Biology - This is Crucial to Doing Well on Lab Reports Part 3

This introduction is only meant to provide a brief introduction to the concepts of statistical analysis, with a few example tests. Figure B13provides a summary of some of the commonly used statistical tests that you may encounter in biological studies. B13 Some Common Methods of Statistical Inference This flow chart shows some of the commonly used methods of statistical inference for different combinations of data. Detailed descriptions of these methods can be found in most introductory biostatistics textbooks. KEY TO THE ONISCOIDEA OF VERMONT 1a. Uropods short, not extending beyond outline of body; antenna flagellum with 3 segments; body very convex. (ARMADILLIDIIDAE) 1b. Uropods long, extending well beyond outline of the body. .. .. 2 .. .. 3 2a. Frontal line notched at midline; area above mouth forming rectangular projecting lobe; tip of uropod broadly rounded. *Armadillidium nasatum 2b. Frontal line not notched at midline; area above mouth not conspicuously projecting; uropod squarely truncate. Armadillidium vulgare 3a. Last abdominal segment rounded or slightly emarginate posteriorly; flagellum with 3-11 segments. 3b. Last abdominal segment acutely triangular; flagellum with 2-3 segments. (ONISCIDAE) .. .. 4 .. .. 6 4a. Flagellum with 11 segments; last abdominal segment conVexly rounded; compound eyes large, with many facets (LIGIIDAE) Ligidium longicaudatum 4b. Flagellum with 3-4 segments; last abdominal segment emarginate between uropods; compound eye with 1-3 facets, (TRICHONISCIDAE) .. .. 5 5a. Compound eye with 3 facets; flagellum with 4 segments. Trichoniscus pusillus 5b. Compound eye with only 1 facet; flagellum with 3 segments. *Haplophthalmus danicus 6a. Flagellum with 3 segments; a large, very flat species with wide pale margins. Oniscus asellus 6b. Flagellum with 2 segments. .. .. 7 7a. Basal segment of flagellum twice as long as apical segment; abdomen abruptly narrower than thorax. Metoponorthus pruinosus 7b. Basal segment of flagellum at most 1 ½ times as long as Apical segment, usually much shorter; abdomen not abruptly narrowed. .. .. 8 8a.Dorsal surface smooth or nearly so (at most with minute Granules which are visible only under high magnifycation). 8b.Dorsal surface with conspicuous tubercles. .. .. 9 ... .. 10 9a.Lateral angles of first thoracic segment forming acute points; dorsal surface extremely convex; five pairs of white bodies visible in live animal. Cylisticus convexus 9b. Lateral angles of first thoracic segment rectangular; body only moderately convex; two pairs of white bodies visible in live animal. *Porcellio laevis 10a. Head gray, contrasting conspicuously with first thoracic segment, which has pale spots; dorsal surface with rather regularly arranged pale and dark spots, giving a checkered appearance, Porcellio spinicornis 10b. Head not contrasting in color with first thoracic segment. 11a.Live animal with 2 pairs of white bodies; dorsal surface with very coarse rounded tubercles which are conspicuous in all parts of body. Porcellio scaber 11b.Live animal with 5 pairs of white bodies; dorsal tubercles less conspicuous, particularly posteriorly. Porcellio rathkei .. .. 11 PLATE 3 PLATE 4 Measuring Isopods using ImageJ You can use ImageJ to determine the width, length, perimeter, and area of your isopods. 1. Proceed to the back of the lab room (with your camera phone) where there will be a ruler, a petri dish, and a blank white sheet of paper underneath both. 2. Place the small ruler below the petri dish as shown in the figure. For identification purposes, label a slip of paper “Replicate #” or “Experiment #” (see Figure 1) and place it on the ruler. 3. Dump the set of isopods from your experiment into the petri dish and cover (preferably no more than 20 at a time). Avoid setting the petri dish on top of the ruler. 4. Gently swirl the petri dish to separate the isopods from each other and centralize them in the dish. You need the isopods as individuals to easily take measurements. 5. Take several photos and repeat the swirling of the dish if the isopods retreat to the edges of the dish or aggregate. You may have to repeat this a few times before you produce a picture that allows you to collect data on length, width, perimeter, and area with ImageJ. 6. Repeat this process for all of the isopods you want to analyze from your experiments. 