26.5: Possible Theoretical and Practical Issues with Discussed Approach - Biology

26.5: Possible Theoretical and Practical Issues with Discussed Approach - Biology

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A special point must be made about distances. Therefore, there are some algorithms that try to take into account less conserved genes in reconstructing trees but these algorithms tend to take a long time due to the NP-Hard nature of reconstructing trees.

Additionally, aligned sequences are still not explicit in regards to the events that created them. That is, combinations of speciation, duplication, loss, and horizontal gene transfer (hgt) events are easy to mix up because only current DNA sequences are available. (see [11] for a commentary on such theoretical issues) A duplication followed by a loss would be very hard to detect. Additionally, a duplication followed by a speciation could look like an HGT event. Even the probabilities of events happening is still contested, especially horizontal gene transfer events.

Another issue is that often multiple marker sequences are concatenated and the concatenated sequence is used to calculate distance and create trees. However, this approach assumes that all the concatenated genes had the same history and there is debate over if this is a valid approach given that events such as hgt and duplications as described above could have occurred differently for different genes. [8] is an article showing how different phylogenetic relationships were found depending on if the tree was created using multiple genes concatenated together or if it was created using each of the individual genes. Conversely, additional [4] claims that while hgt is prevalent, orthologs used for phylogenetic reconstruction are consistent with a single tree of life. These two issues indicate that there is clearly debate in the field on a non arbitrary way to define species and to infer phylogenetic relationships to recreate the tree of life.

26.5: Possible Theoretical and Practical Issues with Discussed Approach - Biology

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1.1 The Science of Biology

In this section, you will explore the following questions:

  • What are the characteristics shared by the natural sciences?
  • What are the steps of the scientific method?

Connection for AP ® courses

Biology is the science that studies living organisms and their interactions with one another and with their environment. The process of science attempts to describe and understand the nature of the universe by rational means. Science has many fields those fields related to the physical world, including biology, are considered natural sciences. All of the natural sciences follow the laws of chemistry and physics. For example, when studying biology, you must remember living organisms obey the laws of thermodynamics while using free energy and matter from the environment to carry out life processes that are explored in later chapters, such as metabolism and reproduction.

Two types of logical reasoning are used in science: inductive reasoning and deductive reasoning. Inductive reasoning uses particular results to produce general scientific principles. Deductive reasoning uses logical thinking to predict results by applying scientific principles or practices. The scientific method is a step-by-step process that consists of: making observations, defining a problem, posing hypotheses, testing these hypotheses by designing and conducting investigations, and drawing conclusions from data and results. Scientists then communicate their results to the scientific community. Scientific theories are subject to revision as new information is collected.

The content presented in this section supports the Learning Objectives outlined in Big Idea 2 of the AP ® Biology Curriculum Framework. The Learning Objectives merge Essential Knowledge content with one or more of the seven Science Practices. These objectives provide a transparent foundation for the AP ® Biology course, along with inquiry-based laboratory experiences, instructional activities, and AP ® Exam questions.

Big Idea 2 Biological systems utilize free energy and molecular building blocks to grow, to reproduce, and to maintain dynamic homeostasis.
Enduring Understanding 2.A Growth, reproduction and maintenance of living systems require free energy and matter.
Essential Knowledge 2.A.1 All living systems require constant input of free energy.
Science Practice 6.4 The student can make claims and predictions about natural phenomena based on scientific theories and models
Learning Objectives 2.3 The student is able to predict how changes in free energy availability affect organisms, populations and ecosystems.

Teacher Support

Illustrate uses of the scientific method in class. Divide students in groups of four or five and ask them to design experiments to test the existence of connections they have wondered about. Help them decide if they have a working hypothesis that can be tested and falsified. Give examples of hypotheses that are not falsifiable because they are based on subjective assessments. They are neither observable nor measurable. For example, birds like classical music is based on a subjective assessment. Ask if this hypothesis can be modified to become a testable hypothesis. Stress the need for controls and provide examples such as the use of placebos in pharmacology.

Biology is not a collection of facts to be memorized. Biological systems follow the law of physics and chemistry. Give as an example gas laws in chemistry and respiration physiology. Many students come with a 19th century view of natural sciences each discipline is in its own sphere. Give as an example, bioinformatics which uses organism biology, chemistry, and physics to label DNA with light emitting reporter molecules (Next Generation sequencing). These molecules can then be scanned by light-sensing machinery, allowing huge amounts of information to be gathered on their DNA. Bring to their attention the fact that the analysis of these data is an application of mathematics and computer science.

