Writing Manual for Research Report

Writing Manual for Research Report PLB 423 Wetland Plants and Algae 1. About This Manual This writing manual is adopted directly from the manual used in the Biocore program at the University of Wisconsin, Madison. Dr. Janet Batzli, Associate Director of Biocore, and I developed the components of this manual when she was at MSU. 2. Avoiding Plagiarism Plagiarism is presenting someone else's words or ideas as your own. You are all aware that copying word for word from a source without quotation marks and a citation is plagiarism, but so is paraphrasing or using ideas without citing the source, and so is paraphrasing another student's lab report.

You all conducted your wetland research as a member of a team. We want you to work together and to discuss the progress of the project and the ideas that you have about them with your team members. Science often is a collaborative enterprise. However, this research report must be your own individual work. If this were a group report, you would identify your collaborators, just as all scientists do.

Do not put yourself and our teaching team in the unpleasant situation of having to deal with academic misconduct. If you use someone else's exact words, you must put them in quotation marks and cite the source. If you use someone else's ideas, even if you paraphrase them, you must cite the source. This includes your classmates' work as well as published sources.

The following excerpt from a handout prepared by the UW-Madison Writing Center illustrates what is and is not appropriate. Paraphrasing, and Acknowledging Sources

To Create a Successful Summary or Paraphrase 1. When reading source material, treat each passage as a discrete unit of thought to be assimilated into your own thoughts. Try to understand the passage as a whole, rather than pausing to write down ideas or phrases that seem, on first inspection, significant. Read purposefully, with a larger conceptual framework in clear view, and integrate each reading into that controlling purpose.

2. After reaching a clear understanding of the ideas contained in the source, summarize that information in your own words. Remember that you are taking notes, not copying down quotations. Your task is to extract, distill and compress essential content that will be useful in creating a paraphrase. Occasionally you may find it useful to quote words or phrases directly from the source, but limit yourself to very brief quotations, and be sure to use quotation marks and to record page numbers in your notes. Sample Paraphrases--Unsuccessful and Successful Based on paragraph A below, consider two improper ways of handling source material: (B) word-for-word plagiarism and (C) "The Mosaic." Finally, paragraph D provides a model of a legitimate paraphrase.

A. The Source "How important is our power of nonanalytical thought to the practice of science? It's the most important thing we have, declares the Princeton physicist historian Thomas Kuhn who argues that major breakthroughs occur only after scientists finally concede that certain physical phenomena cannot be explained by extending the logic of old theories. Consider the belief that the sun and the planets move around the earth, which reigned prior to 1500. This idea served nicely for a number of centuries, but then became too cumbersome to describe the motions of heavenly bodies. So the Polish astronomer Copernicus invented a new reality that was based on a totally different `paradigm' or model--that the earth and planets move around the sun" (Hoover, 124).

B. Word-for-word plagiarism Non-analytic thought is considered very important to the practice of science by Princeton physicist historian Thomas Kuhn who claims that major breakthroughs happen only when scientists finally concede that some physical phenomena defy explanation by extending the logic of old theories. One idea which served nicely for many centuries but then became too cumbersome was the belief that the sun and planets revolved around the earth. This was held prior to 1500 until Copernicus invented a new reality: the earth and planets move around the sun.

The underlined words are directly copied from the source. Notice that the writer has not only "borrowed" Hoover's ideas with no acknowledgment, he or she has maintained the author's method of expression and sentence structure. Even if the student-writer had acknowledged Hoover as the source of these ideas, this passage would still be plagiarized because much of its exact wording comes from Hoover with no quotation marks to indicate that the language is Hoover's. It's not that using a single phrase such as "prior to 1500" without quotation marks constitutes plagiarism; it's the repeated use of exact wording and sentence structure without any quotation marks. If, for example, you used just that one phrase without quotation marks--a phrase whose language isn't particularly distinctive--and acknowledged the source of the ideas, that would be fine.

If quotation marks were placed around all material directly taken from Hoover, this paragraph would be so cluttered as to be unreadable. If you like the ideas and the wording of the original this much, if it is important to your paper, and if it is stated more concisely in the original than it would be in your paraphrase or summary, then quote the original.

C. The Mosaic Intuition plays an important role in scientific progress. Thomas Kuhn believes that nonanalytical thought allows scientists to break through the logic of old theories to formulate new paradigms to explain a new reality. Copernicus' invention of one such model (a reversal of the Ptolemaic view which reigned prior to 1500) claimed that the earth and planets rotate around the sun.

Note the underlined phrases that have been borrowed from the original and shifted around. Hoover's structure has been modified to a certain extent by the writer, but numerous key phrases have been retained without quotation marks, and the source has not been credited.

2 D. A Legitimate Paraphrase In "Zen: Technology and the Split Brain," Hoover suggests that the power of intuition--that suprarational half of our intelligence--is more important to scientific advancement than the function of the left hemisphere of our brain--the rigidly logical and process-oriented portion. He cites the revolution in thinking created by Copernicus' new paradigm of cosmic movement, a leap in understanding made possible only by the creative invention of "a new reality" after rational consideration of the old reality had exhausted itself (124).

Hoover's ideas and specific language have been documented (by direct references to the author, by citations to his article, and by quotation marks where specific language has been used). Notice too that Hoover's language and structure have been modified to fit this student-writer's own purpose.

Please keep these guidelines in mind when using sources in your papers. 3. Structure of a Research Report (See the Paper Review Form at the end of this section for evaluation criteria.)

A primary way that scientists communicate with one another is through scientific papers. We will model our research report on the format most commonly used by scientific journals. (Some journals deviate from this format, and you should always consult the guidelines for the particular journal before preparing a manuscript for submission.) Your research reports should follow the guidelines described below. 1. Title 2. Abstract 3. Introduction 4. Methods and Materials 5. Results (including figures and tables) 6. Discussion 7. Literature Cited Each section of the paper (except for "Title") should begin with one of these terms as its heading.

Target audience. We consider the target audience for the research reports to be fellow students who majoring in a biological science within CNS or CANR; the target audience for oral presentations (posters and Powerpoint) are your peers in this course. A clearly written report should provide a person in the target audience with enough information that she could completely understand, critique, and duplicate your experiment. This sort of clarity depends on a solid understanding of the concepts behind the research, sound logic, careful organization, and proper English usage.

Listing you Teammates Normally, scientists who work together on an investigation write the paper collaboratively and include all researchers names as authors. Here, we ask for individual lab reports because we want to give you the opportunity to work on your writing and thinking skills. Thus, your teammates are not co-authors, but list them as contributors at the top of the page in alphabetical order.

Title The title is a clear, specific statement of the subject of your report. It introduces the reader to your paper and lets them know what to expect. Titles should be concise and informative and need not be complete sentences. Avoid filler words like "Studies on" or "Investigations of" and opening words like A, An, or The. Be as specific as possible. Avoid abbreviations and jargon. A particularly effective title states the results. VAGUE: A Study of Aquatic Plants in a Pickle Jar SPECIFIC: Competition Between Elodea canadensis and Ceratophyllum demersum in a Model Aquatic Ecosystem PARTICULARLY EFFECTIVE: Drosophila melanogaster Wingless Gene Maps to Chromosome 2 If your report constitutes the results of an experiment where you manipulated variables and analyzed the result, include the independent and dependent variables, the direction of your results as well as the study organism/ subject in your title. PARTICULARLY EFFECTIVE: Addition of caffeine (INDEPENDENT VARIABLE) to aquatic

3 culture decreases (DIRECTION) the stem length (DEPENDENT VARIABLE) of Phalaris arundinacea, reed canary grass (STUDY ORGANISM)

Abstract The Abstract is often the most difficult step in writing a paper since it forces the author to distill the essence of the paper to a very brief summary (100-200 words). Always write the Abstract last, after you thoroughly understand the research and its meaning. Use the Abstract to highlight the rationale behind the research, the general approach you took, and the principle results and conclusions. One way to do this is to summarize, in one sentence each, the 4 sections of your paper.

