Trixie Anne Roque: Electronic Lab Notebook

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May 18, 2015 (Monday)

Purpose of Normalization

  • Gives us a basis
  • Plots that were made in R gives a graphical representation that we then want to convert
  • We want to "correct for dye bias"
  • Convert graphical images into numerical
  • Note: we want to think about what form the data is in; in this case, our data is continuous. Also, how many sets do we have: if more than 2, we use ANOVA.

Data & Observations

  • For Within-chip (ratios on each microarray) and Between-chip (ratios for a set of slides in an experiment) Normalization:
    • We ended up with 27 images.
  • Statistical Analysis:
    • We ended up with 477 replacements at the end.
  • For Within-Strain ANOVA:
    • Trixie and Tessa worked on dCIN5.
    • The number of total data points we had was n=20.
    • Of 6189 genes:
      • 1995(32.23%) have p < 0.05
      • 1157 genes (18.69%) have p < 0.01
      • 566 genes (9.14%) have p < 0.001
      • 280 genes (4.52%) have p < 0.0001
  • For Calculate the Benjamini & Hochberg p value Correction:
    • Of 6189 genes:
      • 109 genes (1.76%) have p < 0.05 for the Bonferroni-corrected p value
      • 1117 genes (18.05%) have p < 0.05 for the B-H corrected p value

A powerpoint slide with all the compiled data is located here.

  • NSR1 Sanity Check:
    • Unadjusted: 7.49666E-08
    • Bonferroni-corrected: 0.000463968
    • B-H-corrected: 3.8664E-05
    • Average Log fold change:
      • NSR1_AvgLogFC_t15: 4.046975
      • NSR1_AvgLogFC_t30: 3.39825
      • NSR1_AvgLogFC_t60: 4.2347
      • NSR1_AvgLogFC_t90: -2.8035
      • NSR1_AvgLogFC_t120: -0.948275

Steps for this session

Within-chip (ratios on each microarray) and Between-chip (ratios for a set of slides in an experiment) Normalization

  • A more detailed protocol can be found on this page. An abbreviated protocol is summarized below.

Installing R 3.1.0 and the limma package

The following protocol was developed to normalize GCAT and Ontario DNA microarray chip data from the Dahlquist lab using the R Statistical Software and the limma package (part of the Bioconductor Project).

  • The normalization procedure has been verified to work with version 3.1.0 of R released in April 2014 (link to download site) and and version 3.20.1 of the limma package ( direct link to download zipped file) on the Windows 7 platform.
    • Note that using other versions of R or the limma package might give different results.
    • Note also that using the 32-bit versus the 64-bit versions of R 3.1.0 will give different results for the normalization out in the 10-13 or 10-14 decimal place. The Dahlquist Lab is standardizing on using the 64-bit version of R.
  • To install R for the first time, download and run the installer from the link above, accepting the default installation.
  • To use the limma package, unzip the file and place the contents into a folder called "limma" in the library directory of the R program. If you accept the default location, that will be C:\Program Files\R\R-3.1.0\library (this will be different on the computers in S120 since you do not have administrator rights).

Running the Normalization Scripts

Within Array Normalization for the Ontario Chips
  • Launch R x64 3.1.0 (make sure you are using the 64-bit version).
  • Change the directory to the folder containing the targets file and the GPR files for the Ontario chips by selecting the menu item File > Change dir... and clicking on the appropriate directory. You will need to click on the + sign to drill down to the right directory. Once you have selected it, click OK.
  • In R, select the menu item File > Source R code..., and select the Ontario_Chip_Within-Array_Normalization_modified_20150514.R script.
    • You will be prompted by an Open dialog for the Ontario targets file. Select the file Ontario_Targets_wt-dCIN5-dGLN3-dHAP4-dHMO1-dSWI4-dZAP1-Spar_20150514.csv and click Open.
    • Wait while R processes your files.
Within Array Normalization for the GCAT Chips and Between Array Normalization for All Chips
  • These instructions assume that you have just completed the Within Array Normalization for the Ontario Chips in the section above.
  • In R, select the menu item File > Source R code..., and select the Within-Array_Normalization_GCAT_and_Merged_Ontario-GCAT_Between-Chip_Normalization_modified_20150514.R script.
    • You will be prompted by an Open dialog for the GCAT targets file. Select the file GCAT_Targets.csv and click Open.
    • Wait while R processes your files.
  • When the processing has finished, you will find two files called GCAT_and_Ontario_Within_Array_Normalization.csv and GCAT_and_Ontario_Final_Normalized_Data.csv in the same folder.
    • Save these files to LionShare and/or to a flash drive.

