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The Scientific Method: Hypothesis Testing and Experimental Design

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The Scientific Method: Hypothesis Testing and Experimental Design Appendix I The Scientific Method The study of science is different from other disciplines in many ways. Perhaps the most important aspect of “hard” science is its adherence to the principle of the scientific method: the posing of questions and the use of rigorous methods to answer those questions. I. Our Friend, the Null Hypothesis As a science major, you are probably no stranger to curiosity. It is the beginning of all scientific discovery. As you walk through the campus arboretum, you might wonder, “Why are trees green?” As you observe your peers in social groups at the cafeteria, you might ask yourself, “What subtle kinds of body language are those people using to communicate?” As you read an article about a new drug which promises to be an effective treatment for male pattern baldness, you think, “But how do they know it will work?” Asking such questions is the first step towards hypothesis formation. A scientific investigator does not begin the study of a biological phenomenon in a vacuum. If an investigator observes something interesting, s/he first asks a question about it, and then uses inductive reasoning (from the specific to the general) to generate an hypothesis based upon a logical set of expectations. To test the hypothesis, the investigator systematically collects data, either with field observations or a series of carefully designed experiments. By analyzing the data, the investigator uses deductive reasoning (from the general to the specific) to state a second hypothesis (it may be the same as or different from the original) about the observations. Further experiments and observations either refute or support this second hypothesis, and if enough data exist, the hypothesis may eventually become a theory, or generally accepted scientific principle. Proper scientific method requires that the investigator state his/her hypothesis in negative terms, forming a null hypothesis (Ho) concerning the expected results of the study. The null hypothesis states the expected results by predicting that there will be no difference between the test groups. For example, if a pharmaceutical company is attempting to test a new weight loss drug (Fat-B-Gontm), its scientific investigators might put forth a null hypothesis stating: "There is no difference in the rate of weight loss between members of the population who use Fat-B-Gontm and those who do not use Fat-B-Gontm" A second hypothesis, the alternative hypothesis (Ha), states the exact opposite of the null hypothesis. Ha is, of course, the hypothesis of interest: "There is a difference in the rate of weight loss between members of the population who use Fat-B-Gontm and those who do not use Fat-B-Gontm." By stating the question as a null hypothesis, the investigator allows much less ambiguity in accepting or rejecting one or the other hypothesis. Once the null hypothesis is rejected, the alternative hypothesis becomes subject to greater scrutiny and further testing. Note that the null hypothesis does not necessarily state that people who don’t use Fat-B-Gontm are less likely to lose weight! It states only that there is no difference AI-1 between the groups being compared. Such an hypothesis, which does not predict a direction in which the data might deviate from the expected (e.g., "higher" or "lower") is called a two-tailed hypothesis (it can “go either way”). Similarly, the alternate hypothesis does not state whether Fat-B-Gontm users are more or less likely to lose weight. It simply says there is a difference. The analyzed data will suggest the direction (i.e. "higher," "lower," "less likely," "more likely") of the alternate hypothesis. In some situations, it is of great interest to determine the direction in which observed results deviate from the expected. In this case, one should design a one- tailed hypothesis. It is more difficult to reject a one-tailed hypothesis than a two-tailed hypothesis, as you will learn when we analyze probabilities. Statistical formulas specially designed to test one- and two-tailed hypotheses do exist, but they are beyond the scope of this appendix. Before you begin any experiment in this laboratory, you must formulate a null hypothesis pertaining to your experimental groups. If you are writing a report on your experiment, the null hypothesis should be stated in the INTRODUCTION of your report. II. Experimental Design To test the null hypothesis, the investigators design an experiment. In the Fat-B- Gontm example, they will hire a group of volunteers to serve as experimental subjects. These will be divided into treatment and the control groups. In a properly designed experiment, the treatment