Module 4 (Effect of Alcohol on Worms): Data Analysis Michael Dunn Capuchino High School Introduction In this exercise, you will first process the timelapse data you collected. Then, you will cull (remove) the aberrant data that you identified in the previous exercise. Finally, you will assess the statistical significance of your results. You will use the program Microsoft Excel to aid you in calculating the velocity of each worm and in determining the statistical significance of your results. However, it is important to understand the meaning of these values and how they are derived. What is the formula for velocity? What values were used to make that calculation in this laboratory? What is a mean and why is this value important to your experiment? What is a standard deviation and what does it tell you about your data? Is a velocity of zero an indication that the value should be culled from the data set? Once you have calculated the velocity at which worms in both populations were moving, you must determine whether or not one population was moving at a statistically different velocity than the other. Since the worms may not have qualitatively been moving differently enough for your eyes to discern, a statistical test, such as a t-test, will help you determine whether or not the two populations are statistically different. The formula for calculating the t value is: signal difference between means x 1 x 2 t = --------- = ------------------------------------- = ------------------- noise sqrt(variance / sample size) s 1 s 2 + n 1 n 2 _ where x = sample mean velocity s = standard deviation of the sample n = sample size A null hypothesis must be made in any statistical comparison. It predicts that there is no statistical difference between the values being compared. What is the null hypothesis in this experiment? Express this hypothesis symbolically using variables from above. The alternative hypothesis predicts that there is a difference between the data being compared. What is your alternative hypothesis for this experiment? Express this hypothesis symbolically using variables from above. At the end of the experiment you will either accept or reject the null hypothesis based on the values your data yields. To better understand the t-test, consider the values in the formula above. What happens to the t value if the difference between the means is large? Does the t value increase or decrease as the n values increases? How does the t value change in relation to changing variance of the samples? The larger the t value, the more likely the null hypothesis will be rejected. Do your preceding conclusions make sense? Introduction (Student Guide) Page 7-9S
Once a t-value is calculated, you would normally compare this value to the values in a standard table of significance, taking into account sample size (expressed as degrees of freedom) and p-value (the chance that the data yields a statistical difference between the samples just by chance). Usually, a p-value less than 0.05 is considered significant. What does p = 0.05 mean? In this exercise, the Microsoft Excel program will perform these calculations and comparisons for you. Now that you understand this statistical analysis, follow the procedure to analyze your data. Introduction (Student Guide) Page 7-10S
1. In your control folder, find the control trackresults file you created in ImageJ. Open the file in Microsoft Excel. Each tracked object should have 3 columns called frame, x, and y. These are the x and y coordinates of the object in each frame of the video. 2. Below the XY coordinate data, another set of data is organized into 4 columns: Column A: Track = the label assigned to each object tracked Column B: Length = the total distance traveled by the object during the video (includes backtracking) Column C: Distance traveled = the net distance traveled Column D: Number of Frames = the number of frames the worm was tracked Data Analysis 3. Right click on the tab in the lower left and select Rename. Rename your data sheet Control Raw Data. 4. Add the title Velocity to Column E. 5. The formula for velocity is distance divided by time. In this case, distance is measured as length and time is measured as the number of frames that have elapsed. Therefore, velocity or speed = Length/Nr. Frames. Click inside the first cell in column E beneath the heading Velocity, (in the example above, this would be cell E2). Type = followed by the 1 st cell in B / 1 st cell in D. In this example, this would be =B2/D2. Then click Enter. Lab Exercise (Student Guide) Page 7-11S
6. To calculate the remaining velocities, highlight all of column E, starting with the 1 st cell with data and ending with the last cell with data (in this example, E2-E14). 7. While the data is highlighted, click Ctrl+d, and Excel will calculate the rest of the velocities using the same formula as found in cell E68. 8. You can now calculate the average velocity by selecting the first empty cell beneath the last velocity data entry. In this example, the average velocity will be calculated in cell E15. Click on the Auto Sum symbol in the formula menu at the top. 9. Click on Average. A generic formula will appear in the cell. Make sure that all of your velocities are within the highlighted portion. Note that E2:E14 are in parentheses. This means that the first data point to be used is found in cell E2, and the last is in cell E14. Excel will calculate the average of all the numbers from cell E2 through cell E14. If all of your velocities, for some reason, are not included in the highlighted area, simply correct the values in the parentheses to include all of your velocities) When ready, click Enter, and the average of your velocities will be calculated. Lab Exercise (Student Guide) Page 7-12S
