Paired or Unpaired T-Test

[Zachariah Rutledge]

Hello, I have a sample of weekly data spanning two years, and I want to test whether the means of a variable are different across the two years. Should I be using a paired T-Test or an unpaired T-Test?

[Clyde Schechter]

You have not described the data sufficiently to answer that question. Let's take two extreme cases:

Case 1. The data in the first year are measured on a sample from a different population altogether than the data in the second year (so that year is actually confounded with the population). In this situation, an unpaired t-test would be called for because there is nothing that relates any one datum from the first year to any other specific datum in the second year.

Case 2. The data are weekly closing prices of the same securities in each year. So the same entity (price of a specific security) is measured twice: once in the first year and once in the second year. Moreover, there is reason to believe that these prices exhibit some degree of seasonality, so that there is a correlation between the price of a security on week N of year 1 and its price on week N of year 2. These are completely paired observations and a paired T-test would be mandatory here.

Put in general terms, if there is an actual real-world correspondence between each of the observations in year 1 and some specific corresponding observation in year 2, then you need a paired T-test. But if there is nothing that links an observation in year 1 with any particular observation in year 2, then they can be treated as independent samples and an unpaired T-test can be used.

[Carlo Lazzaro]

Zachariah:
as an aside to Clyde's helpful advice, you may want to consider:

regress <depvar> i.year