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InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
Page 1 of 17
Extended Paired t-test
Analysis and Within-subject
Analysis
User Guide
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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Contents
1 Introduction ......................................................................................... 3
2 Dataset format ..................................................................................... 4
3 Analysis procedure .............................................................................. 5 3.1 Select the analysis module ........................................................................................................ 5 3.2 Select the dataset to be analysed ............................................................................................... 5 3.3 Select the response to analyse and terms to include in the statistical model ............................ 6 3.4 Select a transformation for the response ................................................................................... 6 3.5 Select the covariance structure ................................................................................................. 7 3.6 Select the overall analysis results ............................................................................................. 7 3.7 Least square (predicted) means ................................................................................................ 8 3.8 All pairwise tests ...................................................................................................................... 8 3.9 Run the analysis ........................................................................................................................ 9
4 Output results ...................................................................................... 9
5 Controlling the output ...................................................................... 10
6 Test dataset example output ............................................................ 13 6.1 InVivoStat options .................................................................................................................. 13 6.2 Sample output ......................................................................................................................... 14
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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1 Introduction
The Extended Paired t-test Analysis and Within-subject Analysis module in
InVivoStat is available from the Statistics drop-down menu entitled ‘Extended Paired
t-test Analysis and Within-subject Analysis’. The user interface is:
The Extended Paired t-test Analysis and Within-subject Analysis module performs a
mixed model repeated measures analysis. It should be used when the subjects have
been measured at each level of the treatment factor. This module allows the user to fit
a single treatment factor, other design (block) factors and covariates. The user can
also assess the interactions involving the covariates by choosing the ‘Assess covariate
interactions’ option in the Output Options interface.
This module performs a paired t-test (if the treatment factor has only two levels) or a
within-subject repeated measures analysis (if the treatment factor has more than two
levels).
Note as the paired t-test is implemented using a mixed model approach, in InVivoStat
it has been defined as an ‘Extended’ paired t-test. Differences will occur (with the
orthodox paired t-test) if there are missing data or additional blocking factors or
covariates included in the statistical model.
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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2 Dataset format
The Extended Paired t-test Analysis and Within-subject Analysis module accepts data
in the repeated measures format, for example:
Response Treatment
(within subject) Subject
(within subject)
1.17 D0 1
1.30 D1 1
1.72 D2 1
1.17 D3 1
1.39 D0 2
1.44 D1 2
1.60 D2 2
1.57 D3 2
1.33 D0 3
1.57 D1 3
1.66 D2 3
1.47 D3 3
1.72 D0 4
1.17 D1 4
1.06 D2 4
1.24 D3 4
1.60 D0 5
0.99 D1 5
1.37 D2 5
1.50 D3 5
1.59 D0 6
1.37 D1 6
1.50 D2 6
1.37 D3 6
1.64 D0 7
1.53 D1 7
1.50 D2 7
1.59 D3 7
1.77 D0 8
1.86 D1 8
1.26 D2 8
1.64 D3 8
1.53 D0 9
1.77 D1 9
1.44 D2 9
1.92 D3 9
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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3 Analysis procedure
The steps required to perform an analysis are described in this section.
3.1 Select the analysis module
The analysis begins by selecting the
Extended Paired t-test Analysis and
Within-subject Analysis module from
the drop-down list of available modules:
Parametric Analysis →
Extended Paired t-test Analysis
and Within-subject Analysis
3.2 Select the dataset to be
analysed
Once the module is selected, the dataset
is chosen from the drop-down list of
available datasets.
Click ‘Submit’.
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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3.3 Select the response to
analyse and terms to
include in the statistical
model
Once the dataset has been selected, the
user selects the response variable to
analyse by clicking on the Responses
box and selecting the response variable
to analyse.
Similarly, the user can select a
treatment factor, subject factor, other
design (block) factors and covariates.
The subject factor indexes the subjects
(i.e. animals).
3.4 Select a transformation for
the response
Once selected, the user has the option of
applying a transformation to the
response variable, either log10, loge,
square root, arcsine or rank.
If selected, the covariate(s) will be
transformed using the same
transformation, unless otherwise
specified by the user.