Visualizing the Normalized Data

Create MA Plots and Box Plots for the GCAT Chips

Input the following code, line by line, into the main R window. Press the enter key after each block of code. 

GCAT.GeneList<-RGG$genes$ID

lg<-log2((RGG$R-RGG$Rb)/(RGG$G-RGG$Gb))
  • If you get a message saying "NaNs produced" this is OK, proceed to the next step.
r0<-length(lg[1,])
rx<-tapply(lg[,1],as.factor(GCAT.GeneList),mean)
r1<-length(rx)
MM<-matrix(nrow=r1,ncol=r0)

for(i in 1:r0) {MM[,i]<-tapply(lg[,i],as.factor(GCAT.GeneList),mean)}

MC<-matrix(nrow=r1,ncol=r0)

for(i in 1:r0) {MC[,i]<-dw[i]*MM[,i]}

MCD<-as.data.frame(MC)
colnames(MCD)<-chips
rownames(MCD)<-gcatID

la<-(1/2*log2((RGG$R-RGG$Rb)*(RGG$G-RGG$Gb)))
  • If you get these Warning messages, it's OK:
1: In (RGG$R - RGG$Rb) * (RGG$G - RGG$Gb) :
NAs produced by integer overflow
2: NaNs produced
r2<-length(la[1,])
ri<-tapply(la[,1],as.factor(GCAT.GeneList),mean)
r3<-length(ri)
AG<-matrix(nrow=r3,ncol=r2)

for(i in 1:r2) {AG[,i]<-tapply(la[,i],as.factor(GCAT.GeneList),mean)}

par(mfrow=c(3,3))

for(i in 1:r2) {plot(AG[,i],MC[,i],main=chips[i],xlab='A',ylab='M',ylim=c(-5,5),xlim=c(0,15))}
browser()
  • Maximize the window in which the graphs have appeared. Save the graphs as a JPEG (File>Save As>JPEG>100% quality...). Once the graphs have been saved, close the window. To continue with the rest of the code, type the letter "c" and press Enter
x0<-tapply(MAG$A[,1],as.factor(MAG$genes$ID),mean)
y0<-length(MAG$A[1,])
x1<-length(x0)
AAG<-matrix(nrow=x1,ncol=y0)

for(i in 1:y0) {AAG[,i]<-tapply(MAG$A[,i],as.factor(MAG$genes$ID),mean)}

par(mfrow=c(3,3))

for(i in 1:y0) {plot(AAG[,i],MG2[,i],main=chips[i],xlab='A',ylab='M',ylim=c(-5,5),xlim=c(0,15))}
browser()
  • Maximize the window in which the graphs have appeared. Save the graphs as a JPEG (File>Save As>JPEG>100% quality...). Once the graphs have been saved, close the window. To continue with the rest of the code, type the letter "c" and press Enter.
par(mfrow=c(1,3))

boxplot(MCD,main="Before Normalization",ylab='Log Fold Change',ylim=c(-5,5),xaxt='n')

axis(1,at=xy.coords(chips)$x,tick=TRUE,labels=FALSE)

text(xy.coords(chips)$x-1,par('usr')[3]-0.6,labels=chips,srt=45,cex=0.9,xpd=TRUE)

boxplot(MG2,main='After Within Array Normalization',ylab='Log Fold Change',ylim=c(-5,5),xaxt='n')

axis(1,at=xy.coords(chips)$x,labels=FALSE)

text(xy.coords(chips)$x-1,par('usr')[3]-0.6,labels=chips,srt=45,cex=0.9,xpd=TRUE)

boxplot(MAD[,Gtop$MasterList],main='After Between Array Normalization',ylab='Log Fold Change',ylim=c(-5,5),xaxt='n')

axis(1, at=xy.coords(chips)$x,labels=FALSE)

text(xy.coords(chips)$x-1,par('usr')[3]-0.6,labels=chips,srt=45,cex=0.9,xpd=TRUE)
  • Maximize the window in which the plots have appeared. You may not want to actually maximize them because you might lose the labels on the x axis, but make them as large as you can. Save the plots as a JPEG (File>Save As>JPEG>100% quality...). Once the graphs have been saved, close the window.
Create MA Plots and Box Plots for the Ontario Chips