For more information about next generation sequencing, check out this informative review.

What is biology? In simple terms, biology is the study of life. This is a very broad definition because the scope of biology is vast. Biologists may study anything from the microscopic or submicroscopic view of a cell to ecosystems and the whole living planet (Figure 1.2). Listening to the daily news, you will quickly realize how many aspects of biology are discussed every day. For example, recent news topics include Escherichia coli (Figure 1.3) outbreaks in spinach and Salmonella contamination in peanut butter. On a global scale, many researchers are committed to finding ways to protect the planet, solve environmental issues, and reduce the effects of climate change. All of these diverse endeavors are related to different facets of the discipline of biology.

The Process of Science

Biology is a science, but what exactly is science? What does the study of biology share with other scientific disciplines? Science (from the Latin scientia, meaning “knowledge”) can be defined as knowledge that covers general truths or the operation of general laws, especially when acquired and tested by the scientific method. It becomes clear from this definition that the application of the scientific method plays a major role in science. The scientific method is a method of research with defined steps that include experiments and careful observation.

The steps of the scientific method will be examined in detail later, but one of the most important aspects of this method is the testing of hypotheses by means of repeatable experiments. A hypothesis is a suggested explanation for an event, which can be tested. Although using the scientific method is inherent to science, it is inadequate in determining what science is. This is because it is relatively easy to apply the scientific method to disciplines such as physics and chemistry, but when it comes to disciplines like archaeology, psychology, and geology, the scientific method becomes less applicable as it becomes more difficult to repeat experiments.

These areas of study are still sciences, however. Consider archaeology—even though one cannot perform repeatable experiments, hypotheses may still be supported. For instance, an archaeologist can hypothesize that an ancient culture existed based on finding a piece of pottery. Further hypotheses could be made about various characteristics of this culture, and these hypotheses may be found to be correct or false through continued support or contradictions from other findings. A hypothesis may become a verified theory. A theory is a tested and confirmed explanation for observations or phenomena. Science may be better defined as fields of study that attempt to comprehend the nature of the universe.

Natural Sciences

What would you expect to see in a museum of natural sciences? Frogs? Plants? Dinosaur skeletons? Exhibits about how the brain functions? A planetarium? Gems and minerals? Or, maybe all of the above? Science includes such diverse fields as astronomy, biology, computer sciences, geology, logic, physics, chemistry, and mathematics (Figure 1.4). However, those fields of science related to the physical world and its phenomena and processes are considered natural sciences . Thus, a museum of natural sciences might contain any of the items listed above.

There is no complete agreement when it comes to defining what the natural sciences include, however. For some experts, the natural sciences are astronomy, biology, chemistry, earth science, and physics. Other scholars choose to divide natural sciences into life sciences , which study living things and include biology, and physical sciences , which study nonliving matter and include astronomy, geology, physics, and chemistry. Some disciplines such as biophysics and biochemistry build on both life and physical sciences and are interdisciplinary. Natural sciences are sometimes referred to as “hard science” because they rely on the use of quantitative data social sciences that study society and human behavior are more likely to use qualitative assessments to drive investigations and findings.

Not surprisingly, the natural science of biology has many branches or subdisciplines. Cell biologists study cell structure and function, while biologists who study anatomy investigate the structure of an entire organism. Those biologists studying physiology, however, focus on the internal functioning of an organism. Some areas of biology focus on only particular types of living things. For example, botanists explore plants, while zoologists specialize in animals.

Scientific Reasoning

One thing is common to all forms of science: an ultimate goal “to know.” Curiosity and inquiry are the driving forces for the development of science. Scientists seek to understand the world and the way it operates. To do this, they use two methods of logical thinking: inductive reasoning and deductive reasoning.

