One sample t test calculator One sample t test

One sample t test calculator


Table of Contents

What is One sample t-test?

Sometimes known as single sample t-test, One sample t-test is a statistical hypothesis testing method. One sample t-test is commonly used to determine the difference between the calculated mean of the sample data that is collected from a single group and the designated value specified by the researcher. 

The designated values that the researcher specifies is the one that does not have anything to do with the data but is an external value which is based on scientific reasons. This designated value is:

  • Either a mean previously established in a population
  • A standard value of interest
  • Or a mean derived from other studies

Like all the hypothesis tests, One sample t-test also works to determine whether the null hypothesis can be rejected or not in favour of the alternative hypothesis. 

  • Null hypothesis (H0): “The population mean equals the specified mean value.” 
  • Alternative hypothesis (H1): “The population mean is different from the specified mean value.”

The major difference between One sample t-test and other statistical hypothesis tests is that One sample t-test does not compare two groups or does not determine the relationship between two variables. What it straight-up does is compare the data gathered on a single variable from a group with the designated value.

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Requirements and assumptions for One sample t-test

Consider the following points on data before performing One sample t-test:

  • The values collected should be independent; not related to each other. 
  • The variables that the data represents are continuous measurements. 
  • The results are based on the values generated on random from the population.
  • The values are normally distributed, meaning, when plotted on the graph is should resemble a bell-shape.

How One sample t-test works?

Your target is to check whether the assumed H0 is statistically based on a sample average. 

You can use sample standard deviation, sample mean and sample size.

One sample t test calculator One sample t test

When you plot the results on a graph, the resultant graphs should look like:

One sample t test calculator One sample t test

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Examples of One sample t-test

statskingdom specifies two types of examples of One sample t-test as:

  • Two-tailed test 

A farmer calculated last year the average of the apples’ weight in his apple orchard μ0 equals 17 kg, based on the entire population.

The current year he checked a small sample of apples and the sample average x̅ equals 18 kg

Has the average of the apple’s weight changed this year?

The farmer calculates the sample standard deviation of the apple’s weight.

  • Left-tailed test

In the same example as above, the farmer only cares to know if the entire average is lesser this year.

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