Input the following code, line by line, into the main R window. Press the enter key after each block of code. 

Ontario.GeneList<-RGO$genes$Name

lr<-log2((RGO$R-RGO$Rb)/(RGO$G-RGO$Gb))
  • Warning message: "NaNs produced" is OK.
z0<-length(lr[1,])
v0<-tapply(lr[,1],as.factor(Ontario.GeneList),mean)
z1<-length(v0)
MT<-matrix(nrow=z1,ncol=z0)

for(i in 1:z0) {MT[,i]<-tapply(lr[,i],as.factor(Ontario.GeneList),mean)}

MI<-matrix(nrow=z1,ncol=z0)

for(i in 1:z0) {MI[,i]<-ds[i]*MT[,i]}

MID<-as.data.frame(MI)
colnames(MID)<-headers
rownames(MID)<-ontID

ln<-(1/2*log2((RGO$R-RGO$Rb)*(RGO$G-RGO$Gb)))
  • Warning messages are OK:
1: In (RGO$R - RGO$Rb) * (RGO$G - RGO$Gb) :
NAs produced by integer overflow
2: NaNs produced
z2<-length(ln[1,])
zi<-tapply(ln[,1],as.factor(Ontario.GeneList),mean)
z3<-length(zi)
AO<-matrix(nrow=z3,ncol=z2)

for(i in 1:z0) {AO[,i]<-tapply(ln[,i],as.factor(Ontario.GeneList),mean)}

strains<-c('wt','dCIN5','dGLN3','dHAP4','dHMO1','dSWI4','dZAP1','Spar')
  • After entering the call browser() below, maximize the window in which the graphs have appeared. Save the graphs as a JPEG (File>Save As>JPEG>100% quality...). Once the graphs have been saved, close the window and press Enter for the next set of graphs to appear.
for (i in 1:length(strains)) {
  st<-strains[i]
  lt<-which(Otargets$Strain %in% st)
  if (st=='wt') {
      par(mfrow=c(3,5))
  } else {
      par(mfrow=c(4,5))
  }
  for (i in lt) {
    plot(AO[,i],MI[,i],main=headers[i],xlab="A",ylab="M",ylim=c(-5,5),xlim=c(0,15))
  }
  browser()
}
  • To continue generating plots, type the letter c and press enter.
j0<-tapply(MAO$A[,1],as.factor(MAO$genes[,5]),mean)
k0<-length(MAO$A[1,])
j1<-length(j0)
AAO<-matrix(nrow=j1,ncol=k0)

