# T-TEST CALCULATOR WITH STEPS

In this article, we will get a piece of in-depth knowledge on:

• What is a T-test, and what are the different kinds of the t-test?
• What are the steps of calculating a t-test?
• How can you calculate the t-test using our t-test calculator?

## What is a T-test?

In statistics, a t-test is used to compare the means of two population groups. The groups could be related to certain characteristics. The T-test is also a kind of hypothesis testing tool that lets us determine if the significant differences in the sample groups could have happened by chance.

A t-test is conducted when the sample size is less than 30. However, the sample size should not be less than 5.

### Types of t-test

There are three types of t-tests:

• One-sample t-test: It determines if a population’s mean is different from the hypothesized value.
• Two-sample unpaired t-test: It compares the means of two different sample groups to derive if their associated population means are drastically different from each other.
• Paired t-test: it compares the means of two sample groups taken from the same population, whether they have different characteristics or not.

## What are the steps to calculate a t-test?

### Step1: Assumptions

The first assumption would be to assume the scale of measurement. It is assumed to be either ordinal or continuous scale.

The second assumption is to pick the sample from the population randomly.

When the data is plotted on a graph, it should resemble a bell curve with normal distribution.

The variance needs to be homogeneous.

### Step 2: Defining the null and alternative hypothesis

The hypotheses are never about the sample size. It is defined by the population.

### Step 3: Define the significance level (α).

It is the probability that determines whether we should accept or reject the null hypothesis. Any value between 0 and 1 can be used to define the significance level. For easy calculation, we can use the values 0.1, 0.5, or 0.01.

### Step 4: Calculate the degree of freedom (DF).

For one-sample t-test and paired t-test, DF = n-1, where n is the number of observations in a sample.

For a two-sample unpaired t-test, the degree of freedom varies due to the presence of two independent samples (A and B). The general rule is to select the smaller value between nA-1 and nB-1.

### Step 5: Calculate the t-value (t)

For a one-sample t-test,

t = x-Ms∕n

x signifies the observed mean sample

M signifies hypothesized population mean (null hypothesis)

s signifies the standard deviation of the sample

n signifies the number of observations in a sample

For two-sample unpaired t-test,

t=mAmBs2nA+s2nB

mA = mean of Sample A

mB = mean of Sample B

nA = Sample size of A

nB = Sample size of B

s2 = variance

The variance or “measure of variability” is a measure to determine how spread out the data set is.

s2=x-mA2+∑x-mB2nA+nB-2

nA+nB-2 is the degree of freedom

For Paired t-test,

t=d-Msdn

d = sample mean difference between paired observations

M = hypothesized mean difference (null hypothesis)

sd = standard deviation of d values.

‘d’ is the paired difference. d=x1x2, where x1 is the value of a variable x in data set one and x2 is the value of a variable x in data set two (it is paired with x1).

### Step 6: Calculate p-value.

The p-value is calculated under the assumption that the null hypothesis is true. It is the probability of determining results at least as extreme as the t-value of the sample. A lower p-value signifies that the alternative hypothesis is true.

## Our T-Test Calculator Online

We have an excellent t-test calculator to help you with your calculations. You do not have to remember complex formulae or calculate the results by hand. Our t-test calculator helps you save time and provides a clear data interpretation.

When you click on our home page, you will find an option for a t-test calculator.

Once you click on the t-test calculator, it directs you to a page where you find a brief description of the various attributes of the calculator and the different calculations that you can conduct. You can perform a one-sample t-test, two-sample paired t-test, and two-sample unpaired t-test.

Once you click on the “Start Calculator,” you are redirected to the calculation window. Here, you have options to select the type of t-test and select an input format. You can enter the data accordingly and click “Analyze.”

The result page gives us:

• t-score
• standard error of difference
• degree of freedom
• two-tailed p-value
• mean difference
• confidence range

You can choose the confidence interval accordingly.

We have various comprehensive calculators that you can use online for free. You can choose from t-test calculator, graphing, matrix, the standard deviation to statistics, and scientific calculators. Check it here