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The mean of each vector will be equal to:

The standard deviation of each vector will be equal to:

The standard error of each vector will be equal to:

The formula for the t test is as follows:

The t-test is used to test the difference between the means of two test sets, as in before and after studies or matched-pairs studies.There is a confidence interval for the mean and a critical value for t for the chosen level of significance associated with the t-test. For instance, a level of significance equal to0.05 means that 95% of the cases will be within the confidence range if there is no significant difference between the means of the two test sets, or experiments,being compared. The confidence limits set upper and lower bounds on an estimate of the mean for the chosen level of significance (0.05). The confidence interval is therange within the bounds of the confidence limits. The confidence interval can be computed, if you know the shape of your distribution. For normally distributed data, theconfidence limits at the 0.05 significance level for an estimated mean are the sample mean plus or minus 1.96 times thestandard error.

confidence interval (normal distribution): mean +/- 1.96 * SE

For example, if the sample mean is 10 and the standard error is 1.2, then 95% of the cases will be within the range of 10 plus or minus 1.96 times 1.2,or 10 plus or minus 2.4, which is the range from 7.6 to 12.4. Thus, if the experimental mean is outside the limits of this range computed for the reference mean, then the differencebetween the means of the two test sets is considered to be significant within a probability of 95%. The critical value for t at a given significance level fora specific type of distribution can be looked up in a table; most statistics books contain them. In the case of microarray data, if the absolute value of tis greater than the critical value, this indicates a significant difference in the gene expression between the reference and experimental test sets.Because the t-test is a parametric test that assumes a normal distribution, the statistical tests that are commonly used to analyze microarray data are more complexvariations that are used for distributions other than normal distributions.

Tutorial data set
red:green ratio red:green ratio red:green ratio red:green ratio red:green ratio red:green ratio red:green ratio
Gene measurement 1 measurement 2 measurement 3 measurement 4 measurement 5 measurement 6 measurement 7
A(ref) 0.97 1.54 1.32 0.89 1.06 1.21
A(exp) 1.37 1.25 1.15 0.99 1.30 1.53 1.07
B(ref) 1.67 1.78 2.01 1.89 1.75 1.81 1.69
B(exp) 6.21 6.03 5.94 6.14 6.11

Assumptions for example problem:

  • Use the example data set to perform a t-test analysis.
  • Consider each row of the table a separate test set under either experimental or reference conditions.
  • Assume a normal distribution.
  • Choose 0.05 as the level of significance.
  • Compute answers to the second decimal place.
  • Assume the critical value for t is equal to an absolute value of t greater than 2.37.

What are the means for each row of data?

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What are the standard deviations for each row of data?

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What is the standard error for each row of data?

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What is the value for t for the comparison between the reference and experimental test sets for Gene A?

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What is the 95% confidence interval computed for the Gene A reference set?

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Is there a significant difference between the mean values of the experimental versus the reference set for Gene A? (Explain the answer both in terms of the t value and the confidence interval.)

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What is the value for t for the comparison between the reference and experimental test sets for Gene B?

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What is the 95% confidence interval computed for the Gene B reference set?

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Is there a significant difference between the mean values of the experimental versus the reference set for Gene B? (Explainthe answer both in terms of the t value and the confidence interval.)

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If there was a significant difference between the gene expressionunder experimental conditions versus the gene expression under reference conditions for either Gene A or Gene B, then estimate the significant increaseor decrease observed.

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There are many software packages available that have been designed expressly for microarray data analysis. In addition to testing gene expression under aset of experimental conditions versus reference conditions, it is possible to identified "clustered" genes that seem to have similar responses under similarconditions. Also, genes can be identified that show related responses under similar conditions, such as one gene's expression always increases whenanother's decreases. When two or more genes show this kind of clustered behavior, it can be an indication that they are part of the same pathway,or that they are regulating each other. Using this type of microarray data analysis, the scientist can combine the cluster analysis results with what is known through laboratory experiments and often come up with new hypotheses about biochemical pathways and regulation.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Bios 533 bioinformatics. OpenStax CNX. Sep 24, 2008 Download for free at http://cnx.org/content/col10152/1.16
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