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SEMI E66-1103 © SEMI 1997, 2003 13 APPENDIX 2 t-TESTING; COMPARISON OF BACKGROUND MEAN AND DEVICE MEAN NOTE: This appendix was approved as an official pa rt of SEMI E66 by full letter ballot procedure. A2-1 A2-1.1 The ba…
SEMI E66-1103 © SEMI 1997, 2003 12
A1-1.3 Figure A1-2 gives an overall picture of the data collection specified by Table A2-1 for both
“BACKGROUND” and “DEVICE”. There are three phases of data collection:
1. Cleanup
2. Steady-state performance
3. Statistical process control (SPC)
Figure A1-2
Graphical Representation of Data Collection
SEMI E66-1103 © SEMI 1997, 2003 13
APPENDIX 2
t-TESTING; COMPARISON OF BACKGROUND MEAN AND DEVICE
MEAN
NOTE: This appendix was approved as an official part of SEMI E66 by full letter ballot procedure.
A2-1
A2-1.1 The background and DUT are expected to have low particle counts. Therefore, a statistical method is needed
to determine if there is a difference between background and DUT particle counts. The t-test is a method of
determining the actual statistical difference between the mean background particle count and the mean device
particle count. It can be used to characterize the particle contribution by the MFC Record results in Table A2-1.
Table A2-1 Test Worksheet
# Observation log Observation Remarks
Spool Cleanup 1 ... Nx All computations are in the logs of
original observations.
Stable Level X1 ... X25 Compute X
1, S1, UCL, LCL.
SPC X26 ... X334 Use all 8 values to recompute new
values (X
1,S1
).
Connect Device
Device Cleanup X34 ... X35 + n
Stable Level X34 + n + 1 ... X34 + n + 25 Compute X
2, S2, UCL, LCL
.
SPC X34 + n + 26 ... X34 + n + 34 Use all 8 values to recompute new
values (X
2, S2
).
NOTE: Use t-test to compare X’s. (See Appendix 2.)
A2-1.2 Calculate pooled standard deviation using the following equation:
S
pooled
=
(n
1
− 1)S
1
2
+ (n
2
− 1)S
2
2
n
1
+ n
2
− 2
where :
S
1
= background standard deviation
S
2
= device standard deviation
n
1
= background sample size
n
2
= device sample size
A2-1.3 Calculate the value of T (the t-test’s namesake) as follows:
t =
X
1
− X
2
S
pooled
1
n
1
+
1
n
2
where :
1 = background mean
2 = device mean
SEMI E66-1103 © SEMI 1997, 2003 14
A2-1.4 The degrees of freedom (dof) is n
1
+ n
2
- 2. For example, if n
1
= n
2
= 8, then dof = 14.
A2-2 Interpretation
A2-2.1 If |t| > t
.975
, then the two means are significantly different at the 95% level. If |t| > t
.995
, then the two means
are significantly different at the 99% level (e.g., by “95% confidence,” it is meant that the difference/no-difference
decision based on the t-test will be correct 95% of the time).
t
.975
= 2.145 (2-sided)
t
.995
= 2.977 (2-sided)
NOTE:
• All readings are log particle counts, not particle counts.
• Since logs are used, zeros have to be replaced by positive values (e.g., 1/2).
• To determine t value for a particular confidence level and (dof), refer to any statistical reference book.
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