Abstracts must relate the main points of the paper and should be understandable without referring to the rest of the paper. Samples are widely available in electronic databases, and many readers use the Abstract to decide whether they want to find and read the entire paper.

Introduction This section provides background information and a clear explanation of the purpose or biological rationale, the general approach of your investigation, and your hypothesis.

Elements of the Introduction:  Background information: key issues, concepts, and terminology needed to understand the reason for the investigation (the biological rationale), the logic of the experimental design (the approach), and the types of data you collected. Remember to be concise and only include relevant information given your audience and your experimental design.  Study Question: This question flows directly from your background information based on an observation or previous research.  Biological Rationale: This is the purpose of your investigation. It may help to think about the rationale as an answer to the questions—how is this investigation related to what we know AND how will this investigation add to our knowledge? You should not over emphasize the relevance of your investigation and the possible connections to large-scale processes. Be realistic and logical—do not over generalize or make grand predictions that are not sensible given the structure of your wetland system. Rationale That Needs Work: Global warming hypotheses predict an increase in average global temperature of 1.3°C in the next 10 years (Seetwo, 2003). Daphnia magna are small zooplankton that live in freshwater inland lakes and are thought to increase a sexual mode of reproduction in response to extreme temperatures. Therefore, Daphnia magna may also be sensitive to increased temperatures and may serve as a good environmental indicator for global warming. Better Rationale: Daphnia magna are small zooplankton that live in freshwater inland lakes with an average surficial summer temperature of 20°C and are queued to reproduce sexually in response to extreme conditions (Mitchell 1999). Lake water temperatures in effluent from power plants, paper mills, or chemical industry facilities may be more than 10% higher than the average summer lake temperatures and could affect the survival and reproductive cycles of many resident aquatic organisms including Daphnia magna as a sensitive environmental indicator species (Baker et al. 2000).

 Hypothesis: Your hypothesis is a specific prediction or set of predictions that you will test during your investigation. This statement should include the independent variable (what you manipulate), the dependent variable (what you measure), the organism or system, the direction of your results, and comparison to be made. Hypothesis that needs work: We hypothesized that the addition of 1% n-butanol to Sacchromyces cerevisae culture exposed to alpha factor will increase the sexual mating response. [The dependent variable “sexual response” has not been specified enough to be able to make this hypothesis testable or falsifiable. In addition, no comparison has been specified— increased sexual mating response as compared to what?] Better Hypothesis: We hypothesized that Sacchromyces cerevisae [study organism]

4 grown in the presence of alpha mating factor and 1% n-butanol [indep. var] would exhibit a reduced [direction] amount of budding [depend. var] and increased [direction] transcription at the FUS1 promoter [depend. var] as compared with S. cerevisae exposed to alpha factor and grown in n-butanol free medium.

 Experimental Approach: Briefly give the reader a general sense of the experiment, the type of data it will yield, and the kind of answers you expect to obtain from the data. Do not confuse the experimental approach with the experimental protocol. The experimental protocol consists of the detailed step-by-step procedures and techniques used during the experiment which are to be reported in the Methods and Materials section.

 In the case of field investigations, include a description of the type and location of the site studied.

Be Concise yet Specific: As you write, keep asking, "Is this necessary information or is this irrelevant detail?" For example, if you are writing a paper claiming that a certain compound is a competitive inhibitor for alkaline phosphatase and acts by binding to the active site, you need to explain (briefly) Michaelis- Menton kinetics and the meaning and significance of Km and Vmax. This is not necessary if you are reporting the dependence of the activity of the enzyme on pH because you do not need to measure Km and Vmax. Another example, if you are writing a paper reporting the increase in Daphnia magna heart rate kupon exposure to caffeine you need not describe the reproductive cycle of the organism unless it is germane to your results and discussion. Be specific and concrete, especially when making introductory or summary statements. Poor: Many factors affect the general well-being of Daphnia. Better: Daphnia growth and survival are dependent on temperature and food availability, but not on the kind of food available.

Background information can come from our class discussions, your textbooks, or the lab manual. In some cases you are also expected to use the library. If you use information from the text or lab manual, put it into your own words. Whether you paraphrase or quote an idea directly, you must cite the source in your paper. (See the sections on Avoiding Plagiarism [pp. 2-4] and on Citations and References [pp. 9-10].)

One of the most important features in the introduction is a statement of the study question, hypothesis and/or associated problem. The paper should be structured so that the background leads logically to your question, your rationale and then your hypothesis followed by a concise explanation of experimental approach.

Defining the rationale is probably the most critical task for a writer. Correctly done, it will simplify the writing process because it provides the logical framework for your paper. You identify where you are going and how you expect to get there. Articulating the purpose and approach forces you to identify the main point(s) you will address in the Discussion section, the types and sources of evidence, and how you expect to use the evidence to support the points you make. Understanding this will help you organize your thinking and will help your reader follow your train of logic throughout the paper.

Defining the rationale may also be difficult. To do it correctly you must clearly understand the whole point of the experiment. Expect to spend time and mental effort on this before you begin writing the paper. You may have to do considerable digging into the scientific literature to find out how your experiment fits into what is already known and why it is relevant to pursue. It may take several attempts to write a statement that seems consistent with the experiment and the data you will obtain. Furthermore, be open to the possibility that as you work with and think about your data, you probably will develop a deeper, more accurate understanding of the experiment. You may find the original rationale needs to be revised to reflect your new understanding. Achieving this type of understanding takes effort, but it will lead to a better paper.

Methods and Materials This section is often the easiest to write since it is simply a clear explanation of the specific procedures,

5 techniques, and materials you used. Provide enough details that the reader could replicate the experiment. This will also allow him/her to evaluate whether to trust your findings. Focus on essentials that affect the results. For example, in a genetics experiment with flies, it is important to state whether the females used for the crosses were virgins; it is not necessary to list the type of food or anesthetic used. However, these details would be important if your experiment was testing how different diets affected fruit fly activity level or some other physiological parameter.

Mathematical manipulations or statistical analyses applied to the data are part of the experimental methods and should be explained here, but keep these brief. Although calculations are not normally included in a scientific paper, be certain to show your calculations with Charlotte or me to check the accuracy. In cases where detailed protocols are given, (e.g., Nitrate test a la Hach), merely cite the appropriate chapter of the Hach manual, note any details relevant to the experiment but not specified in the protocol (e.g., collection of soil samples that were totally humus), and describe any manipulations you made that are not outlined in the manual. Include only what is vital for the reader’s understanding of how the results were obtained. Drawing white poker chips out of a 1 quart vanilla flavored ice cream container to get two numbers to pace out and place quadrats is not as important as the fact that quadrat placement was random. If you are having trouble deciding what to put in and what to leave out, consult with us.

Organize the procedures in the Materials and Methods section logically: use subheadings, put related methods together, and describe procedures in chronological order (if it makes sense to do so). Since you refer to procedures that you carried out in the past, use the past tense for this section.