for(i in 1:k0) {AAO[,i]<-tapply(MAO$A[,i],as.factor(MAO$genes[,5]),mean)}
  • Remember, that after entering the call readline('Press Enter to continue'), maximize the window in which the graphs have appeared. Save the graphs as a JPEG (File>Save As>JPEG>100% quality...). Once the graphs have been saved, close the window and press Enter for the next set of graphs to appear.
for (i in 1:length(strains)) {
  st<-strains[i]
  lt<-which(Otargets$Strain %in% st)
  if (st=='wt') {
      par(mfrow=c(3,5))
  } else {
      par(mfrow=c(4,5))
  }
  for (i in lt) {
    plot(AAO[,i],MD2[,i],main=headers[i],xlab="A",ylab="M",ylim=c(-5,5),xlim=c(0,15))
  }
  browser()
}
  • To continue generating plots, type the letter c and press enter.
for (i in 1:length(strains)) {
  par(mfrow=c(1,3))
  st<-strains[i]
  lt<-which(Otargets$Strain %in% st)
  if (st=='wt') {
      xcoord<-xy.coords(lt)$x-1
      fsize<-0.9
  } else {
      xcoord<-xy.coords(lt)$x-1.7
      fsize<-0.8
  }
  boxplot(MID[,lt],main='Before Normalization',ylab='Log Fold Change',ylim=c(-5,5),xaxt='n')
  axis(1,at=xy.coords(lt)$x,labels=FALSE)
  text(xcoord,par('usr')[3]-0.65,labels=headers[lt],srt=45,cex=fsize,xpd=TRUE)
  boxplot(MD2[,lt],main='After Within Array Normalization',ylab='Log Fold Change',ylim=c(-5,5),xaxt='n')
  axis(1,at=xy.coords(lt)$x,labels=FALSE)
  text(xcoord,par('usr')[3]-0.65,labels=headers[lt],srt=45,cex=fsize,xpd=TRUE)
  ft<-Otargets$MasterList[which(Otargets$Strain %in% st)]
  boxplot(MAD[,ft],main='After Between Array Normalization',ylab='Log Fold Change',ylim=c(-5,5),xaxt='n')
  axis(1,at=xy.coords(lt)$x,labels=FALSE)
  text(xcoord,par('usr')[3]-0.65,labels=headers[lt],srt=45,cex=fsize,xpd=TRUE)
  browser()
}
  • To continue generating plots, type the letter c and press enter.
  • Warnings are OK.
  • Zip the files of the plots together and upload to LionShare and/or save to a flash drive.

Statistical Analysis

  • For the statistical analysis, we will begin with the file "GCAT_and_Ontario_Final_Normalized_Data.csv" that you generated in the previous step.
  • Open this file in Excel and Save As an Excel Workbook *.xlsx. It is a good idea to add your initials and the date (yyyymmdd) to the filename as well.
  • Rename the worksheet with the data "Compiled_Normalized_Data".
    • Type the header "ID" in cell A1.
    • Insert a new column after column A and name it "Standard Name". Column B will contain the common names for the genes on the microarray.
      • Copy the entire column of IDs from Column A.
      • Paste the names into the "Value" field of the ORF List <-> Gene List tool in YEASTRACT. Then, click on the "Transform" button.
      • Select all of the names in the "Gene Name" column of the resulting table.
      • Copy and paste these names into column B of the *.xlsx file. Save your work.
    • Insert a new column on the very left and name it "MasterIndex". We will create a numerical index of genes so that we can always sort them back into the same order.
      • Type a "1" in cell A2 and a "2" in cell A3.
      • Select both cells. Hover your mouse over the bottom-right corner of the selection until it makes a thin black + sign. Double-click on the + sign to fill the entire column with a series of numbers from 1 to 6189 (the number of genes on the microarray).
  • Insert a new worksheet and call it "Rounded_Normalized_Data". We are going to round the normalization results to four decimal places because of slight variations seen in different runs of the normalization script.
    • Copy the first three columns of the "Compiled_Normalized_Data" sheet and paste it into the first three columns of the "Rounded_Normalized_Data" sheet.
    • Copy the first row of the "Compiled_Normalized_Data" sheet and paste it into the first row of the "Rounded_Normalized_Data" sheet.
    • In cell C2, type the equation =ROUND(Compiled_Normalized_Data!C2,4).
    • Copy and paste this equation in the rest of the cells of row 2.
    • Select all of the cells of row 2 and hover your mouse over the bottom right corner of the selection. When the cursor changes to a thin black "plus" sign, double-click on it to paste the equation to all the rows in the worksheet. Save your work.
  • Insert a new worksheet and call it "Master_Sheet".
    • Go back to the "Rounded_Normalized_Data" sheet and Select All and Copy.
    • Click on cell A1 of the "Master_Sheet" worksheet. Select Paste special > Paste values to paste the values, but not the formulas from the previous sheet. Save your work.
    • There will be some #VALUE! errors in cells where there was missing data for genes that existed on the Ontario chips, but not the GCAT chips.
      • Select the menu item Find/Replace and Find all cells with "#VALUE!" and replace them with a single space character. Record how many replacements were made to your electronic lab notebook. Save your work.
  • This will be the starting point for our statistical analysis below.

