Download Paired t-test

Statistical Inference for the Mean: t-test
Comparison of paired samples:
- Interfering factors in the comparison of two sample means
using unpaired samples may inflate the pooled estimate of
variance of test results.
- It is possible to pair the measurements.
Only the value of one variable is changed among the
two members of each matched pair, but everything else
is nearly the same (as closely as possible) for the members
of the pairs.
-Then the difference between the members of a pair
becomes the important variable, which will be examined by
a t-test.
We test “Is the mean difference significantly different from
zero?”
Statistical Inference for the Mean: t-test
Comparison of paired samples:
Pair No.
Sample A
Sample B
d = xAi- xBi
1
xA1
xB1
2
xA2
xB2
3
xA3
xB3
4
xA4
xB4
5
xA5
xB5
6… n
xA6... xAn
xB6… xBn
xA1- xB1 xA2- xB2 xA3- xB3 xA4- xB4 xA5- xB5 xA6- xB6…xAn- xBn
Mean difference
d

:d 
n
H 0 :  d  0 no real difference between th e two methods
Ha :
 d  0 (two - tailed test)
 d  0 or  d  0 (one - tailed test)
Statistical Inference for the Mean: t-test
Comparison of paired samples:
Standard Deviation of d:
n
sd 
2
(
d

d
)
 i
i 1
Degrees of freedom is
n-1
n 1
The test statistics t is:
d 0
t
sd
n
The paired t-test compares the mean difference of pairs to
an assumed population mean difference of zero.
Statistical Inference for the Mean: t-test
Test of Significance: Comparing paired samples
 d  0.
- State the null hypothesis in terms of the mean difference, such as
- State the alternative hypothesis in terms of the same population
parameters.
- Determine the mean and variance of the difference of the pairs.
- Calculate the test statistic t of the observation using the mean and
variance of the difference.
d 0
df
=
n-1
t
- Determine the degrees of freedom:
sd
- State the level of significance – rejection limit.
- If probability falls outside of the rejection limit, we reject the Null
Hypothesis, which means the difference of the two samples are
significant.
Assume the samples are normally distributed and neglect any
possibility of interaction.
Assume that if the interfering factor is kept constant within each pair, the
difference in response will not be affected by the value of the interfering
factor.