Results The Results section is a logically organized presentation of your observational and numeric data. In many cases the organization and subheadings of this section should be consistent with those of the Methods and Materials section. There are usually two parts to this section: 1. text 2. tables and figures.

Text The key purpose of the text in the results section is to point out and emphasize trends/ patterns in your data. These patterns are often illustrated in figures or tables. However, each figure and table needs accompanying text to point out the obvious—or sometimes the not so obvious. Briefly describe, but do not interpret, key results. (Interpretation of the data belongs in the Discussion section.) Refer your reader to Table 1 or Figure 1 as you explicitly identify relationships, patterns, or general trends that you see in the data. Remember that relationships that are obvious to you may not be obvious to someone who has not carried out the experiment. Never write a sentence that just tells the reader where the data are. Observe the general trends in the data, then refer to the figure or table parenthetically. Poor: The data from the competition experiment are presented in Figure 1. Better: The Selenastrum outcompeted the Gomphonema in every treatment (Figure 1).

The Results section should not be controversial since you are merely reporting findings, not saying what you think they mean. Avoid judging your data as "good" or "bad." Data are facts and facts simply are what they are. Remember: you are not graded on your results you are graded on how you handle them. Always report what you saw, not what you think you should have seen. Again, DO NOT interpret your data in this section. Leave interpretation for the discussion.

6 Tables and Figures Tables are organized lists of numbers, ideas, or other data. Figures are graphs, charts, diagrams, or photos. Tables and figures are key elements of a scientific paper. First, they offer a concise way to present a large amount of information. Second, they carry the bulk of the experimental evidence needed to support your conclusions. Third, they offer the reader a chance to assess your data and determine whether or not your conclusions are valid. Finally, the values in them can be used by other scientists who wish to build on your work. Usually, summarized (e.g., averages and measures of variation) rather than raw data are included in a paper. Always make it clear whether you are presenting actual data or averages. (In some cases we will ask you to include raw data as an appendix.) Please refer to the section 11 on production of figures using Excel.

Each table or figure should be referred to in the text of your paper at least once. If you have nothing to note about a particular table or figure, leave it out. Identify and number tables or figures according to the order they appear in the text (Table 1, Table 2, Figure 1, Figure 2, etc.). This way the reader will know exactly what data you are discussing.

Tables and figures should be neat, logically organized, and informative. If properly prepared they can stand independently of the paper. Always remember that readers are not familiar with your data. A table or figure that seems self-explanatory to you may not seem so to a reader.

Here are some rules for presentation graphs and tables:

 Present your final data in table or graphical form. The choice of table or figure should be based on the type of data you have. If you are trying to show trends or simple comparisons it may be best to use a figure. If you have long lists or many comparisons to be made across groups a table may be more appropriate. [DO NOT present the same data in both table and graphic form.]

 The most common way to present graphical data is either an XY scatterplot for continuous data or bar chart for categorical data.

 Keep it simple! The amount of time it takes a reader to interpret a figure is inversely proportional to how well those data are presented. Do not over use transformations or ratios if they are unnecessary for accuracy and clarity of your results.

 Clearly label all axes or columns including units (e.g. Moisture (% dry weight), Nitrate (ppm)). Provide a key for any symbols used.

 Table and figures should always have a legend (description) that fully describes them (so that they can stand alone). Avoid using the term vs. o POOR LEGEND: Species diversity vs. pH o BETTER: Frequency distribution of Typha along a pH gradient in a marsh and bog. o  It is not necessary to create titles for figures or tables. A simple legend is sufficient numbering each table and figure consecutively is sufficient. Do not use titles like “Chart 1” that are automatically generated by Excel.

 For graphs that present an average value as a single point or bar, include error bars and state what they represent. Usually, this will be 1 standard deviation (SD) or 1 standard error (SE) on either side of the mean. For tables presenting means, include some measure of variation (SD or SE).

 State the number of samples used to calculate an average. If you measured the height of 20 Juncus plants and reported an average height of 82 cm, indicate the number of samples used to generate that statistic as n=20.

 Do not connect the points on a line graph unless you really mean to say that the values in between the points shown should follow the line drawn. Trend lines have very limited predictive

7 value or validity when connecting 3 points or less.

An example of a well-labeled figure with an effective legend is shown below.

Figure 1. Metabolic rate (in kcal/min) of a female subject while stepping on an exercise step at two different stepping rates (110 and 122 steps/minute) and with backpack loads of 0, 10, 29, and 42% of her body mass. Each point represents the average of two days. Error bars are + or - 1 SE. Lines are the best-fitting lines for each stepping cadence.

Discussion This is where you interpret your results for the reader. It is the most important part of your paper and often one of the most difficult to write; be sure to allow enough time to work on it. The purpose and approach statements from the Introduction should guide the organization of the Discussion. Be specific. The following is not an appropriate conclusion: "The results were pretty much what we expected (see Results section)." State specifically what you conclude and the specific reason(s) for that conclusion. The Discussion should lead the reader through the specific conclusions drawn from the data to their more general implications beyond the experiment.

Here are some key elements to think about for the Discussion section:  State your conclusion(s) clearly in the opening paragraph. Restate your hypothesis and whether you accept or reject your hypothesis based on what you expected given what you observed. (Note that finding that there was no difference between 2 treatments is still a conclusion.)  Science cannot prove anything. Without getting into too much philosophical detail, the role of science is not to find proof, but rather to move closer to truth by disproving what is not true. Therefore, you will not be ‘proving your hypothesis’ in an experiment. You will be merely accepting or rejecting your hypothesis given the construct of your experiment and the data you have gathered.  Guide your readers through the steps in your reasoning that lead you to your conclusion. Present the arguments that explain how your experimental approach and the pieces of evidence (data) convinced you of your conclusion. Form an argument (see section on writing logical arguments)  Do not over-interpret your data. Recognize the magnitude of the variation within your data and the level of departure you would need to find to conclude true differences.  In most cases you are trying to attach meaning to a group of numbers generated by some procedure. Help your readers make sense of these numbers by explaining how the patterns and relationships you observed reflect the biological concepts or issues you set out to explore. How does your data fit with your biological rationale?  For experiments where you carried out a literature search, compare your findings with information from the literature, citing appropriate references. How do your findings add to those that others have observed? Are your results consistent or inconsistent with others findings—why or why not?  In some cases you may discover unexpected inaccuracies in your data or that the methods you used were not appropriate or precise enough to address your question or test your hypothesis. Address the errors, unresolved issues and speculate how the experimental approach might be improved.  Inconclusive results may show that you weren't asking a relevant question in the first place or that

8 the experiment was not able to test the question you posed. This, in turn, can generate specific new questions and experimental approaches.  Evaluate the strengths of your experiment and speculate on the implications of your findings. Implications are specific, reasonable extensions of your results or the meaning of your results for the larger picture. Your results may lead to new insights about relationships in nature. An unexpected result (if it holds up on repeating the experiment) may yield insight to guide a more effective experimental approach.  Science is built on an iterative cycle of questions, experiments, results and conclusions. Often it is appropriate to suggest the next step in the investigation. Be sure to include the reasoning that leads to your insights. They may be speculative, but they should be well reasoned. Your experiment will likely provide many opportunities to ask new questions.  End your paper strongly with a clear, brief conclusion that relates directly to the question, hypothesis, or problem you stated in the Introduction.

