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Two subgroup t-Test
Main points:
Objective:
This example should show how statistical tests are
Conducting statistical tests
carried out in general, and then in a second step, how
especially the two-subgroup t-Test is performed. The
Application of
results of the two-subgroup t-Test are introduced comthe test using
the twoprehensively.
subgroup t-Test
as an example
After working through this case study, you will be able
to conduct a two-subgroup t-Test on your own and – Pre-Requisites:
with respective pre-knowledge – also other statistical
Basics of statistical testing
tests.
Important:
Please switch to the qs-STAT Analysis of Regression/Variance program module in order to be
able to access the function as described below (menu
item Module|qs-STAT Analysis of Regression/Variance).
Initial situation:
A new welding method is considered for a welding
process. The new welding method is to be compared
with the old method using a sample of 10 welded parts
each. A trial is to be performed to investigate whether
the tensile strength [kN] of the weld connection can be
improved significantly by using the new welding method.
MODULE|
ANALYSIS
REGRESSION-/
VARIANCE
The values of the samples are summarized in the table Remark:
The data can also
below:
Old method
2.6
2.0
1.9
1.7
2.1
2.2
1.4
2.4
2.0
1.6
Version: 1
New method
2.1
2.9
2.4
2.5
2.5
2.8
1.9
2.7
2.7
2.3
© 2008 Q-DAS GmbH & Co. KG, 69469 Weinheim
be found in the
TENSILE_STRENG
TH.DFQ file
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Two-subgroup t-Test
Task:
The measured data should be compared for a significant difference in the tensile strength using a twosubgroup t-Test.
Procedure:
1. Please click on the File|New menu function, select the “Create factors” option under Analysis of
regression/variance, and then create two characteristics in the new characteristic… window using the Add Characteristic button as follows:
2. After clicking on the OK button, the Values Mask
opens up where you can enter all values for the
tensile strength with the old and the new method.
ANALYSIS/PROCEDURE |
TEST PROCEDURE
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3. Please select TEST PROCEDURE from the ANALYSIS /
PROCEDURE menu item. The following selection
menu will pop up:
© 2008 Q-DAS GmbH & Co. KG, 69469 Weinheim
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Two subgroup t-Test
Basically, it is possible to directly select the desired
test from the Test selection pull-down menu– if
the test has not been recognized automatically.
PULL-DOWN MENU /
TEST SELECTION
In this case however, we want to use the second option for the test selection which is deducted from simple decisions on the basis of fundamental statistical
knowledge.
The first step is to decide whether we are dealing with
a discrete or a continuous distribution. As the tensile
strength is recorded in variable measurement, (1)
continuous distributions is selected.
Afterwards, we have to decide how many populations
are to be evaluated. In our case it would be (2) 2
populations.
In the next step we determine that the characteristics
are (3) normally distributed and that we are
testing for (4) Differences in the location
test.
In this example, (5) σ1 and σ2 are unknown, so that
the two-subgroup t-Test ((6) t-Test 2) is selected.
The selection tree of decisions is displayed in the picture below:
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© 2008 Q-DAS GmbH & Co. KG, 69469 Weinheim
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Two-subgroup t-Test
4. By clicking on t-Test 2 or on the Next button,
the Data tab can be opened up. The characteristics
can be selected here. In this example, only two
characteristics are available which are selected automatically.
Excursion:
The Planning that is following next is not required for
this example, but its functionalities should briefly be
explained nevertheless.
The basic function of this tab is to calculate the required sample size for a test. For this, certain previous
knowledge has to be available and some assumptions
have to be made.
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© 2008 Q-DAS GmbH & Co. KG, 69469 Weinheim
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Two subgroup t-Test
Assumptions:
The Error of the 1st kind (α) determines the probability
with which the Null-Hypotheses could be wrongly rejected. The Error of the 2nd kind (β) stands for the
probability with which the Alternate Hypothesis could
wrongly be rejected.
Determinations:
For the evaluation of the subgroup size, the user has
to determine which Difference of means should
be recognized by the test as significant. Of course, the
information about the Standard deviation is required for this as well.
The Sample sizes that are displayed on the right
side of the graphic, are entered in the respective data
field on the left. In addition to that, the user can determine whether the test should be performed one-sided
or two-sided.
5. The test result itself is displayed on the Test tab
with additional information.
The output of the test results shall be explained using
three areas in the output window, starting with the test
results in the center:
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© 2008 Q-DAS GmbH & Co. KG, 69469 Weinheim
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Two-subgroup t-Test
The top portion of the result output shows a short test
description followed by the statistical numerical values
of the two subgroups below. Below that, the definition
of the Null-Hypothesis (H0) and of the Alternate Hypothesis (H1) are listed.
On the right side below, you can find the test statistic
with its respective formula. On the left side of it, the
different test levels (α-levels) are listed in a table with
the associated critical values. Immediately below the
test result is displayed in forma of a statement whether
the Null-Hypothesis has been rejected or accepted.
In our current example, the Null hypothesis has been
rejected on a level of α 1% this means the error of
the 1st kind is smaller than 1 %. The exact value is
listed below as P-value (0.4756 %).
The lower area of the result output displays the confidence level of the tested statistical value. For the twoDoc-No.:
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© 2008 Q-DAS GmbH & Co. KG, 69469 Weinheim
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Two subgroup t-Test
subgroup t-Test, the tested statistic is the difference of
the two averages ( x1 − x 2 ). The area in the middle
(green color) indicates the 95% confidence area. Next
to it are the 99% and the 99.9% confidence area. The
graphics shows that the Null hypothesis (E=0) lies outside the 99% confidence area.
Above the graphic, the different levels with the respective confidence interval limits are listed as a table.
On the left side of the Test tab,
the descriptions and the statistical values for the test are entered.
It is also possible to perform the
test directly by entering statistical
values in the respective fields.
In addition, it is also possible to
determine whether the test shall
be performed one-sided or twosided.
Version: 1
© 2008 Q-DAS GmbH & Co. KG, 69469 Weinheim
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