You are conducting a study comparing the efficacy of two different statin medications. Two groups are placed on different statin medications, statin A and statin B. Baseline LDL levels are drawn for each group and are subsequently measured every 3 months for 1 year. Average baseline LDL levels for each group were identical. The group receiving statin A exhibited an 11 mg/dL greater reduction in LDL in comparison to the statin B group. Your statistical analysis reports a p-value of 0.052. Which of the following best describes the meaning of this p-value?

There is a 5.2% chance of observing a difference in reduction of LDL of 11 mg/dL or greater even if the two medications have identical effects

There is a 95% chance that the difference in reduction of LDL observed reflects a real difference between the two groups

Though A is more effective than B, there is a 5% chance the difference in reduction of LDL between the two groups is due to chance

If 100 permutations of this experiment were conducted, 5 of them would show similar results to those described above

This is a statistically significant result

A randomized control double-blind study is conducted on the efficacy of 2 sulfonylureas. The study concluded that medication 1 was more efficacious in lowering fasting blood glucose than medication 2 (p ≤ 0.05; 95% CI: 14 [10-21]). Which of the following is true regarding a 95% confidence interval (CI)?

If the same study were repeated multiple times, approximately 95% of the calculated confidence intervals would contain the true population parameter.

The 95% confidence interval is the probability chosen by the researcher to be the threshold of statistical significance.

When a 95% CI for the estimated difference between groups contains the value ‘0’, the results are significant.

It represents the probability that chance would not produce the difference shown, 95% of the time.

The study is adequately powered at the 95% confidence interval.

A student health coordinator plans on leading a campus-wide HIV screening program that will be free for the entire undergraduate student body. The goal is to capture as many correct HIV diagnoses as possible with the fewest false positives. The coordinator consults with the hospital to see which tests are available to use for this program. Test A has a sensitivity of 0.92 and a specificity of 0.99. Test B has a sensitivity of 0.95 and a specificity of 0.96. Test C has a sensitivity of 0.98 and a specificity of 0.93. Which of the following testing schemes should the coordinator pursue?

Test C on the entire student body followed by Test A on those who are positive

Test A on the entire student body followed by Test B on those who are positive

Test A on the entire student body followed by Test C on those who are positive

Test C on the entire student body followed by Test B on those who are positive

Test B on the entire student body followed by Test A on those who are positive

A patient with HCC and a long history of alcohol dependence and chronic hepatitis C has been using the mTOR inhibitor sirolimus 100 mg for cancer treatment. Her cancer has shown a partial response. She also has a history of hypertension and poorly controlled type 2 diabetes mellitus complicated by diabetic retinopathy. Current medications include enalapril and insulin. She asks her oncologist and hepatologist if she could try everolimus for its purported survival benefit in treating HCC. Based on clinical considerations, which of the following statements is most accurate?

The patient is not a good candidate for everolimus due to her history of diabetes

The patient should start everolimus 50 mg because of the survival benefit relative to sirolimus 100 mg

The patient is not a good candidate for everolimus due to her history of hypertension

The patient should start everolimus 100 mg because of the survival benefit relative to sirolimus 100 mg

The patient should start everolimus 50 mg because of her history of alcohol use disorder and hepatitis C

One-sided vs two-sided tests | P-values and confidence intervals

Hypothesis Testing - The Core Logic

Foundation: A formal procedure to accept or reject a statistical hypothesis.
Null Hypothesis ($H_0$): Assumes no effect, no association, or no difference between groups (e.g., new drug = placebo).
Alternative Hypothesis ($H_A$): Contradicts the null; assumes an effect or difference exists. The goal of research is often to find evidence for $H_A$.

Two-sided T-distribution with 14 degrees of freedom

⭐ The Decision Rule: If the p-value is less than or equal to the pre-specified alpha ($oldsymbol{\alpha}$), typically 0.05, we reject the null hypothesis ($H_0$). This means the observed result is "statistically significant."

One-Sided vs. Two-Sided - The Main Event

The choice between a one-sided and two-sided test hinges on the research hypothesis and must be decided before data collection to maintain integrity.

Feature	Two-Sided Test (Standard)	One-Sided Test
Research Question	Is there any difference?	Is group A better/worse than B?
Alternative ($H_a$)	Non-directional ($H_a: \mu_1 \neq \mu_2$)	Directional ($H_a: \mu_1 > \mu_2$)
$\alpha$ Region	Split between two tails (e.g., 0.025 each)	Entire $\alpha$ in one tail (e.g., 0.05)
Power	Lower (more conservative)	Higher (to detect effect in one direction)
Use Case	Default for most clinical trials	Strong a priori evidence for direction

A two-sided test is the rigorous standard, as it accounts for the possibility of an effect in the opposite direction of what is expected (e.g., a new drug causing harm instead of benefit).
⚠️ Using a one-sided test can inflate the significance of findings; it's easier to get a smaller p-value.

⭐ If a two-sided test yields a p-value of 0.06, a one-sided test on the same data (assuming the effect is in the hypothesized direction) would yield a p-value of 0.03, crossing the threshold for significance.

P-Values & CIs - Reading the Results

Two-Sided Test (Standard Approach)
- Tests for a difference in either direction (e.g., drug is better OR worse).
- Alternative hypothesis: $H_A: \mu_1 \neq \mu_2$.
- The $\alpha$ level (e.g., 0.05) is split between two tails of the distribution curve.
One-Sided Test
- Tests for a difference in one pre-specified direction (e.g., drug is better).
- Alternative hypothesis: $H_A: \mu_1 > \mu_2$.
- Concentrates the entire $\alpha$ level in one tail, increasing statistical power for that direction.

Two-sided test critical regions (alpha = 0.05)

⭐ A one-sided p-value is roughly half the two-sided p-value. A result that is non-significant in a two-sided test may become significant in a one-sided test. This requires strong justification before the study begins.

High‑Yield Points - ⚡ Biggest Takeaways

Two-sided tests evaluate for a difference in either direction (e.g., A ≠ B) and are the most common type in clinical trials.

One-sided tests assess for a difference in one pre-specified direction only (e.g., A > B or A < B).

For the same dataset, the p-value of a one-sided test is half that of a two-sided test.

This gives one-sided tests greater statistical power to detect an effect, but only in the hypothesized direction.

Use a one-sided test only with a strong, pre-existing hypothesis about the direction of the effect.