| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Raw data Listing |
| Obs | TIME | VOLTAGE | GROUP | LogTime |
|---|---|---|---|---|
| 1 | 5.79 | 26 | GROUP 1 | 1.75613 |
| 2 | 1579.52 | 26 | GROUP 1 | 7.36488 |
| 3 | 2323.70 | 26 | GROUP 1 | 7.75092 |
| 4 | 68.85 | 28 | GROUP 2 | 4.23193 |
| 5 | 108.29 | 28 | GROUP 2 | 4.68481 |
| 6 | 110.29 | 28 | GROUP 2 | 4.70311 |
| 7 | 426.07 | 28 | GROUP 2 | 6.05460 |
| 8 | 1067.60 | 28 | GROUP 2 | 6.97317 |
| 9 | 7.74 | 30 | GROUP 3 | 2.04640 |
| 10 | 17.05 | 30 | GROUP 3 | 2.83615 |
| 11 | 20.46 | 30 | GROUP 3 | 3.01847 |
| 12 | 21.02 | 30 | GROUP 3 | 3.04547 |
| 13 | 22.66 | 30 | GROUP 3 | 3.12060 |
| 14 | 43.40 | 30 | GROUP 3 | 3.77046 |
| 15 | 47.30 | 30 | GROUP 3 | 3.85651 |
| 16 | 139.07 | 30 | GROUP 3 | 4.93498 |
| 17 | 144.12 | 30 | GROUP 3 | 4.97065 |
| 18 | 175.88 | 30 | GROUP 3 | 5.16980 |
| 19 | 194.90 | 30 | GROUP 3 | 5.27249 |
| 20 | 0.27 | 32 | GROUP 4 | -1.30933 |
| 21 | 0.40 | 32 | GROUP 4 | -0.91629 |
| 22 | 0.69 | 32 | GROUP 4 | -0.37106 |
| 23 | 0.79 | 32 | GROUP 4 | -0.23572 |
| 24 | 2.75 | 32 | GROUP 4 | 1.01160 |
| 25 | 3.91 | 32 | GROUP 4 | 1.36354 |
| 26 | 9.88 | 32 | GROUP 4 | 2.29051 |
| 27 | 13.95 | 32 | GROUP 4 | 2.63548 |
| 28 | 15.93 | 32 | GROUP 4 | 2.76820 |
| 29 | 27.80 | 32 | GROUP 4 | 3.32504 |
| 30 | 53.24 | 32 | GROUP 4 | 3.97481 |
| 31 | 82.85 | 32 | GROUP 4 | 4.41703 |
| 32 | 89.29 | 32 | GROUP 4 | 4.49189 |
| 33 | 100.59 | 32 | GROUP 4 | 4.61105 |
| 34 | 215.10 | 32 | GROUP 4 | 5.37110 |
| 35 | 0.19 | 34 | GROUP 5 | -1.66073 |
| 36 | 0.78 | 34 | GROUP 5 | -0.24846 |
| 37 | 0.96 | 34 | GROUP 5 | -0.04082 |
| 38 | 1.31 | 34 | GROUP 5 | 0.27003 |
| 39 | 2.78 | 34 | GROUP 5 | 1.02245 |
| 40 | 3.16 | 34 | GROUP 5 | 1.15057 |
| 41 | 4.15 | 34 | GROUP 5 | 1.42311 |
| 42 | 4.67 | 34 | GROUP 5 | 1.54116 |
| 43 | 4.85 | 34 | GROUP 5 | 1.57898 |
| 44 | 6.50 | 34 | GROUP 5 | 1.87180 |
| 45 | 7.35 | 34 | GROUP 5 | 1.99470 |
| 46 | 8.01 | 34 | GROUP 5 | 2.08069 |
| 47 | 8.27 | 34 | GROUP 5 | 2.11263 |
| 48 | 12.06 | 34 | GROUP 5 | 2.48989 |
| 49 | 31.75 | 34 | GROUP 5 | 3.45789 |
| 50 | 32.52 | 34 | GROUP 5 | 3.48186 |
| 51 | 33.91 | 34 | GROUP 5 | 3.52371 |
| 52 | 36.71 | 34 | GROUP 5 | 3.60305 |
| 53 | 72.89 | 34 | GROUP 5 | 4.28895 |
| 54 | 0.35 | 36 | GROUP 6 | -1.04982 |
| 55 | 0.59 | 36 | GROUP 6 | -0.52763 |
| 56 | 0.96 | 36 | GROUP 6 | -0.04082 |
| 57 | 0.99 | 36 | GROUP 6 | -0.01005 |
| 58 | 1.69 | 36 | GROUP 6 | 0.52473 |