If you get stuck: The hard work of making meaning of data will be easier if you have a clear idea of what it was that you set out to do in the first place. Re-read your biological rationale or purpose statement. Do your results allow you to answer the question posed in your statement? Do you understand your data? If not, discuss with your instructors. Be sure to discuss your results thoroughly with your research team. They may have some insight, intriguing literature for comparison, or thoughts about the data that could benefit your interpretation.

Other things you can do: Make a concept map. This is especially useful for seeing new connections, structuring ideas, and finding interactions at multiple levels.

Explain the experiment and its significance to a friend who knows nothing about it. If you understand the full content, context, results and relevance of your experiment, you should be able to explain what was done and what it means. This should help provide some organization to your paper.

Literature Citations and References

Citations You must cite all information that you use from published or unpublished sources in the body of your paper and then give the complete name of the author(s) and source in the References section at the end of the paper. Use the parenthetical author-date system preferred by most scientific journals. Within a sentence or at the end of a block of text, give the last name of the author(s) and the date the work was published, both enclosed by parentheses: Global warming is a looming threat to biodiversity (Peters and Lovejoy, 1992).

If you wish to cite more than one source, list them in chronological order: e.g. (Jones, 1992; Smith & Jacobs, 1993; Torrez, 1995). If a work has more than two authors, you may list the first followed by et al. (Latin for “and others”) and the date: (Jones et al., 1995). However, the names of all of the authors must be included in the list of references at the end of the paper.

The format for unpublished information or data communicated to you by a colleague is the source followed by "personal communication" or "unpublished data": e.g. (Maria Rodriguez, personal communication 2002; Biocore 302 class, unpublished data). Use these sparingly as they cannot be verified. Personal/unpublished communications do not go in the list of references at the end of the paper.

References List all works cited in the text - and no others - alphabetically in the References section at the end of your paper. The specific format used for references varies depending on each journal's conventions, web-site format and the type of source to which you are referring. We would like you to use the format demonstrated below. Each reference should include the names of all the authors, the date the article or book was published and/or the date the website was accessed and its title.

9 We will use the format used in Bioscience: Journal article: Include the author(s), title of the article (with only the first word capitalized), name and volume of the journal, and pages for the article. Vitousek PM. 1994. Beyond global warming: ecology and global change. Ecology 75: 1861-1876. Post WM, Emanuel WR, Zinke PJ, and Stangenberger AG. 1982. Soil carbon pools and world life zones. Nature 298: 156-159.

Internet Sources Include the author(s), title of the work (in quotation marks), title of the complete work or site, if applicable (in italics), website URL or address (except for personal email), and date of visit or message. (The method for citing online sources has not yet been standardized.) email: Carbon JJ. "Physiology data." Personal email (7 July 01). listserv or newslist: Blystone RV. "Setting up a digital classroom and other stuff." [email protected] (10 May 96). World Wide Web: Waterman M, Stanley E, Soderberg P, and Jungck JR. "Kingdoms entangled: molecules, malaria, and maise." BioQUEST Curriculum Consortium. Accessed: 10 Aug. 99. URL: http://bioquest.org/case.html

Macreal H. "Large Fish, Small Pond." April 10, 2001. Accessed: April 20, 2001. URL: http://www.bigfish.org/articles

Splice G. "Mutations are the Ultimate form of Variation" University Press Weekly 21 July 2000: 22. Electric Library. Accessed: 17 Oct.1997. URL: http://www.elibrary.com/.

*Note: Do not write out a website address as a parenthetic citation within the text. Whenever possible, list the author. If you can’t find an author, list the organization that provided the information. If you can’t find the name of the organization, question the quality of your source.

Book Include the author(s), title, edition number (if it is not the first edition), the publisher, the city of publication, and the state (omit the state for well known cities like New York). Kuhn TS. 1962. The Structure of Scientific Revolutions. Chicago: University of Chicago Press. Purves WK, Sadava D, Orians GH, and Heller HC. 2001. Life, the Science of Biology, 6th ed. Sunderland, MA: Sinauer Associates.

Chapter in a Book Naes A. 1986. Intrinsic value: will the defenders of nature please rise? pp. 504-515. in Soulé ME., ed. Conservation Biology: the Science of Scarcity and Diversity. Sunderland, MA: Sinauer Associates.

Formatting Your Lab Report We want you to use a computer to write your papers. This will make it easier to revise, edit, and spell check your paper. Avoid disasters by saving papers often (e.g., every 10 minutes) and backing up all important files. Spell check and proofread before turning it in.

Please use the following conventions for your reports: • Double space your text. This allows your TA or peer reviewer to write comments between the lines without struggling to squeeze words into the margins. • Use a 10-12 point font. • Keep a 1 inch margin around all of your text. Margins make your papers easier to read and provide room for comments. • Use headings. Headings and subheadings help you to organize your paper and provide clear signposts for your readers to follow. Examples of headings are the major sections we described above (Introduction, Methods, etc.). Long sections and those that include distinct parts should

10 have subheadings. For example, the Methods section of an ecology paper might have the following subheadings: Organism, Study Sites, Statistical Analyses. Use a 2 point larger bold font for headings and a bold font for subheadings. • Don’t prepare a title page - save a tree. Simply center the title at the top the first page of your report. Likewise, don’t bother with a special folder for the report - a single staple in the corner is sufficient.

11 Paper Review Form Author: Reviewer: Key: + = Excellent  = Adequate NW = Needs work 0 = Missing NA=Not applicable in this paper Title Specific (e.g., includes the independent and dependent variables to be tested, and the organism or subject that is the focus of the study) Conveys the main point of the paper Appropriately concise All authors / contributors names beneath the title

Abstract key points; biological rationale, hypothesis, experimental approach, brief methods, major results/conclusions; Concise (absolutely essential in an Abstract) <200 words Can stand alone (understandable without the rest of the paper)

Introduction Proceeds logically from general background to specific goals of the study Gives biological rationale for study Clearly states question or hypothesis being investigated Gives overall approach used Appropriately concise Cites appropriate references (for some labs, this is simply the lab manual) Big Picture: Conveys why experiment was performed & what it is designed to test

Methods Methods (data collection and analysis) appropriate for the study Description is clear, concise, and flows logically (e.g., subheadings, chronological order) Describes study so that a knowledgeable reader could replicate it Big Picture: Describes how researcher went about testing hypothesis

Results Results/trends/ patterns clearly presented with narrative that cites figures and tables Free from interpretation Data appropriately analyzed & organized and clearly displayed in tables and figures Figures and tables have appropriate legends and labels (can stand on own). Clear, concise, logically organized Calculations (if required, put them in an appendix) are done correctly Big Picture: Data present and presented appropriately

Discussion Restates hypothesis to be accepted or rejected based on data Interprets/discusses results and draws conclusions regarding the question or hypothesis Conclusions are appropriate for the results obtained. Compares findings with information from the literature (if literature search required) Discusses what the results mean for the system being studied (tie to biological rationale) Discusses problems (if there were any) and/or unresolved issues Clear, concise, logically organized Ends with clear, brief conclusion statement Big Picture: Conclusions backed by data taken as evidence to accept or reject hypothesis

References

12 Listed alphabetically, by author, using the proper format

4. Logical Arguments Many beginning writers feel that to show readers the steps in their reasoning about an issue or conclusion is to state the obvious. This is not so. When you write a paper you are inviting the reader to see the issues and the data from your perspective. The following quotations from A Rulebook for Arguments, 2nd ed. by Anthony Weston (1992) offers this perspective on argument as a means of both inquiry and persuasion:

Some people think that arguing is simply stating their prejudices in a new form. This is why many people also think that arguments are unpleasant and pointless ... 'To give an argument' means to offer a set of reasons or evidence in support of a conclusion ... arguments are attempts to support certain views with reasons. Argument is essential ... because it is a way of trying to find out which views are better than others. Not all views are equal. Some conclusions can be supported by good reasons; others have much weaker support. But often we don't know which are which. We need to give arguments for different conclusions and then assess those arguments to see how strong they really are. Argument in this sense is a means of inquiry.

