T-test

The Student’s t-test is an inferential statistical test that compares the mean and standard deviation of two samples to see if there is a significant difference between them or if a difference could have occurred by chance alone.

The T-test is appropriate when comparing means between two groups or conditions. There are three main scenarios when using a T-test:
1.   comparing a sample mean to a known population value (one-sample T-test)
2.  comparing means between two independent groups like control versus treatment (unpaired T-test)
3.  comparing measurements from the same subjects before and after treatment (paired T-test). 

The unpaired T-test would be used to determine if there is a significant difference between the control and treated enzyme activities.

The paired T-test would be used to determine if there is a significant difference between the pre- and post-treatment blood pressures.

The T-test is a test of a  statistical significant difference between two groups.  A "significant difference" means that the results that are seen are most likely not due to chance or sampling error.  In any experiment or observation that involves sampling from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone.  But if result is "significant,"  then the investigator may conclude that the observed effect actually reflects the characteristics of the population rather than just sampling error or chance.  

In any significance test, there are two possible hypothesis:

Null Hypothesis:
"There is not a significant difference between the two groups; any observed differences may be due to chance and sampling error."

For example:  

• There is no significant difference between the control and treatment group enzyme activity; the difference we see in the means of the two groups may be due to chance and sampling error.
• There is no significant difference between the blood pressure before and after treatment; the difference we see in the means of the two groups may be due to chance and sampling error.

Alternative Hypothesis:
"There is a significant difference between the two groups; the observed differences are most likely not due to chance or sampling error."

For example:  

• There is a significant difference between the control and treatment group enzyme activity; the difference seen in the means of the two groups is mostly likely not due to chance or sampling error.
• There is a significant difference between the blood pressure before and after treatment; the difference we see in the means of the two groups is mostly likely not due to chance or sampling error.

Performing a T-test 

• Use an online T-test calculator
• The spreadsheet formular for a test is =TTEST(A1:A4, B1:B4, 2, 2).  Replace A1:A4 with your data from the first sample and B1:B4 with your data from the second sample.
• Performing a T-test in Google Sheets (video)

Interpreting the T-test

The t-test calculator will provide a p-value result.  The p-value indicates the probability that the differences between the two samples are due to random chance alone.  If the P-value is 0.22, it means that there is a 22% likelihood that the difference in the means of your two data sets is due to random chance.  It is standard in biological sciences that a P value of .05 or less is considered significant in which case the null hypothesis is rejected (accept the alternative hypothesis).  If the P value is greater than 0.05, then accept the null hypothesis and conclude that there is no significant difference between the two groups.