Extended Paired t-test Analysis and Within-subject ...invivostat.co.uk/.../Paired_t-test_and_Within_Subject_Analysis.pdf · The steps required to perform an analysis are described

InVivoStat User Guides – Paired t-test Analysis and Within-subject Analysis Version 4.0 December 2019

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Extended Paired t-test

Analysis and Within-subject

Analysis

User Guide


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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


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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.


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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


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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’.


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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.


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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.


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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.


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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.


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6 Test dataset example output

6.1 InVivoStat options


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6.2 Sample output


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Documents

Extended Paired t-test Analysis and Within-subject ...invivostat.co.uk/.../Paired_t-test_and_Within_Subject_Analysis.pdf · The steps required to perform an analysis are described