| 59 | 1.97 | 36 | GROUP 6 | 0.67803 |
| 60 | 2.07 | 36 | GROUP 6 | 0.72755 |
| 61 | 2.58 | 36 | GROUP 6 | 0.94779 |
| 62 | 2.71 | 36 | GROUP 6 | 0.99695 |
| 63 | 2.90 | 36 | GROUP 6 | 1.06471 |
| 64 | 3.67 | 36 | GROUP 6 | 1.30019 |
| 65 | 3.99 | 36 | GROUP 6 | 1.38379 |
| 66 | 5.35 | 36 | GROUP 6 | 1.67710 |
| 67 | 13.77 | 36 | GROUP 6 | 2.62249 |
| 68 | 25.50 | 36 | GROUP 6 | 3.23868 |
| 69 | 0.09 | 38 | GROUP 7 | -2.40795 |
| 70 | 0.39 | 38 | GROUP 7 | -0.94161 |
| 71 | 0.47 | 38 | GROUP 7 | -0.75502 |
| 72 | 0.73 | 38 | GROUP 7 | -0.31471 |
| 73 | 0.74 | 38 | GROUP 7 | -0.30111 |
| 74 | 1.13 | 38 | GROUP 7 | 0.12222 |
| 75 | 1.40 | 38 | GROUP 7 | 0.33647 |
| 76 | 2.38 | 38 | GROUP 7 | 0.86710 |
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Plot of the raw data |
Plot of TIME*VOLTAGE. Legend: A = 1 obs, B = 2 obs, etc.
TIME |
|
2500 +
|
| A
|
|
|
2000 +
|
|
|
|
| A
1500 +
|
|
|
|
| A
1000 +
|
|
|
|
|
500 +
| A
|
| A
| D
| C B D A
0 + A E J R O H
|
---+--------------+--------------+--------------+--------------+--------------+--------------+--
26 28 30 32 34 36 38
VOLTAGE
|
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Initial fit of the raw data |
| Simple Regression with REG |
| Number of Observations Read | 76 |
|---|---|
| Number of Observations Used | 76 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 1 | 2150408 | 2150408 | 24.27 | <.0001 |
| Error | 74 | 6557345 | 88613 | ||
| Corrected Total | 75 | 8707754 | |||
| Root MSE | 297.67898 | R-Square | 0.2470 |
|---|---|---|---|
| Dependent Mean | 98.55776 | Adj R-Sq | 0.2368 |
| Coeff Var | 302.03504 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | 1886.16945 | 364.48121 | 5.17 | <.0001 |
| VOLTAGE | 1 | -53.95492 | 10.95264 | -4.93 | <.0001 |
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Initial fit of the raw data |
| Plot of residuals |
Plot of resid*VOLTAGE. Legend: A = 1 obs, B = 2 obs, etc.
resid |
2000 +
|
| A
|
|
|
1500 +
|
|
|
|
| A
1000 +
|
|
|
| A
|
500 +
|
|
|
| H
| A A O
0 +----------------------------------------------------------F------------------------------
| C D M
| A J
| B G
| A
|
-500 + A
|
---+-------------+-------------+-------------+-------------+-------------+-------------+--
26 28 30 32 34 36 38
VOLTAGE
|
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Initial fit of the raw data |
| Plot of residuals |
Plot of resid*YHat. Legend: A = 1 obs, B = 2 obs, etc.
