The t-test is used to test for a significant difference between two sets of normally distributed data. It compares the mean and standard deviation (the spread of the data) of both sets to determine if they are significantly different.

Null hypothesis (Ho):

Alternative hypothesis (H1):

Enter your data in the table below under x1 and x2 and then square the individual values to give x12 and x22 values.

Observation No. / Site 1: / Site 2:
x1 / x12 / x2 / x22
1
2
3
4
5
6
7
8
9
10
11
12
∑x1: / ∑x12: / ∑x2: / ∑x22:

Calculate the mean for both sets of data (n = the number of observations):

x1 = / ∑x1 / = / =
n1
x2 = / ∑x2 / = / =
n2

Calculate the standard deviation of both sets of data with the equations below:

∑x12 - / (∑x1)2
s12 = / n1 / = / =
n1 - 1
∑x22 - / (∑x2)2
s22 = / n2 / = / =
n2 - 1

Calculate your t value using the equation below

Note that the modulus sign (the vertical lines around the mean values) shows that you take the positive value of the difference between the two mean values.

√ / ( / ) / = / √ / ( / )
t = / | x1 – x2 | / =
( / s12 / + / s22 / ) / ( / + / )
n1 / n2
To see if your t value is significant you will need to calculate the degrees of freedom and compare your calculated t value to the appropriate critical value.
These critical values give 95% confidence. This means that if your calculated t value is the same or higher than the critical value, you can be 95% confident that you have a significant difference between your two sets of data.
Degrees of freedom = n1 + n2 - 2 =
Use the table opposite to find your critical value.
Calculated value of t =
Critical value of t =
Remember:
If calculated t ≥ critical t you reject your null hypothesis and accept your alternative hypothesis.
If calculated t critical t you accept your null hypothesis and reject your alternative hypothesis.
Summary Statement: / Degrees of freedom / Critical value
p = 0.05
8 / 2.306
9 / 2.262
10 / 2.228
11 / 2.201
12 / 2.179
13 / 2.16
14 / 2.145
15 / 2.131
16 / 2.12
17 / 2.11
18 / 2.101
19 / 2.093
20 / 2.086
21 / 2.08
22 / 2.074
23 / 2.069
24 / 2.064
25 / 2.060
26 / 2.056
27 / 2.052
28 / 2.048
29 / 2.043
30 / 2.042

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