How to Perform One‑Sample and Two‑Sample t‑Tests in R

Statistical testing uses probability theory to infer the likelihood of differences, allowing comparison of two means to see if the difference is significant, such as whether a new drug leads to better recovery or whether hybrid crops yield more than traditional ones.

One‑Sample t‑Test

Example 1: A sample survey of Monsanto crop yields (in mu) asks whether the yield is higher than that of traditional crops.

You can solve this with R’s t.test() function:

<code>data = c(2531,2659,2487,2398,2771)
t.test(data, mu=2400, alternative='greater')</code>

The result is:

<code> One Sample t-test

data:  data
 t = 2.5756, df = 4, p-value = 0.03081
 alternative hypothesis: true mean is greater than 2400
 95 percent confidence interval:
  2429.151      Inf
 sample estimates:
 mean of x 
    2569.2 </code>

This one‑sided test has the alternative hypothesis that Monsanto crop yield is greater than traditional crops; the returned p‑value leads to rejecting the null hypothesis and accepting the alternative, indicating higher yield.

If a two‑sided test were used, the alternative would be that the yields are not equal; the resulting p‑value would not reject the null, showing no statistically significant difference. In practice, choose one‑ or two‑sided tests based on context and prior information.

Two‑Sample Tests

Two‑sample tests compare the means of two groups to assess whether their population means differ significantly. They can be independent or paired.

Example 2: Scientists create two different mutations (A and B) of a traditional crop to increase yield. Mutation A yields (mu) and Mutation B yields (mu) are sampled; we ask whether the difference is significant.

Since the two groups are independent, we can use t.test() :

<code>data1 = c(2405,2378,2254,2471,2390)
data2 = c(2531,2659,2487,2398,2771)
t.test(x=data1, y=data2, alternative='two.sided')</code>

The result is:

<code> Welch Two Sample t-test

 data:  data1 and data2
 t = -2.5428, df = 6.1295, p-value = 0.04311
 alternative hypothesis: true difference in means is not equal to 0
 95 percent confidence interval:
  -371.123009   -8.076991
 sample estimates:
 mean of x mean of y 
   2379.6    2569.2 </code>

The p‑value leads to rejecting the null hypothesis that the two mutations produce equal yields, indicating a significant difference.

For paired samples, where observations are linked (e.g., before‑and‑after measurements on the same patients), the same t.test() function is used with the argument paired=TRUE to perform a paired two‑sample t‑test.

Source: Liu Hongde, Sun Xiao, Xie Jianming, Biological Data Analysis and Practice