Hhinsch Week 8

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Part 1: Statistical Analysis Part 1

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.

  1. Create a new worksheet, naming it either "dHMO1_ANOVA" as appropriate.
  2. 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.
  3. At the top of the first column to the right of your data, create five column headers of the form dHMO1_AvgLogFC_(TIME) where (dHMO1) is your strain designation and (TIME) is 15, 30, etc.
  4. In the cell below the dHMO1_AvgLogFC_t15 header, type =AVERAGE(
  5. Then highlight all the data in row 2 associated with dHMO1 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 dHMO1_AvgLogFC_t120 calculation, create the column header dHMO1_ss_HO.
  10. In the first cell below this header, type =SUMSQ(
  11. Highlight all the LogFC data in row 2 for dHMO1 (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 dHMO1_ss_HO, create the column headers dHMO1_ss_(TIME) as in (3).
  13. Make a note of how many data points you have at each time point for your strain. For most of the strains, it will be 4, but for dHAP4 t90 or t120, it will be "3", and for the wild type it will be "4" or "5". Count carefully. Also, make a note of the total number of data points. Again, for most strains, this will be 20, but for example, dHAP4, this number will be 18, and for wt it should be 23 (double-check).
  14. In the first cell below the header dHMO1_ss_t15, type =SUMSQ(<range of cells for logFC_t15>)-COUNTA(<range of cells for logFC_t15>)*<AvgLogFC_t15>^2 and hit enter.
    • The COUNTA function counts the number of cells in the specified range that have data in them (i.e., does not count cells with missing values).
    • 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 dHMO1_ss_t120, create the column header dHMO1_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 dHMO1_Fstat and dHMO1_p-value.
  19. Recall the number of data points from (13): call that total n.
  20. In the first cell of the dHMO1_Fstat column, type =((n-5)/5)*(<dHMO1_ss_HO>-<dHMO1_SS_full>)/<dHMO1_SS_full> and hit enter.
    • Don't actually type the n but instead use the number from (13). Also note that "5" is the number of timepoints and the dSWI4 strain has 4 timepoints (it is missing t15).
    • Replace the phrase dHMO1_ss_HO with the cell designation.
    • Replace the phrase <dHMO1_SS_full> with the cell designation.
    • Copy to the whole column.
  21. In the first cell below the dHMO1_p-value header, type =FDIST(<dHMO1_Fstat>,5,n-5) replacing the phrase <dHMO1_Fstat> with the cell designation and the "n" as in (13) with the number of data points total. (Again, note that the number of timepoints is actually "4" for the dSWI4 strain). 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 dHMO1_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, dHMO1_Bonferroni_p-value.
  2. Type the equation =<dHMO1_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 dHMO1_Bonferroni_p-value header: =IF(dHMO1_Bonferroni_p-value>1,1,dHMO1_Bonferroni_p-value), where "dHMO1_Bonferroni_p-value" refers to the cell in which the first Bonferroni p value computation was made. 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 "dHMO1_ANOVA_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 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 dHMO1_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 "dHMO1_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.

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 dHMO1_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)?
      • 1092 genes have p < 0.05 and this is 17.64 percent of the genes.
    • How many genes have p < 0.01? and what is the percentage (out of 6189)?
      • 485 genes have p < 0.01 and this is 7.836 percent of the genes.
    • How many genes have p < 0.001? and what is the percentage (out of 6189)?
      • 144 genes have 0< 0.001 and this is 2.326 percent of the genes.
    • How many genes have p < 0.0001? and what is the percentage (out of 6189)?
      • 56 genes have p < 0.0001 and this is 0.904 percent of the genes.
  • 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)?
      • 24 genes are p < 0.05 for the Bonferonni-corrected p value and this is 0.387 percent of the genes.
    • How many genes are p < 0.05 for the Benjamini and Hochberg-corrected p value? and what is the percentage (out of 6189)?
      • 171 genes are p < 0.05 for the Benjamini and Hochberg-corrected p value and this is 2.762 percent of the genes.
  • 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 "dHMO1_AvgLogFC_(TIME)" in step 3 of the ANOVA analysis.
    • unadjusted p-value = 0.00873268
    • Bonferoni p-value = 1
    • B-H p-value = 0.11983753
    • The average Log fold changees are :
      • 15 = 2.165213447
      • 30 = 2.365281279
      • 60 = 2.162321897
      • 90 = -0.864707461
      • 120 = -0.068357851
      • NSR1 changes expression due to cold shock. We can see this because it is immediately increased then durastically decreases near the end of the timeframe.
  • For fun, find "BRO1" (from your web page) in the 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? Does your favorite gene change expression due to cold shock in this experiment?
    • unadjusted p-value = 0.623002056
    • Bonferoni p-value = 1
    • B-H p-value = 0.902354254
    • The average Log fold changes are :
      • 15 = 0.31136366
      • 30 = -0.9056212
      • 60 = -0.001991017
      • 90 = 0.022259535
      • 120 = -0.042916782
      • As you can see, the gene expression changed due to the cold shock. It should be noted that the gene expression changed only slightly, wavering just above and below zero.
  • 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. Upload your slide to the wiki.

Summary Paragraph

  • In summary, we learned how to utilize excel calculations in order to analyze the data. We found that as we performed different p-value calculations, the amount of the genes with a significant p-value changed. In regards to the p-value corrections, we found that not many of the genes changed expression as induced by the cold shock.

Electronic Notebook

  • I found it fairly easy to follow the steps from the Week 8 assignment. I copied the Week 8 assignment onto my page and corrected the steps, so one could follow the steps and come to the conclusions about dHMO1 that I came to. On the computer I was using it was a bit difficult to complete the sanity check. I simply sorted the genes instead of filtering them to fix this.

Acknowledgments

  1. I collaborated with Zachary Van Ysseldyk, Corinne Wong, and Arash Lari regarding the utilization of excel and the completion of the assignment.
  2. Dr. Dahlquist explained how to complete most of the calculations in class.
  3. While I worked with the people noted above, this individual journal entry was completed by me and not copied from another source. Hhinsch (talk) 22:49, 23 October 2017 (PDT)

References

  1. LMU BioDB 2017. (2017). Week 8. Retrieved October 19, 2017, from https://xmlpipedb.cs.lmu.edu/biodb/fall2017/index.php/Week_8

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