Independent t-test

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What an Independent T-Test Does
The independent t-test is an inferential test designed to tell us whether we should accept or reject our null hypothesis. You have learned that any two samples from the same population are unlikely to have the same mean. If you carry out an experiment or collect data from two samples because you expect to see a difference between them, you have a problem because there will almost always be some difference due to sampling! It is vital to know whether the difference between the means of your two samples is due to the effect of sampling or to a true difference between the populations they were sampled from.

The independent t-test answers this question. It tells you whether the difference that you have found is due to sampling or a true difference between the populations.

When to use an Independent T-Test
You use an independent t-test when you want to compare the mean of one sample with the mean of another sample to see if there is a statistically significant difference between the two. As the name suggests, you use an independent t-test when your samples are independent! There is more on this topic on the pages about choosing a t-test.

How to use an Independent T-Test
This level assumes that you will use a software package to perform a t-test. If you want to know how to do it by hand, read level two. The result of using a t-test is that you know how likely it is that the difference between your sample means is due to sampling error. This is presented as a probability and is called a p-value. The p-value tells you the probability of seeing the difference you found (or larger) in two random samples if there is really no difference in the population.

Generally, if this p-value is below 0.05 (5%), you can reject the null hypothesis and conclude that there is a statistically significant difference between the two population means. If you want to be particularly strict, you can decide that the p-value should be below 0.01 (1%). The level of p that you choose is called the significance level of the test. The p-value is calculated by first using the t-test formula to produce a t-value. This t-value is then converted to a probability either by software or by looking it up in a t-table. The next topic covers this part of the process.


For each of the following examples, answer Yes or No to say whether or not you would use an independent t-test.

Example ScenarioUse an Independent T-Test?
Comparing the average height of men and women   Help
Comparing the weight of slimmers before and after a diet   Help
Testing whether height and weight are related   Help
Testing patients given a drug with those given a placebo   Help


Your data contains samples under two samples:
  • When altitude (km) is altitude (km), the mean of vo2 % of max is 3.58
  • When altitude (km) is vo2 % of max, the mean of vo2 % of max is 80.15
The mean in the second sample (vo2 % of max) is greater than the mean in the first sample (altitude (km)).
What can you conclude from this?   Help

How can we tell whether the differences in these means are due to sampling error or a true effect?
Performing a t-test on your data produces a p-value of p=0.0001 and a t-value of -16.377.
Which of these values tells you the probability of the difference between your samples being due to sampling error?   Help

Choosing a T-Test | P-Values and T-Tables