The t test compares two averages (means) and tells you if they are different from each other. The t test also tells you how significant the differences are; In other words it lets you know if those differences could have happened by chance. For example, if listening to brain wave beats, makes one smarter or not, 2 groups are created, where one group listens to the real brain wave frequencies andvthe other group listens to a made up sound, then try to record the outcome (if it was by chance, a placebo effect, or actually true).
The outcome is recorded in the form of a t-score. This t score is the ratio of the difference between two groups and the difference within the groups. The larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups.
How can you really tell that the difference between the two groups is significant?, by calculating the P value. Every t-score has a p-value to go with it. A p-value is the probability that the results from your sample data occurred by chance. P-values are from 0% to 100%. They are usually written as a decimal. For example, a p value of 5% is 0.05. Low p-values are good; They indicate your data did not occur by chance. For example, a p-value of .01 means there is only a 1% probability that the results from an experiment happened by chance. In most cases, a p-value of 0.05 (5%) is accepted to mean the data is valid.
There are three main types of t-test:
1.)An Independent Samples t-test compares the averages (means) for two groups.
2.)A Paired sample t-test compares averages (means) from the same group at different times (say, one year apart).
3.)A One sample t-test tests the average of a single group against a known average.
For example, using a paired sample t test (in which everything is recorded in figures), we have two scenarios or conditions which we label A and B, individuals are tested in these two scenarios separately and the result is recorded for both.Let's say the experiment is carried out 10 times on 10 different days (not consecutively). Record everything in a table, the responses gotten in scenario A at the 10 different occasions (labelled 1 to 10) and the same for scenario B.
Next step is to subtract the results gotten in B from the ones gotten in A in each of the occassions. After that, sum of the differences gotten from each occasion. Next, square the differences you obtained from each occassion and sum up the squared differences. ( do not square the sum gotten from the differences, but instead square each difference in each occassion, then get their sum).After which we calculate the t-score using the formula for paired sample t-test. After you have calculated the t-score. You have to compare it to the t-table value which you can find in books or even online. To be able to compare your results to the one already written down in the table, first calculate the degree of freedom by subtracting 1 from the number of occasions you did the experiment (in this case;10-1)= 9. Then check the value you are closest to on the t-table reading the values on the same line as the degree of freedom 9, that way you can obtain your p-value (which is also written down in the t-table), if p is =/<0.05= then your result is significant.
