STUDYING 6 Statistical exercise: Corals and Temperature Science often involves gathering data. The data may be counts or measurements or lists of species or may take many other forms; however, it is very common that biological data can be represented numerically. Raw data are often too repeti- tive and boring to be appreciated directly. They need to be sta- tistically summarized. The most ordinary way to get started on summarizing data is to enter them in a spreadsheet, such as Excel. Excel also allows one to graph data and do simple analyses. Today and in future labs, you will use Excel in these statistical exercise sections; today we will focus on how to cre- ate and use a spreadsheet. We will start with data gathered by Hollie Putnam, a stu- dent interested in understanding how water temperature af- fected the growth of coral. To determine this, Hollie took cor- als from their native habitat, where the average water tempera- 1 2 3 4 5 6 7 8 9 10 11 12 13 Create an Excel file with the data in the lab manual for the four treatment temperatures: 26°C, 28°C, 30°C, and 26- 30°C fluctuation. Proofread the data you enter to avoid typos. The screenshot on page 185 gives an example of what the data will look like in the spreadsheet. Calculate the means, standard deviations, sample sizes, and standard errors for each temperature. Make a graph. Then, please answer the following questions in a textbox in your spreadsheet next to your data/graph: 1. What was the mean + standard error of coral growth (= change mg/cm2) at each of the four temperature categories? 2. Remember that the average water temperature of the coral's natural habitat was 28 °C. What would happen if global climate change causes the average seawater temperature to increase to 30°C? 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 B Initial Treatment (°C) (mg/cm2) (mg/cm2) 26 26 26 26 26 26 26 26 26 26 26 28 28 28 28 28 28 28 28 28 28 30 30 30 30 30 30 30 30 30 26-30 26-30 26-30 26-30 26-30 26-30 26-30 26-30 26-30 26-30 26-30 552 341 461 430 312 364 468 449 398 394 360 517 428 407 441 472 383 466 345 382 494 573 354 532 393 269 517 469 306 431 306 372 333 567 379 490 391 с Final 509 369 337 365 563 352 467 437 320 374 479 460 415 401 369 528 443 415 452 488 391 479 354 393 503 585 369 545 410 277 526 484 322 446 312 378 344 578 392 505 401 523 377 351 373 ture was 28 °C, and grew them in a lab. She measured coral growth in four temperature regimes: 26 °C, 28 °C, 30 °C, and a regime that fluctuated daily between a low of 26 °C and a high of 30 °C. She weighed the corals at the beginning of the experiment and at the end. Growth is to be calculated as the final weight minus the initial weight. D Change (mg/cm2) 11.000 • Open a new Excel spreadsheet, and try to make it look like the one to the right with the first number in cell A2. Al- though it is not necessary, you may want to make the head- ings in row 1 wrap inside the cells; to do this, select row 1 by clicking on the 1 in the gray margin, right click to format, go to alignment and click on the box in front of "wrap text." • Type in all the numbers from the data to the right. When done, carefully proofread them to be sure you have entered the data correctly. • In row 2, column D, type the formula =C2-B2 and press re- turn. This will give you the difference, in other words, the amount of growth. Now, copy that cell down to D42. If you have done it right, the formula will change in each cell so as to maintain the same relative position. In D24, you will have =C24-B24, which comes to 15. • To calculate the mean for the 26 °C temperature regime, type =AVERAGE(D2:D12) into cell E2 then press return. The mean is the sum of all the growth amounts divided by the number of replicate coral fragments. Now calculate the averages for the other three treatments by using the same function in cells E13, E23, and E32 for the other treatment groups. Be sure the cell range in your equations is correct. • Calculate the standard deviations, samples sizes, and stan- dard errors. Make a graph. Taking into account the standard errors, think about what aspects of the results are believable. 1. What was the mean ± SE (n) coral growth at: 26 °C 28 °C 30 °C 26-30 °C fluctuating daily 2. Remember that the average water temperature of their natu- ral habitat was 28 °C. What would happen if climate change were to cause the average water temperature to increase to 30 °C? If you made a mistake, double check your data entry and the cell range in your equations. Data are often very expensive to gather, so you need to get in the habit of proofreading your data to avoid typos.