## One-sample t-test [General Statistics]

❝ If I have a bioavailability study and want to compare its PK results with published data, is there any specific statistical test that could be used to prove there is no significant difference between both results?

If you have the subject’s data of the previous study, you could work with log-transformed values and use a paired

*t*-test.

If not,

*i.e.*, you have only the mean (\(\small{\mu}\)), you could use a one-sample

*t*-test, where \(\small{t=\frac{\overline{x}-\mu}{s/\sqrt{n}}}\) with \(\small{df=n-1}\).

Example in :

```
set.seed(1234567)
```

x <- rnorm(n = 24, mean = 20, sd = 5) # give a vector of your study data instead

summary(x)

Min. 1st Qu. Median Mean 3rd Qu. Max.

11.11 16.98 20.09 19.82 23.15 27.71

t.test(x, mu = 20, conf.level = 0.90)

One Sample t-test

data: x

t = -0.1917, df = 23, p-value = 0.8497

alternative hypothesis: true mean is not equal to 20

90 percent confidence interval:

18.25799 21.39151

sample estimates:

mean of x

19.82475

t.test(x, mu = 25, conf.level = 0.90)

One Sample t-test

data: x

t = -5.6612, df = 23, p-value = 9.191e-06

alternative hypothesis: true mean is not equal to 25

90 percent confidence interval:

18.25799 21.39151

sample estimates:

mean of x

19.82475

Problems:

- You have to assume that \(\small{\mu}\) is the true mean without any error. Strong assumption, likely false.
- Based on normal distributed data. Likely the reported \(\small{\mu}\) is the arithmetic mean. If you have also its standard deviation, you could try to bootstrap values from a lognormal distribution. Not trivial.

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- statistical test for Bioavailability studies Loky do 2021-10-13 15:06 [General Statistics]
- One-sample t-testHelmut 2021-10-14 10:59
- One-sample t-test Loky do 2021-10-18 09:59

- One-sample t-testHelmut 2021-10-14 10:59