# The T-test in R programming [One Sample and Paired T-Test]

Filed Under: R Programming Hello, readers! In this article, we will be focusing on an important statistical test in Analysis — the T-test in R programming.

So, let us being!

## What is T-test all about?

Statistical tests give us an idea about the distribution of data on a statistical scale. This distribution plays an important role in analyzing the data prior to modelling.

There are various statistical tests such as `Chi-square test`, `ANOVA test`, etc.

One such test is `T-test` in statistics.

T-test is a statistical test that works on regression data variables. It is basically used to compare and analyze the mean of the data variable/variables. With T-test, we can understand the distribution of the passed data variables in terms of the mean values of them and analyze a sense of association between them.

There are broadly two kinds of T-tests:

• One-sample T test
• Paired T-test

We will be covering both the techniques in the upcoming section!

### Assumptions of T-test in R

• The data is assumed to follow a normal distribution in terms of the values.
• The passed variables are observed to have equal variance.

### Hypothesis for T-testing in R

1. Null-hypothesis: The mean value of the groups are equal.
2. Alternate-hypothesis: The mean value of the groups is not the same i.e. they are unequal.

## 1. One-sample T test in R

In One-sample T test, we analyze and compare the mean value of the variable against a static mean value passed to the function to judge its credibility.

Have a look at the below syntax!

```t.test(variable, mu=value)
```

As a result of this function, we get a p-value which can be observed in the below manner:

• If the p-value is greater than 0.05 (assumed significance level), then we accept the NULL hypothesis.
• If the p-value is less than or equal to 0.05, we reject the Null hypothesis i.e. we accept the Alternate hypothesis value.

Example:

```#Removed all the existing objects
rm(list = ls())

data = rnorm(10,5.99)
print(data)

print(t.test(data,mu=6))
```

Output:

Here, we have generated a vector of 10 data points with a mean of 5.99 using rnorm() function. After applying the t-test, we avail the below results.

```> data = rnorm(10,5.99)

> print(data)
 5.472294 6.922749 6.680573 4.839677 5.692492 6.584267 6.960417 5.836062 6.166102 5.422624

> print(t.test(data,mu=6))

One Sample t-test

data:  data
t = 0.2539, df = 9, p-value = 0.8053
alternative hypothesis: true mean is not equal to 6
95 percent confidence interval:
5.543403 6.572048
sample estimates:
mean of x
6.057726
```

It is clearly understood that the p-value is greater than 0.05, thus we cannot reject the NULL hypothesis because the values are close estimates and p-score is greater than the estimated value i.e. 0.05.

## 2. Paired T-test in R

In a Paired T-test, we compare the mean of two different groups and check if they have same mean or a contrast value of mean. That is, it checks if the difference between the mean values of the two groups is equal to 0.

Syntax:

```t.test(var1,var2,var.equal=TRUE)
```

Example:

Here, we have passed two different data vectors created using `rnorm()` function to the `t.test()` function.

```#Removed all the existing objects
rm(list = ls())

data = rnorm(10,5.99)
print(data)

info = rnorm(10,5.55)
print(info)
print(t.test(data,info,var.equal = TRUE))
```

Output:

As a result, we see that the p-value is greater than 0.05. So, we accept the NULL hypothesis because the difference between the mean of the groups can be as low as -0.5 and as high as 1.5 which is considered a small portion.

```> print(info)
 5.526671 4.743747 5.833444 8.278065 7.042861 5.718028 4.152188 4.670495 5.334782 5.040747

> print(t.test(data,info,var.equal = TRUE))

Two Sample t-test

data:  data and info
t = 0.99928, df = 18, p-value = 0.3309
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.5646441  1.5890105
sample estimates:
mean of x mean of y
6.146286  5.634103
```

## Conclusion

By this, we have come to the end of this topic. Feel free to comment below, in case you come across any question. For more such posts related to R programming, Stay tuned!

Till then, Happy Learning!! 🙂

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