Suppose This Were Your Problem Statement

Suppose this were your Problem Statement:

The purpose of this study is to conduct an evaluation of the effectiveness of the Weight Watchers program for males who are 10-20% over ideal Body Mass Index (BMI).

Your Research Hypothesis could read like this:

Males, who 10-20% over ideal Body Mass Index (BMI) and complete a 12-week Weight Watchers program, will reduce their BMI more than will males of similar BMI who do not participate in the program.

Your null and alternative hypotheses would look like this:

Null H0: m1 = m2

In words the null hypothesis would be: The treatment does not work. BMI does not change.

Alternative H1: m1 =/= m2 (non-directional) or H1: m1 < m2 (directional)

In words the alternative hypothesis would be: The treatment works, it leads to changes in BMI.

Where : m1 = Population Average BMI for Weight Watchers Participants

m2 = Population Average BMI for the control group

There are the following four possible outcomes to your study:

H0 is True / H0 is False
You fail to reject
H0 /   Weight Watchers is not effective.
  Your data shows no effect.
  You conclude there is no effect.
  Correct Decision
  Probability = 1 - a /   Weight Watchers is effective.
  Your data shows no effect.
  You conclude no effect.
  Type II Error
  Probability = b
You reject
H0 /   Weight Watchers is not effective.
  Your data shows an effect.
  You conclude there is an effect.
  Type I Error.
  Probability = a /   Weight Watchers is effective.
  Your data shows an effect.
  You conclude it works.
  Correct Decision.
  Probability = 1 - b (Power)

Here is another way to think about these four cells:

You should not marry the person. / You should marry the person.
You decide
not to marry the person. /   You break it off. Good move.
  Correct Decision
  Hope for a better future.
  Probability = 1 - a /   You break it off. Bad move.
  Type II Error
  You missed a good opportunity.
  Probability = b
You decide
to marry
the person. /   You go for it. Bad move.
  Type I Error.
  Quiet desperation.
  Probability = a /   You go for it. Good move.
  Correct Decision
  Be thankful.
  Probability = 1 - b (Power)

Here is another way to think about these four cells:

You should not take the drug. / You need the drug.
You decide
Not to take the drug. /   You don’t take the drug.
  Correct Decision
  Hope for a cure.
  Probability = 1 - a /   You don’t take the drug.
  Type II Error
  You continue to feel your pain.
  Probability = b
You decide
To take the drug. /   You go for it. Bad move.
  Type I Error.
  Side effects and no relief.
  Probability = a /   You go for it. Good move.
  Correct Decision
  You feel no pain.
  Probability = 1 - b (Power)

Here is another way to think about these four cells:

The new drug is not effective. / The new drug is effective.
You decide
the drug is not effective. /   Your study doesn’t support the drug.
  Correct Decision
  R&D continues.
  Probability = 1 - a /   Your study doesn’t support the drug.
  Type II Error
  R&D continues but shouldn’t.
  Probability = b
You decide
the drug is effective. /   Your study supports the drug.
  Type I Error.
  The drug looks better than it really is. An ineffective product comes to market.
  Probability = a /   Your study supports the drug.
  Correct Decision
  An effective product comes to market.
  Probability = 1 - b (Power)