Argument is essential for another reason too. Once we have arrived at a conclusion that is well supported by reasons, argument is the way in which we explain and defend it. A good argument doesn't merely repeat conclusions. Instead it offers reasons and evidence, so that other people can make up their minds for themselves ... you must use arguments to explain how you arrived at your conclusion: that is how you will convince others. Offer the reasons and evidence that convinced you. It is not a mistake to have strong views. The mistake is to have nothing else. (p. XX) 5. Receiving Feedback Writing is a process and even very experienced writers spend a lot of time rewriting. We will give you feedback and suggestions on drafts of your papers to help you in this process. We will also do one round of peer reviews. Note however, that it is not our responsibility to point out every flaw or to revise your papers for you. Revising is your responsibility. It pays to keep working at this. TA comments (and your grade) will focus much more on “The Big Picture” than on editing details. Here is what we mean by big picture: in evaluating your papers, the TAs ask:

1. Can I understand what the experiment was designed to test and how she went about it? 2. Are the appropriate data here and expressed in a way that I can immediately get the picture? 3. Do the conclusions make sense based on the data? (Although it is fine to say what you expected to find, you must base your conclusions on what you actually observed. Also, beware of over-interpreting differences that may simply be experimental variation.)

We may also comment on details and point out examples for editing. Here are some examples of details: only showing trend lines but not actual data points in your figures, reporting your data in too many significant digits, labeling your figure as Graph 1 instead of Figure 1, incorrect citation of the lab manual. Although, these details seem fairly trivial, together they affect the way in which you communicate which is very important in deciding a final grade. Therefore, it is important to address changes to the Big Picture and minor editorial details in your revisions.

Writing is a form of communication and a peer can tell you whether or not your paper makes sense. It is to your advantage to take seriously your responsibility to review a peer's paper. We find that the review process benefits the reviewer as well as the author because it gives you practice evaluating a paper applying the same criteria we will use to evaluate your paper.

Note that you do not need to wait for us to assign a formal review to take advantage of the peer review process. You can always get together with another student and act as reviewers for each other's papers

13 even when it is not required as part of an assignment.

We hold you to high standards and want to help you reach them. Here are our grading standards: 4.0: Truly excellent paper. All sections address relevant issues in a clear and concise form that communicates an impressive understanding of the topic at hand. All ideas in the paper flow logically. Your analysis is fresh and exciting, posing new ways to think of the material. Your conclusion is persuasive. You show a great deal of resourcefulness, independent insight and originality. You are not wordy or redundant. Your sentences structure, grammar, spelling and citations are excellent. You support every point (argument) with references or data. Paper is a pleasure to read.

3.5: The very good paper. Missing a few of the characteristics of the truly excellent paper. Most sections communicate a high degree of understanding. You give examples or references to support most points. Your analysis is clear and logical and shows independent thought.

3.0: The good paper. Complete and adequate, reasonably thorough though not impressive; demonstrates understanding. Your logic is generally clear and appropriate, although it may wander occasionally. You have a few unclear transitions, or paragraphs without an identifiable purpose. Your analysis usually makes sense, although sometimes misses the bigger picture.

2.5: the borderline paper. Not adequate or has parts that are not adequate; demonstrates some understanding. Your paper may wander, with few transitions or clear paragraphs. There is little logic flow. You do a fair job synthesizing material but do not develop your own insight or conclusions.

2.0: The paper with issues. Many problems, e.g., missing key components, misunderstanding the experiment or data, drawing inappropriate conclusion from the data. Your purpose is difficulty to identify, or it may be a bland restatement of an obvious point. You structure may be unclear. The paper may be a loose collection of statements rather than a cohesive argument or may just miss the purpose entirely. Your results are weak and hard to follow, fail to support conclusions adequately. The evidence you give is poorly analyzed, poorly integrated into the paper, or simply incorrect.

<2.0: The inadequate to totally inadequate paper. Major, major problems. Obviously little time or thought was put into it. Basically, better to turn it in late than to turn in something like this.

6. Writing Style Style refers to the way writing is used to express ideas, distinct from the ideas themselves. Style can also refer to specific guidelines for spelling, punctuation, and formatting established by an instructor or publisher. In this manual we focus on the scientific writing style required by most journals in the sciences as well as by faculty in this department. Scientific writing is clear and concise and uses correct grammar and spelling. Clarity demands that you follow the conventions of proper English usage. Two of the best aids available to writers are a style book, such as The Elements of Style (Strunk and White, 1979) or How to Write and Publish a Scientific Paper (Day, 1994), and a dictionary. These books are good investments for anyone interested in improving his writing skills.

Avoid trying to sound "scientific." Choose the simplest, most precise words you can. They will help you convey information quickly and clearly. Do not write to impress your reader; the task is to explain scientific ideas. If you are using a word that is new to your vocabulary or has uncommon usage, make sure you are using it precisely. Look it up in the dictionary if you have any doubts!

14 Use active voice most of the time. In active voice, the actor comes before the verb and the object, whereas in passive voice, the actor comes last. Active voice is more dynamic and less likely to lead to wordiness and ambiguity. POOR: The algae cultures were examined by the research team everyday. (passive) BETTER: We examined the algae cultures daily. (active) This is your story. It is appropriate to say, "This is what we did, this is what we found, and this is what we think it all means." However, there are situations where the passive voice is appropriate, for example, when the subject of the sentence is irrelevant in the context (e.g., MSU was established in 1857ish). It is common to use passive voice in the Methods section.

Word Choice and Wordiness. Ask yourself, “will this paper read poorly without this word or sentence”? Unless the answer is yes, throw it out! Don’t hesitate to throw out a sentence that doesn’t fit, even if it is well written. Avoid unnecessary phrases and words (it is interesting that, due to the fact that, at the present time, there is little doubt that) and verbs turned into nouns. POOR: It is interesting that at the present time there are many people who like to garden due to the fact that it is relaxing. BETTER: Many people find gardening relaxing.

POOR: Many student papers, especially those that consistently exceed 15 pages, are too long. Therefore, in dealing with papers that are not concise, instructors need to resort to drastic measures in order to urge the authors of long papers to edit their papers. BETTER: Many students need to edit their papers to make them shorter.

POOR: The sample was subjected to centrifugation. BETTER: We centrifuged the sample at 500 x g. Make sure the language you use reflects the scientific activity in which you are engaging. Phrases such as “I believe”, “We would hope”, or “I think that” have little place in scientific writing.

Avoid using “one” or “you” as the subject of the sentence; put biology in center stage.

When using a comparative adjective, make sure the object of comparison is clear. Answer ‘lower’, ‘greater’, ‘better’ than what? Poor: The water chemistry made algal diversity lower. Better: Algal diversity was lower at low pH rather than at high pH.

Read your paper aloud. You may be able to hear problems you didn’t recognize previously.

Ways to prevent awkward or wordy sentences:

Many problems stem from overuse of the verb “to be.” If it does not serve the function of an equals sign in the sentence, try to eliminate it.