7. Open the ImageJ program: Open ImageJ on the since site or lab computers by going to All Programs>Biological Sciences>ImageJ>ImageJ icon (microscope). You can also download the software onto your computer or laptop for free. 8. Open your image in ImageJ: In the ImageJ software, click on File>Open and browse for your first image for analysis. Alternatively, you can drag the image to the menu bar and the program will automatically load it into the software. ImageJ Toolbar Key 9. Set the scale in ImageJ for your measurements: Click on the “Line Selection Tool” option on the toolbar to set the scale by dragging the same-distant line as the ruler. Right click to make sure there is a check next to 'Straight Line'. 10. Draw a line along the ruler from the 1 mark to the 15 centimeters mark by clicking at the 1 mark, holding down the mouse button and dragging the yellow line to the 15 mark. 11. Set the scale by selecting the "Set Scale" option under the Analyze tab and put in "14" for the 'known distance' and "cm" as the 'unit of length'. You will most likely prefer your measurements in millimeters (mm) so place 140 in the ‘known distance’ box and mm in the ‘unit of length’ box (Note: 140 mm = 14 cm) 12. Determine length and width measurements: Click the “Line Selection Tool.” Drag the line horizontally (side-to-side) and/or vertically (head-to-tail) to measure the width and length of the isopods respectively (see Figures 2 and 3). You have to click at the beginning position then drag the line and click at the end position to get the line. (You can view the length listed underneath the tool bar before you click the mouse button at the end position of the line if you want a quick idea of the measurement.) 13. After each line is drawn, choose the option "Measure" under the “Analyze” tab to obtain the desired length measurements. A result box will appear from which you can record your data. Repeat this process for all of your length and width isopod measurements. 14. Determine perimeter and area measurements: In order to measure the area and perimeter of each isopod, select the "Freehand Selection" option, (which will be to the left of the 'Line Selection tool') and draw the outline around each of the isopods with precision (See Figure 4). Alternatively, if the isopods are well separated from each other, you can use the wand tool. Select the “Wand (tracing) Tool” and click on the isopod of interest and the program should outline it in yellow. See Troubleshooting below if the “Wand Tool” does not work the first time. a. If the results box do not display area and perimeter, edit it by clicking on the ‘Results’ tab and selecting the option, ‘Set measurements…’ b. Make sure there is a check in the box next to “Area” and “Perimeter.” Measure again for both measurement results. 15. Choose the “Measure” option again under the “Analyze” tab to receive the results and record the data. 16. Troubleshooting the “Wand (tracing) Tool a. Adjust “thresholding” (binary contrast enhancement) by changing the image to 8-bit grayscale. Go to the “Image” tab and select the option “Type”. Choose “8-bit”. b. To complete the image contrast, under the “Process” menu tab, select “Binary” and then choose the option “Make Binary.” Figure 1: Image of isopods with ruler and labels Figure 2: Straight Line Section Tool to measure the isopod's length. Figure 3: Straight Line Section Tool to measure the isopod's width. Figure 4: Freehand Section Tool to measure the isopod's perimeter and area. Isopod Experimental Design Considerations Analyzing categorical data in which “other” categories arise or when there are replica tes. What do I do if I find isopods in “other” unexpected categories, i.e. observational outliers? Experiment: Wet vs. Dry 1. If in your experiment you placed 20 isopods into an arena that has 2 categories, wet and dry. Your null hypothesis was that there would be no preference shown by the isopods for wet verses dry sponges. Your predictions were that 10 isopods would be found under the wet sponges and 10 isopods would be found under the dry sponges. The assumption in your experimental design was that you were only testing two choices, wet and dry sponges. 2. Since isopods are living organisms, their behavior is not always 100% predictable based on your experimental design. In the data below, 14 preferred wet, 3 preferred dry, 1 died, and 2 did not go under a sponge. 3 became observational outliers. How do we analyze these da ta? 3. We can ignore the isopods that did not select a wet or dry sponge. Based on the new total of 17 isopods, we use 8.5 isopods as the expected value for the chi square analysis. 