resid |
2000 +
|
| A
|
|
|
1500 +
|
|
|
|
| A
1000 +
|
|
|
| A
|
500 +
|
|
|
| H
| O A A
0 +------------------------------F----------------------------------------------------------
| M D C
| J A
| G B
| A
|
-500 + A
|
---+-------------+-------------+-------------+-------------+-------------+-------------+--
-164.12 -56.21 51.70 159.61 267.52 375.43 483.34
YHat
|
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Initial fit of the raw data |
| Plot of residuals |
| Moments | |||
|---|---|---|---|
| N | 76 | Sum Weights | 76 |
| Mean | 0 | Sum Observations | 0 |
| Std Deviation | 295.687792 | Variance | 87431.2704 |
| Skewness | 4.02671557 | Kurtosis | 21.9169395 |
| Uncorrected SS | 6557345.28 | Corrected SS | 6557345.28 |
| Coeff Variation | . | Std Error Mean | 33.9177159 |
| Basic Statistical Measures | |||
|---|---|---|---|
| Location | Variability | ||
| Mean | 0.0000 | Std Deviation | 295.68779 |
| Median | -46.0272 | Variance | 87431 |
| Mode | . | Range | 2318 |
| Interquartile Range | 203.20468 | ||
| Tests for Location: Mu0=0 | ||||
|---|---|---|---|---|
| Test | Statistic | p Value | ||
| Student's t | t | 0 | Pr > |t| | 1.0000 |
| Sign | M | -9 | Pr >= |M| | 0.0505 |
| Signed Rank | S | -283 | Pr >= |S| | 0.1440 |
| Tests for Normality | ||||
|---|---|---|---|---|
| Test | Statistic | p Value | ||
| Shapiro-Wilk | W | 0.615009 | Pr < W | <0.0001 |
| Kolmogorov-Smirnov | D | 0.248565 | Pr > D | <0.0100 |
| Cramer-von Mises | W-Sq | 1.204042 | Pr > W-Sq | <0.0050 |
| Anderson-Darling | A-Sq | 6.998223 | Pr > A-Sq | <0.0050 |
| Quantiles (Definition 5) | |
|---|---|
| Quantile | Estimate |
| 100% Max | 1840.3584 |
| 99% | 1840.3584 |
| 95% | 166.4975 |
| 90% | 164.8475 |
| 75% Q3 | 58.5327 |
| 50% Median | -46.0272 |
| 25% Q1 | -144.6720 |
| 10% | -246.5019 |
| 5% | -265.1417 |
| 1% | -477.5515 |
| 0% Min | -477.5515 |
| Extreme Observations | |||
|---|---|---|---|
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| -477.552 | 1 | 165.518 | 75 |
| -306.582 | 4 | 166.498 | 76 |
| -267.142 | 5 | 692.168 | 8 |
| -265.142 | 6 | 1096.178 | 2 |
| -259.782 | 9 | 1840.358 | 3 |
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Initial fit of the raw data |
| Plot of residuals |
Stem Leaf # Boxplot Normal Probability Plot
18 4 1 * 1850+ *
17 |
16 |
15 |
14 |
13 |
12 |
11 0 1 * |
10 | *
9 |
8 |
7 | ++
6 9 1 * | * +++
5 | ++++
4 | +++
3 | +++
2 | ++++
1 66666777 8 | | +++ ***** *
0 256666666666666678 18 +--+--+ | +++********
-0 98776555555555544442221 23 *-----* | *********
-1 6666665543321 13 +-----+ | ******+
-2 776555422 9 | | ** *****++++
-3 1 1 | | * +++
-4 8 1 0 -450+ * +++
----+----+----+----+--- +----+----+----+----+----+----+----+----+----+----+
Multiply Stem.Leaf by 10**+2 -2 -1 0 +1 +2
|
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Examination of the log transformed data |
| Plot of the log transformed data |
Plot of LogTime*VOLTAGE. Legend: A = 1 obs, B = 2 obs, etc.