Put the agent of cause in the subject and the action in the verb. Go for a verb that is interesting and informative.

Use “which” and “that” sparingly.

If a sentence is more than two lines long, try to break it up into two sentences.

Avoid the naked this. “This” should always precede a noun. Poor: This shows that… Better: This behavior indicates…

In the discussion, it’s not necessary to tell the reader that you are basing a particular conclusion on data presented in the results. If you have presented the data well, the reader will know that you are basing your conclusion on your data.

15 Poor: Based on the results presented in figure 1, one can see that the Daphnia grew faster when exposed to higher temperatures. Better: Higher temperatures favored Daphnia growth.

Avoid slang and jargon. Slang (got, neat, cool) is highly informal language that is outside of standard or conventional usage. POOR: We got all kinds of neat stuff from the marsh and dumped it in a pickle jar. BETTER: We collected plants from the marsh and placed them in a 1 gallon glass jar.

Jargon is highly specialized or technical vocabulary used by those in the same work or profession (e.g., using "chemotheraputic agent" instead of "drug"). In science writing, jargon frequently consists of nouns modifying nouns and is common when writers use the passive voice.

Revise these excessive words and jargon into a well-known proverb (Day, 1994, page 174). There is a large body of experimental evidence which clearly indicates that members of the genus Mus tend to engage in recreational activity while the feline is remote from the locale.

Define any technical terms that may be unfamiliar to the reader. Leaf area index (the surface area of leaves in the plant canopy per unit ground area) is often measured in m2/m2.

Use inclusive language. Imprecise word choices may be interpreted as biased, discriminatory, or demeaning. For example, the use of man or men as generic terms for humans is ambiguous and inappropriate POOR: Man's search for answers has led him to pursue avenues of scientific discovery. BETTER: The search for answers has led people to pursue avenues of scientific discovery.

Use she/her as often as he/his when referring to a person who may be either gender.

Use the appropriate format for scientific names. The first time you refer to an organism give the specific epithet (the scientific name- both the genus and species in italics) e.g. Daphnia magna. You may subsequently refer to the species with genus abbreviation, e.g. D. magna.

If you choose to use common names when discussing particular species, present the scientific name, in parenthesis and italicized, after the common name at least once in the paper. Common names are not capitalized unless the name is also a proper noun. common goldenrod (Solidago canadensis) Queen Anne’s lace (Daucus carota)

Learn the correct usage of the following words and abbreviations. Accuracy, precision: Accuracy refers to the closeness of a measurement to the true value. Precision refers to the repeatability of a measurement. If you measure something with a defective ruler many times and obtain the same length, you will have made a precise but inaccurate measurement.

Affect, effect: Affect is a verb that means "to influence" or "to have an effect on"; effect is a noun that means "result."

Among, between: Among refers to more than two; between refers to two of something or indicates geographic location.

Amount of, number of: Amount of refers to general quantities of things; number of refers to amounts that can be counted. A small amount of soil can contain a large number of organisms.

Cannot: This is one word.

16 Data, datum: Data is plural; datum is singular. e.g., i.e.: The term e.g. (exempli gratia) means "for example"; i.e. (id est) means "that is." Both should be italicized (because they are Latin terms) and followed by a comma (i.e., like this).

Ensure, insure: Ensure is to make certain or guarantee; insure is what insurance agents do to protect you from loss. et al.: This stands for et alia, which means "and others." Note the period after al.

Few, less: Use few to answer the question "How many?"; use less to answer the question "How much?"

Hypothesis, theory: Hypothesis is used in everyday language to mean an educated guess; however, scientists use the term hypothesis to mean a provisional idea with explanatory power that is consistent with available information. The hypothesis may be rejected if it turns out not to be supported by data generated by further experiments. A theory (e.g., the theory of evolution by natural selection) is a well- tested idea that has been supported by multiple observations and experiments over a long period of time.

Its, it's: Its is the possessive pronoun (its tail); it's is the contraction of "it is" (It's hot today.)

Percent, percentage: Percentage is used when no figure is given (a high percentage of students); percent is used when a figure precedes it (55 percent or 55%). In science writing, % is more commonly used than percent.

Prove: To prove something is to demonstrate it to be a fact. Scientists support hypotheses with data; they seldom prove something. Do not say you "proved" something when you have limited evidence.

Significant: In science writing, significant is used for statistical analyses. Do not use significant when you mean "important," "notable," "distinctive," or "major."

That, which: That defines and restricts (the book that we need has not arrived); which is explanatory (an afterthought) and nonrestrictive (the plants, which seem bushier than usual, ...). 7. Grammar and Sentence Structure To write effectively, you have to consider not only the substance and style of your paper, but also punctuation and grammar - the nuts and bolts of your writing. The following list represents some of the most common errors we have seen in student papers over the years. For others, consult one of the comprehensive style manuals listed in the References on Writing section of this manual.

Agreement in Number

Subject and Predicate A predicate is a verb or verb phrase of a sentence. Predicates should agree in number with their subjects. Units of measure are often used in the collective sense and the verb should be singular. The datum is... (singular) The data are...(plural) Five milliliters of water was added to the mixture.

Pronouns Pronouns should agree in number with the noun to which they refer. Everyone (singular) must hand in his (not their) lab report on time.

Tense Ask yourself whether you did something (past tense), are doing something (present tense), or will do something (future tense).

17 Describe your completed observations and procedures (e.g., the Methods section) in the past tense. We obtained samples from three different sites.

Use the past perfect tense when events are repeated or continued from the past to the present. Gall formation in goldenrods has been studied in many geographic locations.

Describe generalizations, conclusions, and references to conditions that continue to be true in the present tense. Streptomycin inhibits the growth of M. tuberculosis. Our data suggest that algae, like all autotrophs, require and may be limited by light, water, gases, and mineral nutrients.

Punctuation

Comma Include commas after each word, phrase, or clause in a series, and before the conjunction separating the last two. Grasses, legumes, and composites grow in Wisconsin prairies.

Commas should follow that is, for example, moreover, i.e., and e.g. For example, most Iron Age graves consist of burial mounds sheltering only one individual. The Nature Conservancy has completed a preliminary series-level (i.e., dominant plant species) classification for the western United States.

Semicolon and Colon Use a semicolon between parts of a compound sentence (two or more independent clauses) not connected by a conjunction, such as and, but, or. Light consists of energy packets called photons; the shorter the wavelength of light, the more energy in its photons.

Put a semicolon before, and a comma after, each conjunctive adverb, such as moreover, therefore, nevertheless, consequently, or furthermore, when connecting two parts of a complex sentence. Use commas when these words are used at the beginning of a sentence or when they are part of a simple sentence. (In general, avoid these "filler" words as much as possible!) The deionized water was not available; however, we still completed the experiment. Therefore, the results were significant. Researchers working in other areas, however, failed to document the importance of competition, predation, and disturbance.

Use semicolons when commas occur within one or more of the elements of a series. Familiar examples of species that are extremely vulnerable to human activity are the northern spotted owl, threatened by logging of old-growth forests in the Pacific Northwest; the red-cocked woodpecker, endangered by logging of longleaf pine forests in the Southeastern Coastal plain; and the desert tortoise, often shot or run over by motorized recreationists.

Three cities I will visit are Madison, Wisconsin; Northfield, Minnesota; and Chicago, Illinois.