Within-strain ANOVA

  • The purpose of the witin-stain ANOVA test is to determine if any genes had a gene expression change that was significantly different than zero at any timepoint.
  • Each student in the lab group will be assigned one strain to analyze from this point forward.
    • Anu/Natalie: wt
    • Grace/Monica Δhap4
    • Kevin M./Nicole Δgln3
    • Kevin W./KD Δswi4
    • Tessa/Trixie Δcin5
  1. Create a new worksheet, naming it either "dCIN5_ANOVA" as appropriate. For example, you might call yours "wt_ANOVA" or "dHAP4_ANOVA"
  2. Copy all of the data from the "Master_Sheet" worksheet for your strain and paste it into your new worksheet.
  3. At the top of the first column to the right of your data, create five column headers of the form dCIN5_AvgLogFC_(TIME) where dCIN5 is your strain designation and (TIME) is 15, 30, etc.
  4. In the cell below the dCIN5_AvgLogFC_t15 header, type =AVERAGE(
  5. Then highlight all the data in row 2 associated with dCIN5 and t15, press the closing paren key (shift 0),and press the "enter" key.
  6. This cell now contains the average of the log fold change data from the first gene at t=15 minutes.
  7. Click on this cell and position your cursor at the bottom right corner. You should see your cursor change to a thin black plus sign (not a chubby white one). When it does, double click, and the formula will magically be copied to the entire column of 6188 other genes.
  8. Repeat steps (4) through (8) with the t30, t60, t90, and the t120 data.
  9. Now in the first empty column to the right of the dCIN5_AvgLogFC_t120 calculation, create the column header dCIN5_ss_HO.
  10. In the first cell below this header, type =SUMSQ(
  11. Highlight all the LogFC data in row 2 for your dCIN5 (but not the AvgLogFC), press the closing paren key (shift 0),and press the "enter" key.
  12. In the next empty column to the right of dCIN5_ss_HO, create the column headers dCIN5_ss_(TIME) as in (3).
  13. Make a note of how many data points you have at each time point for your strain. For dHAP4, it will be "3", but for the wild type it will be "4" or "5". Count carefully. Also, make a note of the total number of data points. For dHAP4, this number will be 15, but for wt it should be 23 (double-check).
  14. In the first cell below the header dCIN5_ss_t15, type =SUMSQ(<range of cells for logFC_t15>)-<number of data points>*<AvgLogFC_t15>^2 and hit enter.
    • The phrase <range of cells for logFC_t15> should be replaced by the data range associated with t15.
    • The phrase <number of data points> should be replaced by the number of data points for that timepoint (either 3, 4, or 5).
    • The phrase <AvgLogFC_t15> should be replaced by the cell number in which you computed the AvgLogFC for t15, and the "^2" squares that value.
    • Upon completion of this single computation, use the Step (7) trick to copy the formula throughout the column.
  15. Repeat this computation for the t30 through t120 data points. Again, be sure to get the data for each time point, type the right number of data points, and get the average from the appropriate cell for each time point, and copy the formula to the whole column for each computation.
  16. In the first column to the right of dCIN5_ss_t120, create the column header dCIN5_SS_full.
  17. In the first row below this header, type =sum(<range of cells containing "ss" for each timepoint>) and hit enter.
  18. In the next two columns to the right, create the headers dCIN5_Fstat and dCIN5_p-value.
  19. Recall the number of data points from (13): call that total n.
  20. In the first cell of the dCIN5_Fstat column, type =((n-5)/5)*(<dCIN5_ss_HO>-<dCIN5_SS_full>)/<dCIN5_SS_full> and hit enter.
    • Don't actually type the n but instead use the number from (13).
