Duke University : Inference for Comparing Two Paired Means

(much like the ‘inference of a mean’ with a new column of difference)

Paired Data

• When two sets of observations have this special correspondence (not independent), they are said to be paired.
• To analyze paired data, it is often useful to look at the difference in outcomes of each pair of observations
• The parameter of interest is the average difference between the two events of the population(μ_diff)
• The point estimate would be the average difference between the two events of the sample(x̄_diff)

INSTRUCTIONS

1. Create a new column named ‘difference’ by subtracting event A from B or vice versa.

• Difference = event A – event B

2. Set the hypothesis

• H0 : μdiff = 0 ; There is no difference between the average of the two events
• H1 : μdiff != 0 ; There is difference between the average of the two events

3. Check conditions
4. Calculate the point estimate x̄, standard deviation for this new column. Then we have ; x̄_diff, s_diff, n_diff.
5. Draw sampling distribution, shade p-value,
6. Make a decision, and interpret it in context of the research question:
   See ‘Inference_for_comparing_two_paired_means.pdf’ for an example