# Hypothesis testing: One-tailed and two-tailed tests

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### USMLE® Step 2 style questions USMLE

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A scientist is conducting a clinical trial to determine if a novel medication called Drug A is more effective than metformin in reducing the hemoglobin A1c (HbA1c) of patients with type II diabetes mellitus. In this trial, 100 participants are prescribed Drug A for six months, and another 100 are prescribed metformin for the same duration. The participants' HbA1c is measured at the end of the study. Which of the following statistical analyses would be most helpful in answering this researcher's question?

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Let’s say you want to figure out if a certain medication can lower the systolic blood pressure, so we recruit 100 people, give 50 of them the medication and 50 of them the placebo.

The placebo looks and tastes like the medication but is completely harmless and ineffective - like a tiny capsule filled with water.

After six months of taking the medication or the placebo, you measure the blood pressure of each person in the study.

Now, the unit of measurement for blood pressure is millimeters of mercury, but we’ll just keep it simple and call it “units”.

You find that the mean blood pressure in the medication group is 130 units, and the mean blood pressure in the placebo group is 145 units.

At this point, you might use a statistical test, like unpaired or 2-sample t-test, to see if there’s a significant difference between the two groups’ means.

Typically, an unpaired t-test starts with two hypotheses.

The first hypothesis is called the null hypothesis, and it basically says there’s no difference in the means of the two groups.

For example, our null hypothesis would state that there’s no difference in the mean blood pressure for people that take the placebo compared to people that take the medication.

On the other hand, the alternate hypothesis for a t-test can be either one-sided or two-sided, and this has to be determined at the beginning of the study.

The alternate hypothesis for a one-sided t-test would either state that medication lowers mean blood pressure compared to the placebo or that medication raises mean blood pressure compared to the placebo.

The alternate hypothesis for a two-sided t-test would simply state that the mean blood pressure for the medication group is different than the placebo group, but it wouldn’t specify if medication would raise or lower the mean blood pressure.

Typically, researchers choose to use two-sided t-tests, since they usually don’t know how a treatment will affect the people in the study.

One way to see if there’s a difference between mean blood pressures in the placebo group and the medication group is to make a histogram, which is a plot that shows frequency of an event.

Here, the x-axis represents blood pressure and the y-axis represents the number of people with each blood pressure measurement, and the curve would probably look something like this.

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