    • Replace the phrase dCIN5_ss_HO with the cell designation.
    • Replace the phrase <dCIN5_SS_full> with the cell designation.
    • Copy to the whole column.
  21. In the first cell below the dCIN5_p-value header, type =FDIST(<dCIN5_Fstat>,5,n-5) replacing the phrase <dCIN5_Fstat> with the cell designation and the "n" as in (13) with the number of data points total. Copy to the whole column.
  22. Before we move on to the next step, we will perform a quick sanity check to see if we did all of these computations correctly.
    • Click on cell A1 and click on the Data tab. Select the Filter icon (looks like a funnel). Little drop-down arrows should appear at the top of each column. This will enable us to filter the data according to criteria we set.
    • Click on the drop-down arrow on your dCIN5_p-value column. Select "Number Filters". In the window that appears, set a criterion that will filter your data so that the p value has to be less than 0.05.
    • Excel will now only display the rows that correspond to data meeting that filtering criterion. A number will appear in the lower left hand corner of the window giving you the number of rows that meet that criterion. We will check our results with each other to make sure that the computations were performed correctly.
Calculate the Bonferroni and p value Correction
  1. Now we will perform adjustments to the p value to correct for the multiple testing problem. Label the next two columns to the right with the same label, dCIN5_Bonferroni_p-value.
  2. Type the equation =<dCIN5_p-value>*6189, Upon completion of this single computation, use the Step (10) trick to copy the formula throughout the column.
  3. Replace any corrected p value that is greater than 1 by the number 1 by typing the following formula into the first cell below the second dCIN5_Bonferroni_p-value header: =IF(r2>1,1,r2). Use the Step (10) trick to copy the formula throughout the column.
Calculate the Benjamini & Hochberg p value Correction
  1. Insert a new worksheet named "dCIN5_B&H".
  2. Copy and paste the "MasterIndex", "ID", and "Standard Name" columns from your previous worksheet into the first two columns of the new worksheet.
  3. For the following, use Paste special > Paste values. Copy your unadjusted p values from your ANOVA worksheet and paste it into Column D.
  4. Select all of columns A, B, C, and D. Sort by ascending values on Column D. Click the sort button from A to Z on the toolbar, in the window that appears, sort by column C, smallest to largest.
  5. Type the header "Rank" in cell E1. We will create a series of numbers in ascending order from 1 to 6189 in this column. This is the p value rank, smallest to largest. Type "1" into cell E2 and "2" into cell E3. Select both cells E2 and E3. Double-click on the plus sign on the lower right-hand corner of your selection to fill the column with a series of numbers from 1 to 6189.
  6. Now you can calculate the Benjamini and Hochberg p value correction. Type dCIN5_B-H_p-value in cell F1. Type the following formula in cell F2: =(D2*6189)/E2 and press enter. Copy that equation to the entire column.
  7. Type "STRAIN_B-H_p-value" into cell G1.
  8. Type the following formula into cell G2: =IF(F2>1,1,F2) and press enter. Copy that equation to the entire column.
  9. Select columns A through G. Now sort them by your MasterIndex in Column A in ascending order.
  10. Copy column G and use Paste special > Paste values to paste it into the next column on the right of your ANOVA sheet.
  • Upload the .xlsx file that you have just created to LionShare. Send Dr. Dahlquist an e-mail with the link to the file (e-mail kdahlquist at lmu dot edu).
Sanity Check: Number of genes significantly changed

