General Hypothesis Testing Flashcards
What different types of questions do CIs and Hypothesis testing answer?
CI:What is the plausible range for the population parameter?”
Hyp: “Is there enough evidence to support or reject a specific claim about the population parameter?” (a claim abotu the population)
Describe the difference between the Null hypothesis and the Alternate hypothesis. Which one are we trying to show is true?
Null: A statement that assumes no effect, no difference, or no relationship exists in the population.
Alt: The alternative hypothesis is a statement that posits an effect, a difference, or a relationship exists in the population.
We are trying to show the alt is true
Why do we calculate a test-statistic?
What does the test-statistic tell us in the context of a hypothesis test?
To quantify the difference between the observed data and what is expected under the null hypothesis.
-The test statistic is standardized, meaning it accounts for variability in the data (e.g., standard error) and the sample size
Why do we sometimes call tests left, right, or two-tailed tests?
Based on the direction of the alternative hypothesis and the type of evidence we are testing for in the data.
> upper right tailed
< left tailed
not equal is two tailed
What is the definition of a p-value?
text book standard
What does the p-value tell us for a hypothesis test?
The p-value in a hypothesis test tells us the probability of observing the data (or something more extreme) if the null hypothesis is true.
small p-value strong evidence to reject null
large no evidence to reject null
How does the sample size affect the test-statistic, and as a consequence the p-value, with everything else held constant?
Test statistic
-As the sample size increases, the standard error decreases because the standard error is inversely proportional to the square root of the sample size.
-With a smaller standard error, the test statistic becomes larger in magnitude if the difference between the observed value and the expected value remains the same.
P-value
- Since the p-value is calculated based on the test statistic, a larger test statistic (in magnitude) results in a smaller p-value.
As the sample size increases, the standard error decreases, leading to a larger test statistic and a smaller p-value, making it easier to detect statistically significant results, all else being equal.
How does the standard error affect the test-statistic, and as a consequence the p-value, with everything else held constant?
What is the difference between ‘statistical significance’ and ‘practical significance’?
Statistical significance tells us whether an observed effect is likely to be real (i.e., not due to chance or luck).
Practical significance tells us whether that effect is large enough or meaningful enough to matter in the real world, especially in terms of decision-making and impact.