10. Select the cell to the left of the average you just generated, and type, Avg. Below that, type St Dev. 11. To calculate the standard deviation, select the cell just below your average velocity. In this example, this is cell E16. Click the arrow at the bottom of the Auto Sum button. A window will open with several choices. At the bottom of the window it should say More Functions. Click on this. STDEV should be near the top of the list. Select this option. 12. The window indicates that Excel is ready to calculate the standard deviation of all the numbers in cells E2 through E15. However, E15 is the average, which we do not wish to include in this calculation. What we really need is the standard deviation of cells E2 through E14. Change the second number in the data range to exclude the average velocity. In this example, E15 is changed to E14. Click Ok. 13. Repeat steps 1-12 for the alcohol-treated worms. 14. If you listed any objects in the Not Worms column of your control data, you will need to cull (remove) the data from the spreadsheet. Do NOT delete the data. First, click on the triangle in the upper left corner of your Excel worksheet (between the A and the 1). This should highlight the entire worksheet. Right click and copy the worksheet ( command C on a Mac). 15. Next, click on an unnamed tab in the lower left (probably labeled 2 or 3 ). A blank worksheet should open. Select the first open cell in the upper Culling Data (optional) Lab Exercise (Student Guide) Page 7-13S
left corner. Right click and hit paste ( command V on a Mac) to create an exact copy of your raw data in a new worksheet. 16. Now, right click on the second tab in the lower left (double click on a Mac) to rename this worksheet Control Processed. 17. Highlight the entire row of the object you believe is not a worm based on your assessment of the video. Then hit delete. NOTE: Do NOT delete any worms solely because the velocity does not conform to what you expected. This is a violation of scientific integrity and leads to experimenter bias (when the experimenter sees what is expected rather than what really is there). The numerical data may not be totally consistent. When this happens, it is sometimes frustrating, but it is a normal part of real science. You may only cull (remove data) when there is a logical basis for doing so (e.g., ImageJ has assigned a number to an object it believes to be a worm, but the video clearly shows is a small sphere that doesn t move). 18. Repeat steps 14-17 for all objects that you recorded in the non-worms column of your data table. 19. Repeat steps 14-18 for the alcohol-treated worms. 20. To determine if the average velocity for the 2 sets of data are significantly different, analyze the data with a t-test. Formulate a null and alternative hypothesis for your experiment. 21. Highlight all of your processed control worm velocities. Note: Be sure to exclude the average and standard deviation. Determining the Significance of the Data Lab Exercise (Student Guide) Page 7-14S
22. Open a new worksheet. Right click column B and choose Paste Special. Choose Values and then click OK. 23. Rename this column Control Velocities. 24. Open the Excel workbook for your ethanol worms. Highlight the velocities for these worms and copy them into the next column on the worksheet you just created. Name this column Ethanol Velocities. Lab Exercise (Student Guide) Page 7-15S
25. Click the Data tab at the top of the screen. Click the Data Analysis button at the upper right of the screen. The Data Analysis window will open and allow you to choose the analysis tool. Scroll down and click on t-test: Two-Sample, Assuming Unequal Variance. Click OK. 26. Another window will open that will allow you to enter the data range. Delete anything already in the Variable 1 range and Variable 2 range boxes. 27. Select the Variable 1 range window, and then highlight all the control worm velocities in the worksheet. Repeat for Variable 2 range, this time highlighting all the ethanol worm velocities. Select the New Worksheet Ply: box and title it t-test results. Make sure alpha is set to 0.05. Click OK. 28. A new window will open with your t-test results. Variable 1 is the first set of velocities you entered, the control data. Variable 2 is the second set of velocities, the ethanol-treated data. Lab Exercise (Student Guide) Page 7-16S
29. Use the one-tail P-value to determine whether the null hypothesis should be accepted or rejected. Use this result to make a conclusion regarding the statistical significance of your experimental results. 30. Clean your area. Lab Exercise (Student Guide) Page 7-17S
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