Before we move on to further analysis of the data, we want to perform a more extensive sanity check to make sure that we performed our data analysis correctly. We are going to find out the number of genes that are significantly changed at various p value cut-offs.

  • Go to your dCIN5_ANOVA worksheet.
  • Select row 1 (the row with your column headers) and select the menu item Data > Filter > Autofilter (The funnel icon on the Data tab). Little drop-down arrows should appear at the top of each column. This will enable us to filter the data according to criteria we set.
  • Click on the drop-down arrow for the unadjusted p value. Set a criterion that will filter your data so that the p value has to be less than 0.05.
    • How many genes have p < 0.05? and what is the percentage (out of 6189)?
    • How many genes have p < 0.01? and what is the percentage (out of 6189)?
    • How many genes have p < 0.001? and what is the percentage (out of 6189)?
    • How many genes have p < 0.0001? and what is the percentage (out of 6189)?
  • When we use a p value cut-off of p < 0.05, what we are saying is that you would have seen a gene expression change that deviates this far from zero by chance less than 5% of the time.
  • We have just performed 6189 hypothesis tests. Another way to state what we are seeing with p < 0.05 is that we would expect to see this a gene expression change for at least one of the timepoints by chance in about 5% of our tests, or 309 times. Since we have more than 309 genes that pass this cut off, we know that some genes are significantly changed. However, we don't know which ones. To apply a more stringent criterion to our p values, we performed the Bonferroni and Benjamini and Hochberg corrections to these unadjusted p values. The Bonferroni correction is very stringent. The Benjamini-Hochberg correction is less stringent. To see this relationship, filter your data to determine the following:
    • How many genes are p < 0.05 for the Bonferroni-corrected p value? and what is the percentage (out of 6189)?
    • How many genes are p < 0.05 for the Benjamini and Hochberg-corrected p value? and what is the percentage (out of 6189)?
  • In summary, the p value cut-off should not be thought of as some magical number at which data becomes "significant". Instead, it is a moveable confidence level. If we want to be very confident of our data, use a small p value cut-off. If we are OK with being less confident about a gene expression change and want to include more genes in our analysis, we can use a larger p value cut-off.
  • Comparing results with known data: the expression of the gene NSR1 (ID: YGR159C)is known to be induced by cold shock. Find NSR1 in your dataset. What is its unadjusted, Bonferroni-corrected, and B-H-corrected p values? What is its average Log fold change at each of the timepoints in the experiment? Note that the average Log fold change is what we called "STRAIN)_AvgLogFC_(TIME)" in step 3 of the ANOVA analysis.
  • We will compare the numbers we get between the wild type strain and the other strains studied, organized as a table. Use this sample PowerPoint slide to see how your table should be formatted.
Bonferroni Correction
  • We need to perform the Bonferroni correction to each p value similar to what we did for the within-strain ANOVA.

Benjamini & Hochberg Correction

  • We need to perform the Benjamini & Hochberg correction to each p value similar to what we did for the within-strain ANOVA.

May 19, 2015 (Tuesday)

Data and Observations

  • dCIN5 T-Test total p-values for each timepoint:
    • t15: 1393
    • t30: 756
    • t60: 1250
    • t90: 634
    • t120: 351

A compiled list of p-values is in here

T Test

Modified t test for each timepoint

In the analysis yesterday (May 18), we performed an ANOVA to determine if any genes had a gene expression change that was significantly different than zero at any timepoint. Now we will perform a modified t test to determine if any genes had a gene expression change that was significantly different than zero at each timepoint. We performed our analysis on the same strain as before, dCIN5, adding these calculations to the same Excel workbook.

  • Insert a new worksheet into the Excel workbook and name it "dCIN5_ttest", e.g., "wt_ttest" or "dHAP4_ttest".
  • Go back to the "Master_Sheet" worksheet for your strain. Copy the first three columns containing the "MasterIndex", "ID", and "Standard Name" from the "Master_Sheet" worksheet for your strain and paste it into your new worksheet. Copy the columns containing the data for your strain and paste it into your new worksheet.
  • Go to the empty columns to the right on your worksheet. Create new column headings in the top cells to label the average log fold changes that you will compute. Name them with the pattern <dHAP4>_<AvgLogFC>_<tx> where you use the appropriate text within the <> and where x is the time. For example, "dHAP4_AvgLogFC_t15".
  • Compute the average log fold change for the replicates for each timepoint by typing the equation:
=AVERAGE(range of cells in the row for that timepoint)

into the second cell below the column heading. For example, your equation might read 

=AVERAGE(C2:F2)

Copy this equation and paste it into the rest of the column.

  • Create the equation for the rest of the timepoints and paste it into their respective columns. Note that you can save yourself some time by completing the first equation for all of the averages and then copy and paste all the columns at once.
  • Go to the empty columns to the right on your worksheet. Create new column headings in the top cells to label the T statistic that you will compute. Name them with the pattern <dHAP4>_<Tstat>_<tx> where you use the appropriate text within the <> and where x is the time. For example, "dHAP4_Tstat_t15". You will now compute a T statistic that tells you whether the normalized average log fold change is significantly different than 0 (no change in expression). Enter the equation into the second cell below the column heading:
=AVERAGE(range of cells)/(STDEV(range of cells)/SQRT(number of replicates))

For example, your equation might read: 

=AVERAGE(C2:F2)/(STDEV(C2:F2)/SQRT(4))

(NOTE: in this case the number of replicates is 4. Be careful that you are using the correct number of parentheses.) Copy the equation and paste it into all rows in that column. Create the equation for the rest of the timepoints and paste it into their respective columns. Note that you can save yourself some time by completing the first equation for all of the T statistics and then copy and paste all the columns at once.

