Name:___________________
FSC Derrygonnelly
Students t-test Worksheet
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
x1
2
x22
x2
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
=
FSC Derrygonnelly, Derrygonnelly Field Centre, Tir Navar, Creamery Street, Derrygonnelly, Enniskillen, Co. Fermanagh, BT93 6HW
Tel: 028 686 41673 Fax: 028 686 41771
E-mail: enquiries.dg@field-studies-council.org
Website: www.field-studies-council.org/derrygonnelly
Field Studies Council is a limited Company, registered in England and Wales No. 412621 and a Charity No. 313364. Registered Office; Preston Montford, Shrewsbury, Shropshire SY4 1HW
Calculate the standard deviation of both sets of data with the equations below:
∑x12 s1 2 =
(∑x1)2
n1
=
=
(∑x2)2
n2
=
=
n1 - 1
∑x22 2
s2 =
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 |
s1 2 + s2 2
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
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Critical
value
p = 0.05
2.306
2.262
2.228
2.201
2.179
2.16
2.145
2.131
2.12
2.11
2.101
2.093
2.086
2.08
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.043
2.042
FSC Derrygonnelly, Derrygonnelly Field Centre, Tir Navar, Creamery Street, Derrygonnelly, Enniskillen, Co. Fermanagh, BT93 6HW
Tel: 028 686 41673 Fax: 028 686 41771
E-mail: enquiries.dg@field-studies-council.org
Website: www.field-studies-council.org/derrygonnelly
Field Studies Council is a limited Company, registered in England and Wales No. 412621 and a Charity No. 313364. Registered Office; Preston Montford, Shrewsbury, Shropshire SY4 1HW