One-Way ANOVA Analysis Results
When accessed from a one-way ANOVA folio, the Analysis
Summary window will contain detailed information about analysis
results, including information that describes how the factor levels
affect the response.
If the current response data has been analyzed, you
can open the window by clicking the View
Analysis Summary icon on the control panel.
If the current response data has not been analyzed, the icon will still
be available so you can view the folio's analysis history.
Select an item in the Available Report Items panel to display it on
the spreadsheet. Each item is described next.
Analysis Results
The ANOVA table provides
general information about the effects of the factor levels on
the selected response.
ANOVA Table Columns
-
Source of Variation
is the source that caused the difference in the observed output
values. This can be a factor, factorial interaction, curvature,
block, error, etc. If your design includes more than one factor
and you have selected to use grouped terms in the analysis (specified
on the Analysis Settings page of the control panel), the effects
will be grouped by order (i.e., main effects, two-way interactions,
etc.). Sources displayed in red are considered to be significant.
-
The number of Degrees of
Freedom for the Model
is the number of regression coefficients for the effects included
in the analysis (e.g., two coefficients might be included in the
regression table for a given main effect). The number of degrees
of freedom for the Residual
is the total number of observations minus the number of parameters
being estimated.
-
Sum of Squares is
the amount of difference in observed output values caused by this
source of variation.
-
Mean Squares is
the average amount of difference caused by this source of variation.
This is equal to Sum of Squares/Degrees of Freedom.
-
F Ratio is the ratio
of Mean Squares of this source of variation and Mean Squares of
pure error. A large value in this column indicates that the difference
in the output caused by this source of variation is greater than
the difference caused by noise (i.e., this source affects the
output).
-
P Value (alpha error
or type I error) is the probability that an equal amount of variation
in the output would be observed in the case that this source does
not affect the output. This value is compared to the risk level
(alpha) that you specify on the Analysis Settings page of the
control panel. If the p
value is less than alpha, this source of variation is considered
to have a significant effect on the output. In this case, the
term and its p value
will be displayed in red.
-
The following values are shown underneath the ANOVA table,
and they indicate how well the model fits the data:
-
S is the standard
error of the noise. It represents the magnitude of the response
variation that is caused by noise. Lower values indicate better
fit.
-
R-sq is the
percentage of total difference that is attributable to the
factors under consideration. It is equal to Sum of Squares(factor)/Total
Sum of Squares. Higher values usually indicate better fit.
-
R-sq(adj) is
an R-sq value that is adjusted for the number of parameters
in the model. Higher values indicate better fit.
The Data Summary table
gives the mean and standard deviation of the output at each level
of the factor.
Data Summary Table Columns
- Factor Level
is the name of the qualitative level.
- Number in Level
is the number of data points obtained at the factor
level.
- Estimated Mean
is the average of the data points obtained at the
level.
- Standard Deviation is the standard deviation of the data points
obtained at the level.
The Mean Comparisons table
provides information on comparisons between levels of the factor.
Mean
Comparisons Table Columns
- Contrast
gives the paired comparison of any two levels. Level
1 - Level 2 means the difference between Level 1 and
Level 2. Contrasts displayed in red are considered
to be significant.
- Mean
Difference is the mean value of the difference
in output between the two levels.
- Pooled
Standard Error is the standard error of the
mean difference in output between the two levels.
- Low
Confidence and High
Confidence are the confidence bounds on the
mean difference.
- T
Value is the normalized difference, which is
equal to Mean Difference/Pooled Standard Error.
- P
Value is the probability that an equal amount
of variation in the output would be observed in the
case that there is no significant difference between
the levels. This value is compared to the risk level
(alpha) that you specify on the Analysis Settings
page of the control panel. If the p
value is less than alpha, there is considered to be
a significant difference between the levels. In this
case, the contrast and its p
value will be displayed in red.
The Regression Equation information
is presented using two tables.
Regression
Equation Tables
-
The Response table
displays the response that the regression equation applies to
and the units of measurement that were entered for the response
(if any).
-
The Additional Settings
table shows the transformation and risk level you entered for
the response.