  • Go to the empty columns to the right on your worksheet. Create new column headings in the top cells to label the P value that you will compute. Name them with the pattern <dHAP4>_<Pval>_<tx> where you use the appropriate text within the <> and where x is the time. For example, "dHAP4_Pval_t15". In the cell below the label, enter the equation:
=TDIST(ABS(cell containing T statistic),degrees of freedom,2)

For example, your equation might read: 

=TDIST(ABS(AE2),3,2)

The number of degrees of freedom is the number of replicates minus one. Copy the equation and paste it into all rows in that column.

  • As with the ANOVA, we encounter the multiple testing problem here as well.

Bonferroni Correction

  1. Now we will perform adjustments to the p value to correct for the multiple testing problem. Label the columns to the right with the label, dCIN5_Bonferroni-Pval_tx (do this twice in a row).
  2. Type the equation =<dCIN5_Pval_tx>*6189, Upon completion of this single computation, use the trick to copy the formula throughout the column.
  3. Replace any corrected p value that is greater than 1 by the number 1 by typing the following formula into the first cell below the second dCIN5_Bonferroni-Pval_tx header: =IF(r2>1,1,r2). Use the trick to copy the formula throughout the column.

Benjamini & Hochberg Correction

  1. Insert a new worksheet named "dCIN5_ttest_B-H". You will need to perform the procedure below for the p values for each timepoint. Do them individually one at a time to avoid confusion.
  2. Copy and paste the "MasterIndex", "ID", and "Standard Name" columns from your previous worksheet into the first two columns of the new worksheet.
  3. For the following, use Paste special > Paste values. Copy your unadjusted p values from the first timepoint from your ttest worksheet and paste it into Column D.
  4. Select all of columns A, B, C, and D. Sort by ascending values on Column D. Click the sort button from A to Z on the toolbar, in the window that appears, sort by column D, smallest to largest.
  5. Type the header "Rank" in cell E1. We will create a series of numbers in ascending order from 1 to 6189 in this column. This is the p value rank, smallest to largest. Type "1" into cell E2 and "2" into cell E3. Select both cells E2 and E3. Double-click on the plus sign on the lower right-hand corner of your selection to fill the column with a series of numbers from 1 to 6189.
  6. Now you can calculate the Benjamini and Hochberg p value correction. Type dCIN5_B-H_Pval_tx in cell F1. Type the following formula in cell F2: =(D2*6189)/E2 and press enter. Copy that equation to the entire column.
  7. Type "STRAIN_B-H_Pval_tx" into cell G1.
  8. Type the following formula into cell G2: =IF(F2>1,1,F2) and press enter. Copy that equation to the entire column.
  9. Select columns A through G. Now sort them by your MasterIndex in Column A in ascending order.
  10. Copy column G and use Paste special > Paste values to paste it into the next column on the right of your ttest sheet.
  • Upload the .xlsx file that you have just created to LionShare. Note that when you upload your file, you should check the box to "Overwrite file if it already exists." This will then replace your previous version of your file with the updated one containing today's calculations. Send Dr. Dahlquist an e-mail with the link to the file (e-mail kdahlquist at lmu dot edu).

Sanity Check

  • We will also perform the "sanity check" as follows:
    • Determine how many genes have a p value < 0.05 at each timepoint.
    • Keeping the "Pval" filter at p < 0.05, How many have an average log fold change of > 0.25 and p < 0.05 at each timepoint? How many have an average log fold change of < -0.25 and p < 0.05 at each timepoint? (These log fold change cut-offs represent about a 20% fold change in expression.)
    • How many genes have B&H corrected p < 0.05?
    • How many genes have a Bonferroni corrected p < 0.05?
    • Use this sample PowerPoint slide to see how your table should be formatted.
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