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. This type of reasoning is common in descriptive science. A life scientist such as a biologist makes observations and records them. These data can be qualitative or quantitative, and the raw data can be supplemented with drawings, pictures, photos, or videos. From many observations, the scientist can infer conclusions (inductions) based on evidence. Inductive reasoning involves formulating generalizations inferred from careful observation and the analysis of a large amount of data. Brain studies provide an example. In this type of research, many live brains are observed while people are doing a specific activity, such as viewing images of food. The part of the brain that “lights up” during this activity is then predicted to be the part controlling the response to the selected stimulus, in this case, images of food. The “lighting up” of the various areas of the brain is caused by excess absorption of radioactive sugar derivatives by active areas of the brain. The resultant increase in radioactivity is observed by a scanner. Then, researchers can stimulate that part of the brain to see if similar responses result.

Deductive reasoning or deduction is the type of logic used in hypothesis-based science. In deductive reason, the pattern of thinking moves in the opposite direction as compared to inductive reasoning. Deductive reasoning is a form of logical thinking that uses a general principle or law to predict specific results. From those general principles, a scientist can deduce and predict the specific results that would be valid as long as the general principles are valid. Studies in climate change can illustrate this type of reasoning. For example, scientists may predict that if the climate becomes warmer in a particular region, then the distribution of plants and animals should change. These predictions have been made and tested, and many such changes have been found, such as the modification of arable areas for agriculture, with change based on temperature averages.

Both types of logical thinking are related to the two main pathways of scientific study: descriptive science and hypothesis-based science. Descriptive (or discovery) science , which is usually inductive, aims to observe, explore, and discover, while hypothesis-based science , which is usually deductive, begins with a specific question or problem and a potential answer or solution that can be tested. The boundary between these two forms of study is often blurred, and most scientific endeavors combine both approaches. The fuzzy boundary becomes apparent when thinking about how easily observation can lead to specific questions. For example, a gentleman in the 1940s observed that the burr seeds that stuck to his clothes and his dog’s fur had a tiny hook structure. On closer inspection, he discovered that the burrs’ gripping device was more reliable than a zipper. He eventually developed a company and produced the hook-and-loop fastener often used on lace-less sneakers and athletic braces. Descriptive science and hypothesis-based science are in continuous dialogue.

The Scientific Method

Biologists study the living world by posing questions about it and seeking science-based responses. This approach is common to other sciences as well and is often referred to as the scientific method. The scientific method was used even in ancient times, but it was first documented by England’s Sir Francis Bacon (1561–1626) (Figure 1.5), who set up inductive methods for scientific inquiry. The scientific method is not exclusively used by biologists but can be applied to almost all fields of study as a logical, rational problem-solving method.

The scientific process typically starts with an observation (often a problem to be solved) that leads to a question. Let’s think about a simple problem that starts with an observation and apply the scientific method to solve the problem. One Monday morning, a student arrives at class and quickly discovers that the classroom is too warm. That is an observation that also describes a problem: the classroom is too warm. The student then asks a question: “Why is the classroom so warm?”

Proposing a Hypothesis

Recall that a hypothesis is a suggested explanation that can be tested. To solve a problem, several hypotheses may be proposed. For example, one hypothesis might be, “The classroom is warm because no one turned on the air conditioning.” But there could be other responses to the question, and therefore other hypotheses may be proposed. A second hypothesis might be, “The classroom is warm because there is a power failure, and so the air conditioning doesn’t work.”

Once a hypothesis has been selected, the student can make a prediction. A prediction is similar to a hypothesis but it typically has the format “If . . . then . . . .” For example, the prediction for the first hypothesis might be, “If the student turns on the air conditioning, then the classroom will no longer be too warm.”

Testing a Hypothesis

A valid hypothesis must be testable. It should also be falsifiable , meaning that it can be disproven by experimental results. Importantly, science does not claim to “prove” anything because scientific understandings are always subject to modification with further information. This step—openness to disproving ideas—is what distinguishes sciences from non-sciences. The presence of the supernatural, for instance, is neither testable nor falsifiable. To test a hypothesis, a researcher will conduct one or more experiments designed to eliminate one or more of the hypotheses. Each experiment will have one or more variables and one or more controls. A variable is any part of the experiment that can vary or change during the experiment. The control group contains every feature of the experimental group except it is not given the manipulation that is hypothesized about. Therefore, if the results of the experimental group differ from the control group, the difference must be due to the hypothesized manipulation, rather than some outside factor. Look for the variables and controls in the examples that follow. To test the first hypothesis, the student would find out if the air conditioning is on. If the air conditioning is turned on but does not work, there should be another reason, and this hypothesis should be rejected. To test the second hypothesis, the student could check if the lights in the classroom are functional. If so, there is no power failure and this hypothesis should be rejected. Each hypothesis should be tested by carrying out appropriate experiments. Be aware that rejecting one hypothesis does not determine whether or not the other hypotheses can be accepted it simply eliminates one hypothesis that is not valid (see this figure). Using the scientific method, the hypotheses that are inconsistent with experimental data are rejected.