LogTime |
|
8 +
| A
| A
| A
|
|
6 + A
|
| B A
| B
| B A
| A B A
4 + A A
| A B
| A B A
| D
| B A
| A A
2 + A D
| A B A
| A A B
| A B C A
| C
| A A
0 + A B A
| B A B
| A A
| A A A
| A
| A
-2 +
| A
|
|
|
|
-4 +
|
---+-------------+-------------+-------------+-------------+-------------+-------------+--
26 28 30 32 34 36 38
VOLTAGE
|
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Examination of the log transformed data |
| Transformed regression with REG |
| Number of Observations Read | 76 |
|---|---|
| Number of Observations Used | 76 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 1 | 190.15149 | 190.15149 | 78.14 | <.0001 |
| Error | 74 | 180.07484 | 2.43344 | ||
| Corrected Total | 75 | 370.22633 | |||
| Root MSE | 1.55995 | R-Square | 0.5136 |
|---|---|---|---|
| Dependent Mean | 2.14566 | Adj R-Sq | 0.5070 |
| Coeff Var | 72.70267 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | 18.95546 | 1.91002 | 9.92 | <.0001 |
| VOLTAGE | 1 | -0.50736 | 0.05740 | -8.84 | <.0001 |
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Examination of the log transformed data |
| Plot of residuals |
Plot of resid*VOLTAGE. Legend: A = 1 obs, B = 2 obs, etc.
resid |
|
4 +
|
|
|
| A A A
| A
2 + A A A A
| A A B C
| A C A A
| A
| A A B A
| D C A
0 +----------------B-------------B-------------B-------------B-------------C-------------B--
| A A A
| A C B B A
| A
| A A A
| A A A A
-2 + A A
|
|
| B
| A
| A
-4 + A A
|
---+-------------+-------------+-------------+-------------+-------------+-------------+--
26 28 30 32 34 36 38
VOLTAGE
|
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Examination of the log transformed data |
| Plot of residuals |
Plot of resid*YHat. Legend: A = 1 obs, B = 2 obs, etc.
resid |
|
4 +
|
|
|
| A A A
| A
2 + A A A A
| C B A A
| A A C A
| A
| A B A A
| A C D
0 +--B-------------C-------------B-------------B-------------B-------------B----------------
| A A A
| A B B C A
| A
| A A A
| A A A A
-2 + A A
|
|
| B
| A
| A
-4 + A A
|
---+-------------+-------------+-------------+-------------+-------------+-------------+--
-0.324 0.690 1.705 2.720 3.735 4.749 5.764
YHat
|
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Examination of the log transformed data |
| Plot of residuals |
| Moments | |||
|---|---|---|---|
| N | 76 | Sum Weights | 76 |
| Mean | 0 | Sum Observations | 0 |
| Std Deviation | 1.54951535 | Variance | 2.40099782 |
| Skewness | -0.6488654 | Kurtosis | 0.30321576 |
| Uncorrected SS | 180.074836 | Corrected SS | 180.074836 |
| Coeff Variation | . | Std Error Mean | 0.1777416 |
| Basic Statistical Measures | |||
|---|---|---|---|
| Location | Variability | ||
| Mean | 0.000000 | Std Deviation | 1.54952 |
| Median | 0.036589 | Variance | 2.40100 |
| Mode | . | Range | 6.68044 |
| Interquartile Range | 1.91300 | ||
| Tests for Location: Mu0=0 | ||||
|---|---|---|---|---|
| Test | Statistic | p Value | ||
| Student's t | t | 0 | Pr > |t| | 1.0000 |
| Sign | M | 3 | Pr >= |M| | 0.5666 |
| Signed Rank | S | 93 | Pr >= |S| | 0.6333 |
| Tests for Normality | ||||
|---|---|---|---|---|
| Test | Statistic | p Value | ||
| Shapiro-Wilk | W | 0.956759 | Pr < W | 0.0112 |
| Kolmogorov-Smirnov | D | 0.10799 | Pr > D | 0.0267 |
| Cramer-von Mises | W-Sq | 0.11647 | Pr > W-Sq | 0.0699 |