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3.5 Select the covariance
structure
The user can select a covariance
structure to model the correlation of the
within-subject observations. The default
is the compound symmetric structure
(all observations within subject are
equally correlated regardless of the
‘distance’ separating them). Other
structures available include
autoregressive (recommended if the
time points are equally spaced) or
unstructured (recommended if the
sample size is not too small).
3.6 Select the overall analysis
results
There are several results that are
available. These are selected before
running the analysis and include:
1) Overall tests of model effects
Produces tests of the overall effect of
the terms in the statistical model. This
test is equivalent to a paired t-test if the
treatment factor has only two levels
without missing data.
2) Residuals vs. predicted plot
Allows the user to check the
homogeneity of variance assumption of
the parametric analysis.
3) Normal probability plot
Allows the user to check the normality
assumption of the parametric analysis.
4) Significance level
The significance level default is 0.05, or
5%, although this can be changed.
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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3.7 Least square (predicted)
means
The user can choose to plot the Least
square (predicted) means including
confidence intervals around the means.
These are the predicted means
generated directly from the statistical
analysis and take into account all effects
in the statistical model, such as any
covariates or blocking factors.
3.8 All pairwise tests
Produces pairwise comparisons of the
treatment factor means.
The user can control which group is
used to compare back to by defining a
control group. This is particularly useful
when performing a paired t-test.
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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3.9 Run the analysis
Click ‘Submit’ to run the analysis.
4 Output results
Response, covariance structure and covariates
InVivoStat identifies the response being analysed, the covariance structure used
(where appropriate) and also any covariates (if selected). This section also describes
any transformations that have been applied.
Categorised case profile of the data
InVivoStat produces a categorised case profile of the data (see graphics module for
more details). This plot should be used to identify possible outliers (both subjects and
individual observations) and any overall trends.
Covariate plot of the data
When fitting a covariate in a statistical analysis, certain assumptions are made. This
plot allows the user to assess these assumptions. Underneath the plot a list of the
assumptions is given with advice on how the plot can be used to evaluate them.
Overall table of effects
The ANOVA/ANCOVA-style table contains the overall effect of the model terms.
InVivoStat presents the Type III sums of squares (partial) as this was felt to be a
reasonably robust approach. Below the table any statistically significant effects are
listed.
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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Diagnostic plots
If requested, InVivoStat produces the residuals vs. predicted plot and the normal
probability plot. The residuals plotted on the residuals vs. predicted plot are the
Standardized residuals as these can provide a test for outliers. Any observation with a
residual greater (or less than) 3 could be considered an outlier.
Plot of the predicted means
InVivoStat produces a plot and table of the predicted means of the treatment factor.
Also included are confidence intervals around the means.
All pairwise tests
InVivoStat produces a table of all pairwise comparisons between the means of the
treatment factor. As well as the size of the difference between the predicted means,
InVivoStat also generates p-values to test the significance of these comparisons. A list
of statistically significant comparisons is given below the table.
References
A list of references for the methods applied in the analysis.
5 Controlling the output
The user has the ability to control various aspects of the output. These are available in
the ‘Output Options’ dialogue:
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Users can manipulate various plot
characteristics including line size, fonts
and marker size/type.
If the Least Square (LS) means plot is
produced, then a line can be included on
the plot connecting the means.
The user has control over all text
included on the plots, for example text
position, size and font.
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The user has control over the colour
scheme employed by InVivoStat,
including an option to produce all plots
in black & white.
If a covariate is included in the
statistical model, then the user can
formally assess the covariate
interactions by selecting ‘Assess
covariate interactions’.
The user can also view the covariate
regression coefficients (by selecting the
‘Covariate regression coefficients’
option).
If the response has been log
transformed, by selecting ‘Display
geometric means’ the back transformed
means are given (and plotted).
Additionally, comparisons between the
predicted means will also be back
transformed (and hence be presented as
ratios).
Further information on these options can be found in the Getting Started User Guide.
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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6 Test dataset example output
6.1 InVivoStat options
InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019
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6.2 Sample output
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