To determine whether a t-test is one-tailed (one-sided) or two-tailed (two-sided), and which side is being tested in a one-tailed test, you need to consider the research hypothesis and the direction of the effect being tested.

One-tailed vs. Two-tailed Tests

1. Two-tailed Test:

   • Used when you are testing for the possibility of an effect in both directions, either higher or lower.
   • The alternative hypothesis ($H_1$) does not specify a direction, only that there is an effect: $H_1: \beta \neq \beta_0$
   • Example: Testing if a new drug has a different effect (either more effective or less effective) than an existing one.

2. One-tailed Test:

   • Used when you are testing for an effect in a specific direction.
   • The alternative hypothesis ($H_1$) specifies a direction:
     • Positive Direction: $H_1: \beta > \beta_0$
     • Negative Direction: $H_1: \beta < \beta_0$
   • Example: Testing if a new teaching method is more effective than the traditional method (positive direction).

Determining the Direction in a One-tailed Test

• Research Hypothesis: The direction of the one-tailed test is determined by the specific hypothesis you are testing.
  • Positive Direction: If you are testing whether a parameter is greater than a specified value.
    • Example: Testing if the increase in GDP results in more than a one percentage point increase in votes.
  • Negative Direction: If you are testing whether a parameter is less than a specified value.
    • Example: Testing if a new policy decreases unemployment more than the previous policy.

Application to Your Example

In the context of the regression model for natural parliament elections, the claim being tested is that a percentage point increase in GDP results in more than one percentage point increase in the share of votes. This specifies a direction (more than), indicating a one-tailed test in the positive direction:

• Null hypothesis ($H_0$): $\beta_{\text{growth}} \leq 1$
• Alternative hypothesis ($H_1$): $\beta_{\text{growth}} > 1$

This is a one-tailed test because the researcher is interested in whether the increase in GDP (growth) results in more than one percentage point increase in votes.

Would you like any further details or have additional questions?

Here are five additional questions you might ask:

1. How do I interpret the p-value in a one-tailed test?
2. What are the assumptions underlying a t-test?
3. How do I calculate the critical value for a t-test?
4. Can you explain the difference between Type I and Type II errors in hypothesis testing?
5. What are some common pitfalls to avoid when performing hypothesis testing?

Tip: Always ensure that your hypothesis clearly specifies the direction of the effect you are testing to correctly determine whether to use a one-tailed or two-tailed test.