| Anderson-Darling | A-Sq | 0.834933 | Pr > A-Sq | 0.0311 |
| Quantiles (Definition 5) | |
|---|---|
| Quantile | Estimate |
| 100% Max | 2.6513227 |
| 99% | 2.6513227 |
| 95% | 2.2239282 |
| 90% | 1.8912724 |
| 75% Q3 | 1.2183016 |
| 50% Median | 0.0365886 |
| 25% Q1 | -0.6947034 |
| 10% | -1.9535119 |
| 5% | -3.3657817 |
| 1% | -4.0291137 |
| 0% Min | -4.0291137 |
| Extreme Observations | |||
|---|---|---|---|
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| -4.02911 | 20 | 1.98695 | 3 |
| -4.00784 | 1 | 2.22393 | 8 |
| -3.63607 | 21 | 2.54836 | 68 |
| -3.36578 | 35 | 2.58390 | 53 |
| -3.09084 | 22 | 2.65132 | 34 |
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Examination of the log transformed data |
| Plot of residuals |
Stem Leaf # Boxplot Normal Probability Plot
2 567 3 | 2.75+ +*+* *
2 02 2 | | ++++*
1 5678888999 10 | | *******
1 0222334 7 +-----+ | ***+
0 66778 5 | | | ***
0 00000123334444 14 *--+--* | ******
-0 4432211100 10 | | | ****
-0 9777776665 10 +-----+ -0.75+ ****+
-1 442 3 | | **++
-1 7777 4 | | ****
-2 10 2 | | ++*+
-2 | | +++ *
-3 410 3 | | +++ * *
-3 6 1 0 |+++ *
-4 00 2 0 -4.25+ * *
----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
|
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Testing lack of fit |
| ANOVA of the Untransformed data with GLM |
| Class Level Information | ||
|---|---|---|
| Class | Levels | Values |
| GROUP | 7 | GROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP 5 GROUP 6 GROUP 7 |
| Number of Observations Read | 76 |
|---|---|
| Number of Observations Used | 76 |
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Testing lack of fit |
| ANOVA of the Untransformed data with GLM |
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 6 | 5082509.892 | 847084.982 | 16.12 | <.0001 |
| Error | 69 | 3625243.641 | 52539.763 | ||
| Corrected Total | 75 | 8707753.533 |
| R-Square | Coeff Var | Root MSE | TIME Mean |
|---|---|---|---|
| 0.583676 | 232.5697 | 229.2155 | 98.55776 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| GROUP | 6 | 5082509.892 | 847084.982 | 16.12 | <.0001 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| GROUP | 6 | 5082509.892 | 847084.982 | 16.12 | <.0001 |
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Testing lack of fit |
| Extra SS of fitting means after the slope |
| Class Level Information | ||
|---|---|---|
| Class | Levels | Values |
| GROUP | 7 | GROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP 5 GROUP 6 GROUP 7 |
| Number of Observations Read | 76 |
|---|---|
| Number of Observations Used | 76 |
| Chapter 8 : Time to breakdown of 76 samples of an insulating fluid |
| Testing lack of fit |
| Extra SS of fitting means after the slope |
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 6 | 5082509.892 | 847084.982 | 16.12 | <.0001 |
| Error | 69 | 3625243.641 | 52539.763 | ||
| Corrected Total | 75 | 8707753.533 |
| R-Square | Coeff Var | Root MSE | TIME Mean |
|---|---|---|---|
| 0.583676 | 232.5697 | 229.2155 | 98.55776 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| VOLTAGE | 1 | 2150408.256 | 2150408.256 | 40.93 | <.0001 |
| GROUP | 5 | 2932101.636 | 586420.327 | 11.16 | <.0001 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| VOLTAGE | 0 | 0.000 | . | . | . |
| GROUP | 5 | 2932101.636 | 586420.327 | 11.16 | <.0001 |