4. What are our degrees of freedom? Wet Dry Other Observed 14 3 3 (1 died, 2 did not go under a sponge) Expected 8.5 8.5 3 Experiment: 4 Different Moisture Types 1. Again for this experiment, you begin with 20 isopods. However, you have 4 categories. Your null hypothesis is the same that no preference will be shown by the isopods for any category. Your predications are that 5 isopods will be found in each category. 2. This is a dangerous number of samples for this experiment because the chi square analysis requires greater than 5 samples for each category. If one isopod becomes an observational outlier (eg. It dies) then you would no longer have an adequate number of samples per category to run a chi square analysis (19/4 <5). In the experiment above there were 8.5 samples per category. However in the experiment below there are only 4.5. 3. Based these data you may not use chi square analysis because you do not have an adequate sample size. 2 isopods are observational outliers and must be subtracted from your expected values, leaving only 18 isopods for 4 catego ries. 4. In order to use chi square, increase the number of isopods and repeat the experiment until there are > 5 expected samples for each category after subtracting observational outliers. 5. What are your degrees of freedom for this experimen t? Water Ethanol Saltwater Sucrose Observed 1 3 1 13 Expected 4.5 4.5 4.5 4.5 Other 2 (1 died, 1 did not go under a sponge) 2 How do I complete the chi square (χ2) computation for replicates? A. Do I add up the values for the expected and the observed for each trial and use the degrees of freedom for one of the trials? B. Do I calculate the chi square value for each trial and add up the individual chi square values and degrees of freedom? ANSWER: For this lab use Computation B with the assumption that the trials are not linked. Sometimes there is no difference between the two computations and sometimes there is. In this example, both computations show significance, but Computation A shows greater significance than Computation B. Computation A does not show the true sampling with 3 df, while computation B does with 9 df. Computation A for an experiment on isopod sugar preference (see table below) This computation is sometimes used when replicates are done one right after the other, but by adding up all of the observations you may miss the heterogeneity between the trials. For example, in an experiment comparing water and ethanol only, one trial may show more isopods chose ethanol over water, while another may show that more isopods chose water over ethanol. By adding up the observed for all the trials you may lose this difference because they compensate for one another (trial 1: 16 ethanol, 4 water; trial 2: 4 ethanol, 16 water; total: 20 ethanol, 20 water; χ2=0; P=1) . Trial N water sucrose glucose fructose other 1 28 4 8 2 10 4 2 28 6 6 2 12 2 3 28 6 6 1 15 0 Initial Total 84 16 20 5 37 Final Total 78 16 20 5 37 19.5 19.5 19.5 19.5 Expected =78/4 χ2 = (16-19.5)2/19.5 + (20-19.5)2/19.5 + (5-19.5)2/19.5 + (37-19.5)2/19.5 6 = 0.63 + 0.013 + 10.78 + 15.71 = 27.13 d.f. = 4-1 = 3 P<0.001 extremely significant (actual P = 5.53 E-06) Computation B for an experiment on isopod sugar preference (see table below) This computation is preferred when replicates are done days apart. By computing the chi square values separately, you can see the heterogeneity between the trials. Using the example of water versus ethanol from above, trial 1shows more isopods chose ethanol over water, while trial 2 shows that more isopods chose water over ethanol. Th e chi square value for both trials would be similar and additive. (χ2=7.2 + 7.2 = 14.4; P<0.001. In this example, the P v alues are different depending on which method yo u us e.) Trial N 1 28 Expected =(28-4)/4 2 28 Expected =(28-2)/4 3 28 Expected =(28-0)/4 water 4 6 6 6.5 6 7 sucrose 8 6 6 6.5 6 7 glucose 2 6 2 6.5 1 7 fructose 10 6 12 other 4 15 7 0 2 χ2 Trial 1 = (4-6)2/6 + (8-6)2/6 + (2-6)2/6 + (10-6)2/6 = 0.67 + 0.67 + 2.67 + 2.67 = 6.67 χ2 Trial 2 = (6-6.5)2/6.5 + (6-6.5)2/6.5 + (2-6.5)2/6.5 + (12-6.5)2/6.5 = 0.038 + 0.038 + 3.12 + 4.65 = 7.85 χ2 Trial 3 = (6-7)2/7 + (6-7)2/7 + (1-7)2/7 + (15-7)2/7 = 0.14 + 0.14 + 5.14 + 9.14 = 14.57 χ2 Total = χ2 Trial 1 + χ2 Trial 2 + χ2 Trial 3 = 6.67 + 7.85 + 14.57 = 29.1 d.f. = Σ d.f.Trial = 3 + 3 + 3 = 9 P<0.001 extremely significant (actual P = 6.23 E-04) Final Question: What constitutes a true replicate? If you used the same isopods for each trial, would the trials be considered replicates? No, because you are not sampling randomly from a large population of isopods, but just repeating the experiment with the same sample. In this case, you might average your data.