# Two-sample t-test

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### Preguntas del estilo USMLE Step 2

A researcher is evaluating data obtained from a study examining the effects of rosuvastatin on low-density lipoprotein (LDL) levels. The experimental group consisted of 250 randomly selected individuals prescribed rosuvastatin for six months. The control group consisted of 300 randomly selected individuals prescribed placebo pills. The changes in LDL levels were measured at the end of the study. Which of the following statistical analyses should the researcher perform to determine if rosuvastatin therapy led to a statistically significant change in LDL levels?

### Transcript

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#### Contributors

The Student’s t-test or simply, the t-test, is a type of parametric statistical test used to determine if there’s a significant difference between the means or averages of two groups.

And significance is normally defined by a p-value of less than 0.05 or 5%.

Now when doing any parametric test, there are three key assumptions that we have to make about the population.

First, the sample population must have been recruited randomly.

Choosing names randomly ensures that the people included in the study will have similar characteristics to the target population.

This is important because that ensures that the results of the t-test can be applied to the target population - meaning it has good external validity!

The second assumption is that each individual in the sample was recruited independently from other individuals in the sample.

In other words, no individuals influenced whether or not any other individual was included in the study.

For example, if two friends decided to get their blood pressures measured on the same day, and they were both included in the study, these two individuals would not be independent of each other and the second assumption would not be met.

Like random sampling, independent recruitment of individuals is important because it ensures that the sample population approximates the target population.

The third assumption is that the sample size is large enough to approximate the target population, which usually means having more than 20 people.

If it’s impossible to get a large sample size, then the sample population must follow a normal bell-shaped distribution for the characteristic being studied because that’s what we would expect to see in the target population.

Okay, now let’s say you want to figure out if a certain medication lowers systolic blood pressure.

So you find 25 people who have been on the medication for 6 weeks, and figure out that the mean systolic blood pressure for the whole group is 130 mmHg. Then, you find another 30 people who have not been taking that medication, and find out the mean systolic blood pressure for that group is 138 mmHg.

Now, to figure out if a difference in systolic blood pressure from 130 to 138 is significant, we could perform a t-test.

Specifically, since the two means were measured in two different populations, we would use an unpaired or two-sample t-test.

This is different than a paired t-test, which is used to compare the same population before and after the treatment.

For example, a paired t-test could compare the systolic blood pressure measurements of a group of 25 people before using the medication to the systolic blood pressure measurements of the same people after using the medication for six weeks.

### Resumen

The two-sample t-test is a statistical method used to compare the means of two independent samples of continuous data. It is used to determine whether the means of the two samples are significantly different from each other, taking into account the variability of the data within each sample.

The t-test calculates a t-value, which is then compared to a critical value from a t-distribution with degrees of freedom equal to the sum of the sample sizes minus two. If the calculated t-value is greater than the critical value, the null hypothesis of no difference between the means is rejected, indicating that there is a significant difference between the means of the two samples. The two-sample t-test is commonly used in a variety of research fields, including medicine, psychology, and engineering, to compare two groups or treatments.

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