Use colons to introduce a part of a sentence that expands or clarifies the meaning of what precedes it. The instructor expects the following students to complete their lab reports early: Anna, Dmitry, Jaafar, and Darla.

Quotation Marks Place a comma or period inside the quotation marks whether or not it is part of the quotation; place punctuation other than a comma or period outside the quotation marks unless the punctuation is part of the quotation. We don't label data as "good" or "bad"; however, we can label them "surprising."

18 Parentheses Use parentheses (these things) sparingly. If the words you are enclosing within a parenthesis are not important enough to be included in the sentence, they may be superfluous. Use parentheses for comments or explanations that are independent of the sentence. Solar energy is the basis of virtually all food chains (rare exceptions include chemically based communities in deep-sea vents) and is converted to chemical energy by photosynthetic plants.

Use parentheses to enclose abbreviations and acronyms after they are spelled out. The Global Biodiversity Strategy (GBS) was developed by the World Resources Institute (WRI) and the United Nations Environmental Program (UNEP).

Underlining and Italics Italicizing and underlining are used for the same purposes. Italics are preferred and are easy to do with a computer. Italicize the titles of books and periodicals. Curt found the article in the journal Ecology.

Italicize a genus or species name (and capitalize the genus name). Poison ivy (Toxicodendron radicans) produces a secondary compound which causes an irritating rash on the skin of many people.

Italicize foreign words and abbreviations based on them (e.g., the abbreviation e.g.)

Dangling Participles Participles are verb forms having qualities of both verb and adjective. In the present tense, participles frequently end in -ing (asking); in the past tense, participles commonly end in -en or -ed (asked, spoken). Dangling participles are participles (often acting as adjectives) that modify the "wrong" noun. POOR: A bubble was observed in the jar using a magnifying glass. (The jar is not really using a magnifying glass!) BETTER: We used a magnifying glass to observe a bubble in the jar.

Abbreviations, Acronyms, Numbers Write out a term the first time before abbreviating it. The enzyme isocitrate dehydrogenase (IDH) catalyzes the oxidation of...

Express numbers as figures; do not write out the number name. A sentence, however, should never begin with a figure. Twenty-two gazelles ran past me. Next I counted 10 antelope.

8. References on Writing Starred references are particularly recommended. Booth, V. 1993. Communicating in science: writing a scientific paper and speaking at scientific meetings, 2nd ed. Cambridge University Press, Cambridge, U.K.

CBE Style Manual Committee. 1983. CBE style manual: a guide for authors, editors, and publishers in the biological sciences, 5th ed. Council of Biology Editors, Inc., Bethesda.

*Day, R.A. 1994. How to write and publish a scientific paper, 4th ed. Oryx press, Phoenix.

Kuyper, B.J. 1991. Bringing up scientists in the art of critiquing research. Bioscience 41: 248-250.

*Lertzman, K. 1995. Notes on writing papers and theses. Bulletin of the Ecological Society of America 76: 86-90.

McMillan, V.E. 1988. Writing papers in the biological sciences. St. Martin's Press, New York.

Pechenik, J.A. 1993. A short guide to writing about biology, 2nd ed. Harper Collins, New York.

19 Strunk, W.I. and White, E.B. 1979. The elements of style, 3rd ed., Macmillan, New York.

*Turabian, K.L. 1987. A manual for writers of term papers, theses, and dissertations, 5th ed. University of Chicago Press, Chicago.

Weston, A. 1992. A Rulebook for arguments, 2nd ed., Hackett, Indianapolis.

Zinsser, W. 1988. Writing to learn. Harper and Row, New York

9. Data Analysis and Statistics Primer

Data Types There are two main types of quantitative data most often collected by biologists: discrete data and continuous data. Discrete data are counted; the units are separate items, e.g., the number of leaves on a plant or the number of cells in the field of view on a microscope slide. Continuous data are measured and the units of measurement can be infinitely subdivided (at least to the resolution of the measuring instrument), e.g., length, weight, time. For example the length of the wings of the cardinals found in a field could be measured to the nearest 1 mm, 0.1 mm, 0.01 mm, etc. The type of data influences the kind of analysis and the presentation that is most appropriate.

Sampling In most cases, we actually measure (sample) only a small part of the population we want to know about and then use what we find as estimates of the true parameters in the population. To get good estimates of population parameters, the sample should be of sufficient size and should be representative of the population.

From Sample to Population: the Need for Statistics Most of the data that we will be working with this semester tend to cluster around a central tendency. Suppose, for example, that we want to know the average stem length of red clover growing in a particular field. If we randomly select and measure a large number of plants and plot a histogram of the values, we find a bell-shaped curve called the normal distribution.

20 250

Number of Plants 50

0 0 3 6 9 12 15 18 21 24 27 30 Stem Length (cm)

Figure 1: Frequency distribution of the stem lengths of a large, random sample (n=2128) of red clover (Trifolium pratense) in July 1999.

Two of the most useful measures for characterizing data from a sample are an indication of the central tendency and an indication of the dispersion of the data. Measures of the central tendency are the mean (average value), mode (most common value), and median (value at which half are greater and half are smaller). Locate these on Figure 1 above. The mean is given by summing each individual value (x1, x2, x3, ....xi) and dividing by n, the number individuals or samples measured. Mean =

One way to characterize the dispersion of the data is to give the range (spread from lowest to highest). The problem with using the range as a measure of dispersion is that it increases as we include more samples; furthermore, it tells us nothing about the average variation. We can't simply average the deviations from the mean because the deviations in the negative direction exactly cancel out the deviations in the positive direction and we end up with zero. We can, however, add up the squares of the deviations. This gives the variance (s2).

We would like to be able to use data from our samples to make inferences about the population from which the samples were taken. The squared deviations are divided by n-1, rather than n, because dividing by n tends to underestimate the population variance when the sample size is small (e.g., less than 30).

Think about what the variance tells you compared with what the range tells you.

One problem with variance is that its units don't make sense (e.g., [beats/min.]2 for heart rate). It is more common to use the square root of the variance, known as the standard deviation. You can think of the standard deviation as the average amount of individual deviation from the mean. To determine the standard deviation, square each individual difference from the mean, sum these, divide by n-1, and then take the square root to compensate for the previous squaring. Standard deviation =

For measurements that follow the normal distribution, 68% of all the observations lie within the range covered by one standard deviation on either side of the mean (i.e., the mean  1 SD). 95% of the observations lie within 2 SD of the mean. Practically all (99.7%) of the observations lie within 3 SD of the mean.

21 The standard deviation tells us the variation among our samples; it does not allow us to compare 2 populations. For that we need to determine the standard error of the mean (see below).

Suppose that we measure many sets of samples from our population and calculate the mean for each set. These means will not be identical but will cluster around the average for the whole population. In fact, the means also show the bell-shaped pattern called the normal distribution. It should make sense to you that the amount of variation (dispersion) of the means of the sample values will not be as great as the dispersion of the sample values themselves. The standard deviation of the set of means is called the standard error of the mean. Standard errors are usually not obtained from a frequency distribution by repeated sampling but are estimated from only a single sample and represent the expected standard deviation for a large number of repeated samples. Usually, we do not have many sets of means, just one. Therefore, we calculate the standard error of the mean by dividing the standard deviation by . Standard error of the mean = The beauty of the standard error of the mean is that it tells us a great deal about the population we are studying. The standard error of the mean allows us to determine, with a certain probability, the limiting values between which the "true" value of the population lies. For a sample of reasonable size (e.g., 30 or more) that follows the normal distribution, the 95% confidence level is . This says that there is a 95% chance that the true mean of the population is within these limits. (1.96 is often rounded to 2). In order to be able to say that two populations are different, the limiting values between which the "true" value of the population lies cannot overlap.

