The results of these tests are only valid when the data are normally-distributed. If the data are not normally-distributed, use another statistical test, such as the Mann-Whitney U-test.
Explanation of termsn = The sample size The standard deviation (s) can be calculated using the formula: |
To test whether the mean of a sample (
) differs significantly from a predicted value (µ)...
Calculate the 'standard error of the mean' (SEM):
Calculate the t-statistic:
Use the table of critical values (below) to find out whether or not the result is significant.
To test whether the mean of a sample (1) differs significantly from the mean of another sample (2)...
Calculate the 'standard error of the mean' (SEM):
Calculate the t-statistic:
Use the table of critical values (below) to find out whether or not the result is significant.
Alternatively, type the following formula into Microsoft Excel (where A1:A10 and B1:B10 are the ranges of cells containing the data):
=TTEST(A1:A10,B1:B10,2,3)
This will give you a p-value (see below) indicating how significant the result is.
The table below gives the t-value at which the result has a particular level of 'significance'.
d.f. is the number of 'degrees of freedom'. In this case, d.f. = n -1
(If the exact d.f. value that you want is not included in the table, use the closest value below it that is included.)
p is the probability that the difference between two samples, or the difference between a sample and the theoretical result, is entirely due to chance.
| d.f. | p=0.1 | p=0.05 | p=0.01 |
|---|---|---|---|
| 2 | 2.92 | 4.30 | 9.92 |
| 3 | 2.35 | 3.18 | 5.84 |
| 4 | 2.13 | 2.78 | 4.60 |
| 5 | 2.02 | 2.57 | 4.03 |
| 6 | 1.94 | 2.45 | 3.71 |
| 7 | 1.89 | 2.36 | 3.50 |
| 8 | 1.86 | 2.31 | 3.36 |
| 9 | 1.83 | 2.26 | 3.25 |
| 10 | 1.81 | 2.23 | 3.17 |
| 11 | 1.80 | 2.20 | 3.11 |
| 12 | 1.78 | 2.18 | 3.05 |
| 13 | 1.77 | 2.16 | 3.01 |
| 14 | 1.76 | 2.14 | 2.98 |
| 15 | 1.75 | 2.13 | 2.95 |
| 16 | 1.75 | 2.12 | 2.92 |
| 17 | 1.74 | 2.11 | 2.90 |
| 18 | 1.73 | 2.10 | 2.88 |
| 19 | 1.73 | 2.09 | 2.86 |
| 20 | 1.72 | 2.09 | 2.85 |
| 21 | 1.72 | 2.08 | 2.83 |
| 22 | 1.72 | 2.07 | 2.82 |
| 23 | 1.71 | 2.07 | 2.81 |
| 24 | 1.71 | 2.06 | 2.80 |
| 25 | 1.71 | 2.06 | 2.79 |
| 26 | 1.71 | 2.06 | 2.78 |
| 27 | 1.70 | 2.05 | 2.77 |
| 28 | 1.70 | 2.05 | 2.76 |
| 29 | 1.70 | 2.05 | 2.76 |
| 30 | 1.70 | 2.04 | 2.75 |
| 35 | 1.69 | 2.03 | 2.72 |
| 40 | 1.68 | 2.02 | 2.70 |
| 45 | 1.68 | 2.01 | 2.69 |
| 50 | 1.68 | 2.01 | 2.68 |
| 60 | 1.67 | 2.00 | 2.66 |
| 70 | 1.67 | 1.99 | 2.65 |
| 80 | 1.66 | 1.99 | 2.64 |
| 90 | 1.66 | 1.99 | 2.63 |
| 100 | 1.66 | 1.98 | 2.63 |
| Infinity | 1.64 | 1.96 | 2.58 |
Example: suppose that a t-test on a sample of 10 individuals (d.f. = 9) produced a t-value of 3.0. The table tells us that p is between 0.01 and 0.05 in this case (p=0.05 when t=2.26, and p=0.01 when t=3.25; our t-value lies in between these two). Therefore, the probability of the result arising by chance is less than 5% (p<0.05), so this is a fairly significant result.