and control groups must be subjected to exactly the same physical conditions with the exception of a single variable. Both groups must be carefully monitored, their food intake and physical activity rigorously controlled. Along with their daily rations, the treatment group will receive a dose of Fat-B-Gontm, whereas the control group will receive a dose of a placebo--an inert substance administered in exactly the same way as the Fat-B-Gontm and cannot be physically distinguished from it. The subjects should not know whether they are in the treatment or control group (a single-blind study), and in some cases, not even the investigators know which subjects are in the treatment and control groups (a double-blind study). Thus, the only difference between the treatment and control groups is the presence or absence of a single variable, in this case, Fat-B- Gontm. Such rigor reduces the influence of confounding effects, uncontrolled differences between the two groups that could affect the results. Over the course of the experiment, the investigators measure weight changes in each individual of both groups (Table A1-1). Because they cannot control for the obvious confounding effect of genetic differences in metabolism, the investigators must try to reduce the influence of that effect by using a large sample size--as many experimental subjects as possible--so that there will be a wide variety of metabolic types in both the treatment and control groups. It is a general rule that the larger the sample size, the closer the approximation of the statistic to the actual parameter. Even so, it is never wise to completely ignore the possibility of confounding effects. Honest investigators should mention them when reporting their findings. AI-2 Table A1-1. Change in weight (x) of subjects given Fat-B-Gontm (treatment) and placebo (control) food supplements over the course of one month. All weight changes were negative (weight loss). Mean weight change (x), the square of each data point (x2) and the squared deviation from the mean (x - x)2 are included for later statistical analysis. control weight ( weight (x - x)2 treatment weight ( weight (x - x)2 subjects (kg) (= x) (= x2) subjects (kg) (= x) (= x2) 1 19.36 0.12 11 121.00 13.40 2 36.69 2.43 12 30.25 3.39 3 1.44 12.53 13 38.44 1.30 4 54.76 7.07 14 82.81 3.10 5 36.00 1.59 15 65.61 0.58 6 16.81 0.41 16 36.00 1.80 7 27.04 0.21 17 67.24 0.74 8 9.61 2.69 18 25.00 5.47 9 17.64 0.29 19 51.84 0.02 10 30.25 0.58 20 50.41 0.06 total ( ) 249.6 27.92 total ( ) 73.4 568.60 29.86 x=4.74) (= x2) (= (x-x)2) (x = 7.34) (= x2) (= (x-x)2) III. Data, parameters and statistics Most investigations in the biological sciences today are quantitative. The investigator's goal is to collect biological observations which can be tabulated as numerical facts, also known as data (singular = datum). Biological research can yield several different types of data: 1. Attribute data. This simplest type consists of descriptive, "either-or" measurements, and usually describe the presence or absence of a particular attribute. The presence or absence of a genetic trait ("freckles" or "no freckles") or the type of genetic trait (type A, B, AB or o blood) are examples. Because this type of data has no specific sequence, it is considered unordered data. 2. Discrete numerical data. These data correspond to biological observations which are counted, and are integers (whole numbers). The number of leaves on each member of a group of plants, the number of breaths per minute in a group of newborns or the number of beetles per square meter of forest floor are all examples of numerical discrete data. Although these data are ordered, they do not describe physical attributes of the things being counted. 3. Continuous numerical data. The most quantitative data fall along a numerical continuum. The limit of resolution of such data is the accuracy of the methods and instruments used to collect them. Examples of continuous numerical data are tail length, brain volume, percent body fat...anything that varies on a continuous scale. Rates (such as decomposition of hydrogen peroxide per minute or uptake of oxygen during respiration over the course of an hour) are also numerical continuous data. When you perform an experiment, be sure to determine which type of data you are collecting. The type of statistical test appropriate in any given situation depends upon the type of data! When an investigator collects numerical data from a group of subjects, s/he must determine how and with what frequency the data vary. For example, if one wished to AI-3 study the distribution of shoe size in the human population, one might measure the shoe size of a sample of the human population (say, 50 individuals) and graph the numbers with "shoe size" on the x-axis and "number of individuals" on the y-axis.
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