Note
Just Some Quick Notes
- Model is a set of assumptions.
Choose Test Statistic (something that changes)
The statistic has to be able to help us decide between the model and alternative views about the data.
Example: A natural statistic, then, is the number or count of Black panelists in the sample. Small values of the statistic will favor Robert Swain’s viewpoint.
Example: Distance between two Distributions 0.5 * sum of abs(difference)
By a bit of math that we won’t do here, this is true whenever there are just two categories: the TVD is equal to the distance between the two proportions in one category.
Null Hypothesis vs Alternative Hypothesis
The null hypothesis (H₀) represents the default assumption or the status quo—it assumes that there is no significant effect, no difference, or no relationship.
- We choose H₀ as “no improvement” because we start by assuming that the new method does not work better than the traditional one.
- The null hypothesis is what we test against using data. We assume it is true unless the evidence strongly suggests otherwise.
Alternative hypothesis can be one-sided (directional) or two-sided (non-directional)
Common Forms of H₁:
- Two-tailed test (non-directional): (e.g., “There is a difference in mean test scores between two groups.“)
- One-tailed test (directional):
- (e.g., “This drug increases test scores.“)
- (e.g., “This training program reduces reaction time.“)
One-Tailed vs Two-Tailed Hypothesis
- Two-tailed tests are used when you just want to check for any difference (increase or decrease)
- One-tailed tests are used when you expect a specific direction of change (either increase or decrease)