Stats without Tears
Seven Steps of Hypothesis Tests

See also: Inferential Statistics: Basic Cases
Top 10 Mistakes of Hypothesis Tests

Step 1. Hypotheses

Following are patterns for your hypotheses in the cases covered in the text. With Cases 1 through 5, if you can say anything meaningful about the consequences if each hypothesis is true, add that.

Bad example (adds little or nothing to the symbols):

H₀: μ = 67.6, average 2-liter bottle contains 67.6 fl oz

H₁: μ < 67.6, average 2-liter bottle contains less than 67.6 fl oz

Good example (explains the implications):

H₀: μ = 67.6, average bottle filled properly

H₁: μ < 67.6, average bottle is underfilled

In Cases 1 through 5, a test for < or > is called a one-tailed test, and a test for ≠ is called a two-tailed test. Please see One-Tailed or Two-Tailed? for advice on choosing between them.

Case 1: (Testing mean of one population against a number called μ_o)
H₀: μ = number
H₁: μ < number  or  μ ≠ number  or  μ > number

Case 2: (Testing proportion in one population against a number called p_o)
H₀: p = number
H₁: p < number  or  p ≠ number  or  p > number

Case 3: (Testing mean difference (paired data))
d = _____ − _____
H₀: μ_d = 0
H₁: μ_d < 0  or  μ_d ≠ 0  or  μ_d > 0

Case 4: (Testing difference of independent means)
pop. 1 = _____, pop. 2 = _____
H₀: μ₁ = μ₂
H₁: μ₁ < μ₂  or  μ₁ ≠ μ₂  or  μ₁ > μ₂

Case 5: (Testing difference of population proportions)
pop. 1 = _____, pop. 2 = _____
H₀: p₁ = p₂
H₁: p₁ < p₂  or  p₁ ≠ p₂  or  p₁ > p₂

Case 6: (Testing goodness of fit)
H₀: The _____ model is consistent with the data.
H₁: The model is not consistent with the data.

Case 7: (Testing independence)
H₀: _____ and _____ are independent.
H₁: _____ and _____ are dependent.

Case 7: (Testing homogeneity)
H₀: The proportions are all equal.
H₁: Some proportions are different from others.

Step 2. Significance Level

Short and sweet:

α = _____

Step RC. Requirements Check

Please see Inferential Statistics: Basic Cases for specific requirements. For Cases 6 and 7, it’s easier to check requirements if you move this step after Steps 3/4.

Steps 3/4. Computations

Show screen name. Example: T-Test. You don’t need to write down keystrokes, such as “STAT TESTS 2”.

Show all inputs.

Show new outputs, meaning any that weren’t on the input screen.

Step 5. Conclusion (Statistics Language)

No room for creativity here. Write down whichever one of these applies:

p < α. Reject H₀ and accept H₁.

p > α. Fail to reject H₀.

Step 6. Conclusion (English)

Here you have a lot of latitude as long as you state the correct conclusion in English and give the significance level or p-value, or both.

If you rejected H₀, state H₁ without doubting words like may or could. Examples:

At the 0.05 significance level, the average 2-liter bottle contains less than 67.6 fl oz. Drinkems is underfilling the bottles.

Or,

The average 2-liter bottle contains less than 67.6 fl oz. Drinkems is underfilling the bottles (p = 0.0246).

If you failed to reject H₀, state your non-conclusion in neutral language, using phrases like can’t determine whether or it’s impossible to say whether. Examples:

At the 0.05 significance level, we can’t tell whether Drinkems is underfilling the bottles or not.

Or,

We can’t tell whether Drinkems is underfilling the bottles or not (p = 0.1045).