While this “warm classroom” example is based on observational results, other hypotheses and experiments might have clearer controls. For instance, a student might attend class on Monday and realize she had difficulty concentrating on the lecture. One observation to explain this occurrence might be, “When I eat breakfast before class, I am better able to pay attention.” The student could then design an experiment with a control to test this hypothesis.

In hypothesis-based science, specific results are predicted from a general premise. This type of reasoning is called deductive reasoning: deduction proceeds from the general to the particular. But the reverse of the process is also possible: sometimes, scientists reach a general conclusion from a number of specific observations. This type of reasoning is called inductive reasoning, and it proceeds from the particular to the general. Inductive and deductive reasoning are often used in tandem to advance scientific knowledge (see this figure). In recent years a new approach of testing hypotheses has developed as a result of an exponential growth of data deposited in various databases. Using computer algorithms and statistical analyses of data in databases, a new field of so-called "data research" (also referred to as "in silico" research) provides new methods of data analyses and their interpretation. This will increase the demand for specialists in both biology and computer science, a promising career opportunity.

Science Practice Connection for AP® Courses

Think About It

Almost all plants use water, carbon dioxide, and energy from the sun to make sugars. Think about what would happen to plants that don’t have sunlight as an energy source or sufficient water. What would happen to organisms that depend on those plants for their own survival?

Make a prediction about what would happen to the organisms living in a rain forest if 50% of its trees were destroyed. How would you test your prediction?

Teacher Support

Use this example as a model to make predictions. Emphasize there is no rigid scientific method scheme. Active science is a combination of observations and measurement. Offer the example of ecology where the conventional scientific method is not always applicable because researchers cannot always set experiments in a laboratory and control all the variables.

Possible answers:

Destruction of the rain forest affects the trees, the animals which feed on the vegetation, take shelter on the trees, and large predators which feed on smaller animals. Furthermore, because the trees positively affect rain through massive evaporation and condensation of water vapor, drought follows deforestation.

Tell students a similar experiment on a grand scale may have happened in the past and introduce the next activity “What killed the dinosaurs?”

Some predictions can be made and later observations can support or disprove the prediction.

Ask, “what killed the dinosaurs?” Explain many scientists point to a massive asteroid crashing in the Yucatan peninsula in Mexico. One of the effects was the creation of smoke clouds and debris that blocked the Sun, stamped out many plants and, consequently, brought mass extinction. As is common in the scientific community, many other researchers offer divergent explanations.

Go to this site for a good example of the complexity of scientific method and scientific debate.

Visual Connection

In the example below, the scientific method is used to solve an everyday problem. Order the scientific method steps (numbered items) with the process of solving the everyday problem (lettered items). Based on the results of the experiment, is the hypothesis correct? If it is incorrect, propose some alternative hypotheses.

Scientific Method Everyday process
1 Observation A There is something wrong with the electrical outlet.
2 Question B If something is wrong with the outlet, my coffeemaker also won’t work when plugged into it.
3 Hypothesis (answer) C My toaster doesn’t toast my bread.
4 Prediction D I plug my coffee maker into the outlet.
5 Experiment E My coffeemaker works.
6 Result F What is preventing my toaster from working?
  1. The original hypothesis is correct. There is something wrong with the electrical outlet and therefore the toaster doesn’t work.
  2. The original hypothesis is incorrect. Alternative hypothesis includes that toaster wasn’t turned on.
  3. The original hypothesis is correct. The coffee maker and the toaster do not work when plugged into the outlet.
  4. The original hypothesis is incorrect. Alternative hypotheses includes that both coffee maker and toaster were broken.

