Basic Skills: Simple Comparative Experiments (AP Statistics) One major goal of this course is learn how to design an experiment that will allow us to determine the effects of the relevant factors on the chosen response variable. Some of the key skills in designing a good experiment include the following: Being able to carefully describe what it is that the experiment is supposed to measure. Being able to think up and clearly define explanatory variables that might have a real relationship to the quantity that the experiment is trying to measure. Being able to locate and describe any extraneous factors that might bias the result of the experiment. Being able to minimize the effects of extraneous factors that might otherwise bias the experiment resulting in measurements far away from the true value of quantity that the experiment was trying to measure. Being able to honestly and objectively analyze the results of the experiment. Being able to express either how the results fit into (or change) any overarching theory, or what a given theory would suggest as a follow up experiment. Discussions - What is an experiment and what is the goal of experiment? What is the difference between an experiment and an observational study? Definition – An experiment is a planned intervention undertaken to observe the effects of one or more independent variables on a dependent variable which is the quantity that the experiment is trying to measure. Definition – The independent variables in the experiment are often called explanatory variables or factors Definition – The dependent variable, or the variable that the experiment is trying to measure is called a response variable. Definition – Any particular combination of values for the explanatory variable is called an experimental condition or treatment. Definition – The design of an experiment is the overall plan for conducting an experiment. A good design minimizes ambiguity in the interpretation of the results. Example Experiment Consider the following example: A student wants to measure how E. Coli grows in time when differing levels of sugar are added to a culture containing E. Coli. Describing the quantity the experiment is supposed to measure… One important piece of information you should include when describing the experiment is a description of the quantity that you want to measure. The description needs to be as precise as possible. One way to make a description more precise is to include the units for the quantity that you want to measure. In the example experiment the quantity the student want to measure is ‘how E. Coli grows in time’. The quantity stated this way seems a little vague. A better statement might be ‘A student wants to measure the size of an E. Coli population in a culture over time. She will measure the number of E. Coli cells in a culture every hour’. Here the units are simply ‘number of E. Coli cells each hour’. Clearly defining explanatory variables… Precise descriptions are also important when defining explanatory variables. Units can also help here to make a description more precise or clear. In the example experiment the quantity that the student wishes to vary is the amount of sugar that she uses. The goal is to see whether the amount of sugar alters the growth (rate) of the E. Coli in the culture in any way. The units she might use should be appropriate to the experiment. It is unlikely that she will use pounds of sugar. More likely she would use grams of sugar to measure the explanatory variables. Note that any formal relationship (or formula) relating the explanatory variables with the response variable should have the same units on either side of the equation. What you want to avoid (extraneous factors and confounded variables)… Definition – An extraneous factor is one that is not of interest in the current study but is thought to affect the response variable. Definition – Two factors are confounded if their effects on the response variable cannot be distinguished from one another. In every experiment it is important to identify the extraneous variables that might bias the experiment. In the example experiment some extraneous variables might include the following: Temperature (some bacteria grow faster in warmer temperatures and some temperatures prevent the growth of some bacteria) Other bacteria in the culture (another bacteria in the culture might prevent the growth of the desired bacteria) Brand of sugar (different sugars might alter the growth patterns of the E. Coli) Type of E. Coli (different strains o E. Coli might react differently from each other) Size of Petri dish (the size of the Petri dish might limit growth) Air condition or other source of food in the air (the condition of the air might limit or alter the growth of the bacteria) Light (light might alter the temperature in different parts of the room) Basic techniques that help minimize the affects of extraneous factors and confounded variables… Randomizing is the process of randomly assigning test subjects to experimental groups. The reason for using randomization is to control extraneous factors in a population that an experimenter cannot directly control. The hopeful result of randomization is to ensure that the experiment does not favor one experimental condition over any other and attempts to create ‘equivalent’ experimental groups or groups that are as much alike as possible. In the example experiment air quality might be an extraneous variable that randomizing might help to minimize. It is hard to control the air quality in the room, especially if it has pathogens harmful to E. Coli. Pathogens might also only congregate in certain portions of the room and so making sure the experiment happens in different parts of the room would randomize the effects of air quality on the experiment. Blocking is the process of creating groups that are similar with respect to a specific extraneous factor called a blocking factor. What this means is that a blocking factor often creates different categories within the sample population. What blocking does is make sure that each of these different categories shows up in each tested sample. The result being that different categories created by the blocking factors are tested side by side in the same test so that the blocking factor cannot bias the result of the experiment. In the example experiment the different strains of E. Coli might grow in differing ways. The different strains would be the blocking factor and so each sample would have to include different strains of E. Coli. Then the different strains will be tested in different Petri dishes, but two or more types might show up in a sample. This would allow the student to make generalizations about E. Coli as a whole. Another example of a blocking factor in the example experiment might be different brands of sugar. If the student was only testing one strain of E. Coli she might distribute different brands of sugar randomly (but well recorded) in a given sample. This would allow the student to generalize the results to most sugars instead of a specific brand. Direct Control is the process of holding extraneous variables constant so that their effects are not confounded with those of the experimental conditions. In the example experiment an example of an extraneous variable that might be subject to direct control might be the temperature nearby and in each Petri dish. Temperature surrounding a culture is relatively easy to control, at least to within a few degrees. Having the temperature held constant would eliminate any chance that temperature could affect the growth of the bacteria. Although to high of a temperature might inhibit the growth of the bacteria so Temperature might also be a good variable to randomize. Replication is the process of repeating an experiment to make sure that the results from an experiment are repeatable. One can often learn something form an experiment if after repeating the experiment the results are completely different each time. The goal of replication is often to reduce the chance of overlooking the possibility that results might change from experiment to experiment. Every experiment can benefit from repeated trials in order to show that the results of one sample were not some sort of fluke. Every time someone repeats an experiment and achieves similar results to the other attempts at the experiment the result becomes less uncertain. Other factors that might affect the design or result of an experiment… Here are some other things to keep in mind that can have an affect on the design or the result of an experiment: The cause/reason for designing the experiment in the first place Rival theories (any competing theories that might pose competition or help in making an experiment more clear) Different methods of measuring the same quantity. Historical context (is the experiment a ‘trendy’ experiment or are there trends influencing the need for the experiment) environmental context experimenters’ bias (any preconceived notions that the experimenters bring with them to the experiment) budgetary biases institutional biases cultural biases Note: These are all ideas meant to locate extraneous factors that might affect the results of the experiment An easy way to keep track of the experimenter’s bias is to make sure that they provide an hypothesis with a detailed explanation of why they think that result will occur. But not only should experimenters include their hypothesis of what they think should happen, but what they secretly hope happens and why. Follow up questions to ensure a certain degree of thoroughness… What is the research question that data from the experiment will be used to answer? What is the response variable? How will the values of the response variable be determined? What are the factors (explanatory variables) for the experiment? For each factor, how many different values are there, and what are these values? What extraneous variables might influence the response?
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