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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

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
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are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
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what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
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I'm interested in nanotube
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what is nanomaterials​ and their applications of sensors.
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what is nano technology
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what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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good afternoon madam
AMJAD
what is system testing
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what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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anybody can imagine what will be happen after 100 years from now in nano tech world
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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Damian
silver nanoparticles could handle the job?
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not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
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I'm interested in Nanotube
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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