Accuracy and Precision Since every measurement has some error, it is only an approximation to the true value. The accuracy of a measurement reflects how close the measurement is to the true value. The precision of a measurement indicates how well several determinations of the same quantity agree, i.e., the repeatability of the measurements. This is illustrated by the figure below.

Set 1 Set 2 Figure 2. Two hypotheticalLower setsprecision, of measurements Higherdemonstrating precision, the difference between accuracy and precision. The "true" highervalue isaccuracy indicated by the heavylower line. accuracy

As we sample the vegetation in the wetland and the prairie site, we want our data to be both accurate and precise. However, if time and resources are limited - as they usually are - and we have to make compromises, we are willing to sacrifice precision in order to increase accuracy. In this case, we increase accuracy by increasing the number of samples. The more variable the population, the more measurements it takes to get a good mean. It is better to measure more samples than to spend time agonizing over whether one particular plant is in or out of the quadrat or whether a shrub measures 1.7 or 1.8 meters on the tape.

Comparing Populations Sometimes we want to know whether two populations are the same or different. For example, suppose that we treat different parts of our site in two different ways (mowing and tilling) and then one year later compare the density of thistles in the two parts by sampling a large number of quadrats. Suppose we find that the average thistle density for plots treated in the two ways is different. How do we know whether the difference we observe is due to the treatments or simply to random variation in the samples we happened to measure? We cannot know for sure! All we can do is use statistical methods to calculate the probability of getting a difference this large by chance. (What we actually do is to compare the variation within each set of samples to the variation between the two sets. The standard error of the sample

22 means is very important in these comparisons.) If the probability is very low, this suggests (but does not prove) that the two sets of samples are likely to represent two different populations. We still cannot be absolutely sure that the difference is due to the treatments because we do not know for sure that our experimental design compensated for other possible causes for this difference.

Chi-Square Analysis

Scientists often propose models and then do experiments (in this case genetic crosses) to see whether the world functions in a way consistent with the models. They gather data and compare them with the results predicted by the hypothesis. While it is not possible for experimental results to prove that a particular model is correct, results that differ significantly from those predicted can cause us to reject the model. But what is meant by "differ significantly?" How far from predictions can the data be before it is necessary to reject the model? Chance can also cause results to differ from expectations, particularly when the sample size is small.

There is no method that will tell us for sure whether a deviation is the result of chance alone. However, there are statistical tests that allow us to set some confidence limits. The chi-squared (X2) test is a method commonly used in analyzing genetic crosses. It tells us the probability of getting results that deviate from expectations by as much as we have observed by chance alone, if the model is correct.

To perform the chi-squared test, the first step is to compare the numbers of individuals observed in each category with the numbers expected given the sample size and the proposed model. Note that numbers of individuals, not ratios, are used. (X2 takes the sample size into account.) The deviations are squared and then divided by the expected values, giving the chi-squared value.

X2 = the sum over all classes of (observed - expected)2 expected X2 = (O - E) 2 E

The next step is to determine the degrees of freedom. The degrees of freedom is the number of independently variable classes that exist. Usually, this is equal to one less than the total number of classes. For example, if there are two classes, colored and colorless, only one of them is independently variable: once we know the number of colored kernels for a particular sample size, we also know the number of colorless kernels. Therefore, the degrees of freedom in this example is one.

The final step in the application of the chi-squared test is to look up the calculated chi-squared value and the degrees of freedom on a chart such as the one below and determine the probability value. This value is the probability that chance alone could account for a deviation as large or larger than that observed, if the hypothesis is correct. If the probability is high, the data are considered to be in agreement with the model. (Note that this does not prove that the model is correct, it merely fails to offer evidence against it.) If the probability is low, the deviation most likely is not due to chance and the data do not support the model.

We have to decide how low a probability we will accept before rejecting the model. Usually, the confidence level chosen is 5%. If the probability is less than 0.05, the difference is considered to be "significant," and if it is less than 0.01, it is considered to be "highly significant." Probabilities in these ranges usually cause us to reject our model. (However, continuing to reject hypotheses at the 5% level means that we will reject correct a hypothesis 5% of the time.)

An example is presented on the next page.

Example: Chi-Squared Test for a Dihybrid Cross Model: Two unlinked autosomal genes that affect seed characteristics, two alleles at each locus, complete dominance in both cases Degrees of Freedom: 3 Data for F2 Generation

23 (O - E) 2 Phenotype Observed Expected E 9 (400) Round, Yellow 218 16 = 225 0.22 3 (400) Wrinkled, Yellow 80 16 = 75 0.33 3 (400) Round, Green 72 16 = 75 0.12 1 (400) Wrinkled, Green 30 16 = 25 1.00

Totals 400 ∑ = 1.67 Probability (from the chart below) = 0.64. Deviations as great as this or greater would be expected by chance 64% of the time. Therefore, we do not reject the model.

Chart of X2 To use the chart, place a ruler perpendicular to the x axis at the calculated value of X2 and note where it intersects the appropriate degrees of freedom curve (N). Then read the probability at this point from the y axis at the left of the chart.

References for Further Reading Rowntree, D. 1981. Statistics without Tears: A Primer for Non-mathematicians, Charles Scribner's Sons, New York. Cochran, W. G. and Cox, G. M. 1957. Experimental Designs, John Wiley & Sons, New York.

24 10. Producing Figures using Microsoft Excel

Bar Graphs or Line Graphs

 Enter labels for each condition into cells along a row  Below each label in a column, type in the grouping or mean for that condition  If you have calculated a measure of variation (standard deviation or standard error) enter the values in a separate column..  Highlight the block of cells that includes all labels and means  Click the “Chart Wizard” button or select “Chart or Line” from the “Insert” menu  Select the vertical “column” graph; avoid using three dimensional graphs, they are generally more difficult to read  Click ‘next’  Under the “Titles” tab, type in labels to the x and y axes (remember not to title the chart)  Under the “Gridlines” tab, turn off “Major gridlines” unless gridlines are helpful for interpretation  Under the “Legend” tab, turn off “Show legend,” then click “Finish”  Double-click on one of the numbers on the “Value axis” (y-axis), then go to “Scale” and enter an appropriate “minimum” and “maximum” value, plus a “major unit” that will divide the scale into a nice set of numbered tick marks.. If your data includes zero points that lie along the X or Y axis rescale your axis to go into the negative range so the zero points can be visualized.  Double clicking on any element of the graph to view a dialog box for reformatting or customizing the format of your graph.

Creating Standard Errors Bars in Excel  Generate your column of means and create your figure graph.  Within the graph, double click on the series you want to add error bars (each bar of the series-- not one bar should be highlighted).  A dialog box should appear from which you select ‘y-errors’ followed by ‘custom’.  With the dialog box open but to the side of your spreadsheet (you can move the dialog box around without closing it by dragging it from the top bar/edge of the box) go to a separate column in your spreadsheet in which you have already entered the standard errors. Highlight these numbers (e.g. if you have 3 histogram. bars in a series or three points, there should be  Three standard errors in the same rows as each of those bars/points)  The highlighted cells containing your standard errors will then appear in the custom area of the diaglog box.  Press return and the standard errors should display correctly on your graph.  To do a second series, repeat the procedure.