independant t-test, is this approach correct? Root lenght measurements comparison

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Occasional Contributor
Posts: 12

independant t-test, is this approach correct? Root lenght measurements comparison

hello,

I am helping someone with her statistical analyses for her biology master-dissertation ,

basically, i would like to know if my approach is correct. I will first  explain the setup of the experiment:

the study involves the response of 3 different types of mutants (Smiley SurprisedE,WT or Ty-2) for a specific gene in the lenght of the primary root of a plant species. The measurements of the root lenghts were done on 2 different days and on 3 different concentrations of Nitrate. Because we only need to compare the root lenghts of the mutant types within a specific day for a specific concentration, there is no need to search for differences between concentration or between days. On e.g. day 9, (NO3-) 1mM, the average root lenghts of the three mutants look like this:

naamloos.bmp

I thus thought i could do pairwise comparisons of the root lenghts of the mutants with independant t-tests (the root lenght of one mutant seedline is not affected by the measurements of those of the other mutant). Compare OE with WT, OE with Thy-2 and Wt with Thy-2 and putting the p-values on top of the bars with letters crowned with with asterixes . My first thought on this was to run an Anova (proc glm?) on the 3 mutants, but when upon reading articles, i find that they all only use pairwise comparisons using  independant t-tests so i guess i can do this? When using an Anova i would do a post-hoc and end up with pairwise comparisons using  t-tests anyway, is this a just assumption or should i use an anova despite of the articles doing otherwise?

For the t-test there is thus 1 independant categorical variable (mutant type) and 1 dependant continuous variable (root lenght) for each comparison to make.

is the following testing then correct?: for e.g. day 9, Nitrate concentration 1milliMolair(mM)

proc ttest data=thy2dag91mMthy2vsWT;

class expression;

var count;

run;

class because of the independant t-test, var lenght for testing equality of variances and the output gives me a qqplot where i can check for normality deviations (or should i do a proc univariate for testing normality) or mustn't I oblige to this assumtion if i find some of them are not normally distributed?

given the data:

data thy2dag91mMthy2vsWT; (the sample sizes for the two mutants are different in size due to some seeds not germinating)

input expression $ count;

cards;

thy-2 2.580

thy-2 3.296

thy-2 4.179

thy-2 4.298

thy-2 4.459

thy-2 2.986

thy-2 3.413

thy-2 4.419

thy-2 4.368

thy-2 3.849

thy-2 3.962

thy-2 3.718

thy-2 4.106

thy-2 4.456

thy-2 4.483

thy-2 4.345

thy-2 4.248

thy-2 4.311

thy-2 3.336

thy-2 3.720

thy-2 3.874

thy-2 3.030

thy-2 3.888

thy-2 4.492

thy-2 4.332

thy-2 4.231

thy-2 2.752

thy-2 4.567

thy-2 4.379

thy-2 4.807

thy-2 4.843

thy-2 3.791

thy-2 4.049

thy-2 2.950

thy-2 4.231

thy-2 4.141

thy-2 4.746

thy-2 4.463

thy-2 4.555

WT    3.885

WT    3.968

WT    3.259

WT    3.670

WT    3.572

WT    3.309

WT    3.803

WT    4.074

WT    3.991

WT    4.057

WT    3.786

WT    3.855

WT    3.635

WT    3.415

WT    3.462

WT    3.835

WT    3.976

WT    3.946

WT    3.567

WT    3.344

WT    3.630

WT    1.992

WT    3.605

WT    3.670

WT    3.837

WT    3.702

WT    3.784

WT    3.766

WT    1.884

WT    3.999

WT    3.937

WT    4.144

WT    3.537

WT    3.704

WT    3.657

WT    4.256

run;

kind regards,

Bas

Trusted Advisor
Posts: 1,913

Re: independant t-test, is this approach correct? Root lenght measurements comparison

Because we only need to compare the root lenghts of the mutant types within a specific day for a specific concentration, there is no need to search for differences between concentration or between days.

But yet these terms for concentration and day need to be included in the model somehow, so the model can account for the variability in the data caused by day and concentration, and not use this variability in determining the significance of root length differences.

After adding these terms into the model, you could do a PROC GLM or PROC MIXED (there are differences between these procedures) to test to see if the root lengths are different.

My first thought on this was to run an Anova (proc glm?) on the 3 mutants, but when upon reading articles, i find that they all only use pairwise comparisons using  independant t-tests so i guess i can do this?

I don't know what you were reading, but PROC GLM does not "only use pairwise comparisons". I specifically object to the word ONLY. PROC GLM provides a multitude of tests that may be appropriate here, including the overall ANOVA F-test which is not a pairwise test; and including pairwise comparison tests.

Thus, I can imagine a model that goes something like this (details are still subject to further clarification)

PROC GLM;

     class day expression concentration;

     model count=day concentration expression; /* Presence or absence of interactions is up to the modeler's discretion here */

     means expression/t lines; /* Options chosen here are up to the modeler's discretion */

run;

quit;

Respected Advisor
Posts: 2,655

Re: independant t-test, is this approach correct? Root lenght measurements comparison

This is a horribly inadequate analysis, and fails to account for correlated responses over time within a subject and to the different levels of nitrate applied.  If it is submitted for publication to any of the Agronomy journals that I am familiar with, it will be rejected.

Reformat the data to include nitrate level, day and subject.

Try the following then:

proc mixed data=newdata;

class day nitrate expression subjectid; /*This assumes that root length was measured on the same plant, or on similar plants in a plot */

model count=day|nitrate|expression;

repeated day/subject=subjectid;

lsmeans day|nitrate|expression;

slice day*nitrate*expression/sliceby=day*nitrate diff;

run;

The slice statement gives the extension of the t-test you propose, testing differences on each day at each nitrate level concentration.

There are still multiple testing, variance homogeneity, and distributional questions to be addressed, but this PROC MIXED approach will reflect the experimental design, and is a good start.

Steve Denham

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