon the subject's pretreated score. This is not the case in the additive effect, in which everyone's score changed by a constant amount regardless of the magnitude of the baseline or pretreatment score.