Basic Statistics Using
Minitab
L. GOCH – FEBRUARY 2011
AGENDA

Comparing 1 Group to a Target / Specification OR
Comparing 2+ Groups to Each Other:
1)
2)
3)
4)

Stability – Run Chart (Feb 4th) or Control Chart (Mar 4th)
Shape – Histogram (Feb 4th) or Probability Plot
Spread – Test for Equal Variances
Centering – 1-Sample T-test, 1-Sample Sign, Paired T,
2-Sample T-test, ANOVA or Mood’s Median Test
Comparing Proportions - 1 Proportion, 2
Proportion

Basic Linear Regression – Fitted Line Plot

Chi-Squared – Cross Tabulation and Chi-Square

Trend Analysis – Under Stat > Time Series: We
won’t be covering in this class. See Tutorials for
more information.
PROBABILITY PLOT:
GRAPH > PROBABILITY PLOT
PROBABILITY PLOT:

GRAPH > PROBABILITY PLOT
Use to display overlaid probability plots of multiple
variables and/or multiple groups on the same graph.
Open worksheet FlameRTD.mtw
PROBABILITY PLOT
Probability Plot of Fabric1
Normal
99
C oating
A
B
N one
95
90
90
80
60
50
40
20
10
2.0
2.5
3.0
3.5
Fabric1
4.304
3.544
5
1
StDev N
AD
P
0.4138 15 0.321 0.497
0.3575 15 0.545 0.133
0.5700 15 0.310 0.517
Since all p-values are >
0.05, conclude each data set
is NORMA LLY DISTRIBUTED.
30
3.185
Percent
70
Mean
3.013
2.727
3.573
4.0
4.5
5.0
TEST FOR EQUAL
VARIANCES:
STAT > ANOVA > TEST FOR
EQUAL VARIANCES
TEST FOR EQUAL VARIANCES:

STAT > ANOVA > TEST FOR
EQUAL VARIANCES
Use to display overlaid probability plots of multiple
variables and/or multiple groups on the same graph.
Open worksheet FlameRTD.mtw
TEST FOR EQUAL VARIANCES (SESSION WINDOW & GRAPH RESULTS)
Use for Normal Data
Use for Non-Normal Data
Test for Equal Variances for Fabric1
Bartlett's Test
Test Statistic
P-Value
A
3.19
0.203
Levene's Test
C oating
Test Statistic
P-Value
B
None
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
95% Bonferroni Confidence Intervals for StDevs
1.0
1.1
1.42
0.253
CENTERING COMPARISON ANALYSES
Response is Numeric & Factors are Text or Numeric
Analysis
1-Sample T
1-Sample Sign
# of Grps Comparison Statistic
1
Target
Average
1
Target
Median
Paired Data
Paired T
2
(e.g. before Difference
vs after)
2-Sample T
2
Each Other Average
ANOVA
2+
Each Other Average
Mood’s Median Test
2+
Each Other Median
1-SAMPLE T-TEST:
STAT > BASIC STATISTICS >
1-SAMPLE T
1-SAMPLE T-TEST:

STAT > BASIC STATISTICS > 1-SAMPLE T
Performs a one-sample t-test or t-confidence
interval for the mean.
Open worksheet
EXH_Stat.mtw
1-SAMPLE T (SESSION WINDOW & GRAPH RESULTS)
Note: For n<30, data is assumed to be Normally Dist’d
95% of the time the True
Avg will be between
4.5989 & 4.9789
Boxplot of Values
(with Ho and 95% t-confidence interval for the mean)
The sample Avg is
significantly different
from the Target of 5.
_
X
Ho
4.4
4.5
4.6
4.7
4.8
Values
4.9
5.0
5.1
1-SAMPLE SIGN:
STAT > NONPARAMETRICS>
1-SAMPLE SIGN
1-SAMPLE SIGN:

STAT > NONPARAMETRICS> 1-SAMPLE SIGN
Performs a one-sample t-Sign or t-confidence
interval for the median.
Open worksheet
EXH_Stat.mtw
1-SAMPLE SIGN (SESSION WINDOW RESULTS)
The sample Median is NOT
significantly different from the
Target of 115.
95% of the time the True Median will
be between 108.5 & 211.7
PAIRED T-TEST:
STAT > BASIC STATISTICS >
PAIRED T
PAIRED T-TEST:

STAT > BASIC STATISTICS > PAIRED T
Tests the mean difference between paired (related)
observations.
Open worksheet
EXH_Stat.mtw
PAIRED T (SESSION WINDOW & GRAPH RESULTS)
95% of the time the True
Avg Difference will be
between -0.687& -0.133
which does NOT contain
ZERO.
Boxplot of Differences
(with Ho and 95% t-confidence interval for the mean)
The sample Avgs are significantly
different from each other.
_
X
Ho
-1.2
-0.9
-0.6
-0.3
Differences
0.0
2-SAMPLE T-TEST:
STAT > BASIC STATISTICS >
2-SAMPLE T
2-SAMPLE T-TEST:

STAT > BASIC STATISTICS > 2-SAMPLE T
Performs a two-sample t-test or t-confidence
interval for the mean difference.
Open worksheet
Furnace.mtw
2-SAMPLE T (SESSION WINDOW & GRAPH RESULTS)
95% of the time the True
Avg Difference will be
between -1.450 & 0.980
which contains ZERO.
Boxplot of BTU.In
20
The sample Avgs are
NOT significantly different
from each other.
BTU.In
15
10
5
1
2
Damper
ONE-WAY ANOVA:
STAT > ANOVA > ONE-WAY
ONE-WAY ANOVA:

STAT > ANOVA > ONE-WAY
Compares the Averages for 2 or more Groups.
Open worksheet
Exh_AOV.mtw
ONE-WAY ANOVA (SESSION WINDOW & GRAPH RESULTS)
Boxplot of Durability
At least 1 Pair of Avgs are
significantly different from
each other.
22.5
20.0
Durability
17.5
15.0
12.5
10.0
7.5
5.0
1
2
3
Carpet
4
MOOD’S MEDIAN TEST:
STAT > NONPARAMETRICS>
MOOD’S MEDIAN TEST
MOOD’S MEDIAN TEST: STAT > NONPARAMETRICS> MOOD’S
MEDIAN TEST

Compares the Medians of 2 or more Groups.
Open worksheet
Cartoon.mtw
MOOD’S MEDIAN TEST (SESSION WINDOW RESULTS)
At least one group’s
median is significantly
different from the others.
Group 2 is significantly different
from groups 0 & 1 since the 95%
CI’s do NOT overlap.
Boxplot of Otis
140
130
120
Otis
110
100
90
80
70
0
1
ED
2
1-PROPORTION TEST:
STAT > BASIC STATISTICS >
1-PROPORTION
1-PROPORTION: STAT > BASIC STATISTICS > 1-PROPORTION

Performs a one-sample proportions test or pconfidence interval for a proportion.
No worksheet is
needed for this test.
1-PROPORTION: (SESSION WINDOW RESULTS)
Note: Proportion Testing Should NOT be done when the
sample size n<30!!
95% of the time the True
Proportion will be between
55.74% & 62.10%
The sample Proportion
is significantly different
from the Target of 65%.
2-PROPORTION TEST:
STAT > BASIC STATISTICS >
2-PROPORTIONS
2-PROPORTIONS: STAT > BASIC STATISTICS > 2-PROPORTIONS

Performs a two-sample proportions test or pconfidence intervals for a proportion.
No worksheet is
needed for this test.
2-PROPORTIONS: (SESSION WINDOW RESULTS)
Note: Proportion Testing Should NOT be done when the
sample size for any one group is <30!!
95% of the time the True
Difference between the
Proportions will be
between -9.58% & 17.58%
The difference in Proportions
is NOT significantly different.
BASIC LINEAR
REGRESSION:
STAT > REGRESSION >
FITTED LINE PLOT
REGRESSION: STAT > REGRESSION > FITTED LINE PLOT

Performs a Regression Analysis on 1 Input (X) and
1 Output (Y).
Open worksheet
Exh_REGR.mtw
REGRESSION: (GRAPH RESULTS)
Fitted Line Plot
EnergyConsumption = 1.25 + 0.3218 MachineSetting
EnergyConsumption
40
S
R-Sq
R-Sq(adj)
30
20
10
0
10
15
20
MachineSetting
25
30
The line does NOT fit the curved data. Need a
quadratic, cubic or transformation of the data.
12.1825
2.3%
0.0%
REGRESSION: (SESSION WINDOW & GRAPH RESULTS)
The Regression Equation
shows that Machine
Setting explains 93.1% of
the variability in Energy
Consumption.
Fitted Line Plot
log10(EnergyConsumption) = 7.070 - 0.6986 MachineSetting
+ 0.01740 MachineSetting**2
The Quadratic Term is significant in
the model. NOTE: If a higher order
term is significant than the lower
order term must remain in the model.
EnergyConsumption
100
S
R-Sq
R-Sq(adj)
10
1
10
15
20
MachineSetting
25
30
0.167696
93.1%
91.1%
CROSS TABULATION AND
CHI-SQUARE:
STAT > TABLES > CROSS
TABULATION AND CHISQUARE
CHI-SQUARE: STAT > TABLES > CROSS TABULATION AND CHISQUARE

Performs a Chi-Squared Analysis on Count Data.
Open worksheet
Exh_TABL.mtw
CHI-SQUARE ANALYSIS: (SESSION WINDOW RESULTS)
No significant
association between
Gender and Activity
CONCLUSIONS
Results need to be Supported by data
 Not based on conjecture or intuition
 Shown in 1) Graphical & 2) Statistical format
 Make sense from an 3) Engineering standpoint
 Use P-values to determine if Results could have
happened by Chance!!

Need Significant Differences
for Reliable Conclusions !!