Visual Connection

  1. All flying birds and insects have wings. Birds and insects flap their wings as they move through the air. Therefore, wings enable flight.
  2. Insects generally survive mild winters better than harsh ones. Therefore, insect pests will become more problematic if global temperatures increase.
  3. Chromosomes, the carriers of DNA, separate into daughter cells during cell division. Therefore, DNA is the genetic material.
  4. Animals as diverse as insects and wolves all exhibit social behavior. Therefore, social behavior must have an evolutionary advantage for humans.
  1. 1- Inductive, 2- Deductive, 3- Deductive, 4- Inductive
  2. 1- Deductive, 2- Inductive, 3- Deductive, 4- Inductive
  3. 1- Inductive, 2- Deductive, 3- Inductive, 4- Deductive
  4. 1- Inductive, 2-Inductive, 3- Inductive, 4- Deductive

The scientific method may seem too rigid and structured. It is important to keep in mind that, although scientists often follow this sequence, there is flexibility. Sometimes an experiment leads to conclusions that favor a change in approach often, an experiment brings entirely new scientific questions to the puzzle. Many times, science does not operate in a linear fashion instead, scientists continually draw inferences and make generalizations, finding patterns as their research proceeds. Scientific reasoning is more complex than the scientific method alone suggests. Notice, too, that the scientific method can be applied to solving problems that aren’t necessarily scientific in nature.

Two Types of Science: Basic Science and Applied Science

The scientific community has been debating for the last few decades about the value of different types of science. Is it valuable to pursue science for the sake of simply gaining knowledge, or does scientific knowledge only have worth if we can apply it to solving a specific problem or to bettering our lives? This question focuses on the differences between two types of science: basic science and applied science.

Basic science or “pure” science seeks to expand knowledge regardless of the short-term application of that knowledge. It is not focused on developing a product or a service of immediate public or commercial value. The immediate goal of basic science is knowledge for knowledge’s sake, though this does not mean that, in the end, it may not result in a practical application.

In contrast, applied science or “technology,” aims to use science to solve real-world problems, making it possible, for example, to improve a crop yield, find a cure for a particular disease, or save animals threatened by a natural disaster (Figure 1.8). In applied science, the problem is usually defined for the researcher.

Some individuals may perceive applied science as “useful” and basic science as “useless.” A question these people might pose to a scientist advocating knowledge acquisition would be, “What for?” A careful look at the history of science, however, reveals that basic knowledge has resulted in many remarkable applications of great value. Many scientists think that a basic understanding of science is necessary before an application is developed therefore, applied science relies on the results generated through basic science. Other scientists think that it is time to move on from basic science and instead to find solutions to actual problems. Both approaches are valid. It is true that there are problems that demand immediate attention however, few solutions would be found without the help of the wide knowledge foundation generated through basic science.

One example of how basic and applied science can work together to solve practical problems occurred after the discovery of DNA structure led to an understanding of the molecular mechanisms governing DNA replication. Strands of DNA, unique in every human, are found in our cells, where they provide the instructions necessary for life. During DNA replication, DNA makes new copies of itself, shortly before a cell divides. Understanding the mechanisms of DNA replication enabled scientists to develop laboratory techniques that are now used to identify genetic diseases. Without basic science, it is unlikely that applied science could exist.

Another example of the link between basic and applied research is the Human Genome Project, a study in which each human chromosome was analyzed and mapped to determine the precise sequence of DNA subunits and the exact location of each gene. (The gene is the basic unit of heredity represented by a specific DNA segment that codes for a functional molecule.) Other less complex organisms have also been studied as part of this project in order to gain a better understanding of human chromosomes. The Human Genome Project (Figure 1.9) relied on basic research carried out with simple organisms and, later, with the human genome. An important end goal eventually became using the data for applied research, seeking cures and early diagnoses for genetically related diseases.

While research efforts in both basic science and applied science are usually carefully planned, it is important to note that some discoveries are made by serendipity , that is, by means of a fortunate accident or a lucky surprise. Penicillin was discovered when biologist Alexander Fleming accidentally left a petri dish of Staphylococcus bacteria open. An unwanted mold grew on the dish, killing the bacteria. The mold turned out to be Penicillium, and a new antibiotic was discovered. Even in the highly organized world of science, luck—when combined with an observant, curious mind—can lead to unexpected breakthroughs.

Reporting Scientific Work

Whether scientific research is basic science or applied science, scientists must share their findings in order for other researchers to expand and build upon their discoveries. Collaboration with other scientists—when planning, conducting, and analyzing results—is important for scientific research. For this reason, important aspects of a scientist’s work are communicating with peers and disseminating results to peers. Scientists can share results by presenting them at a scientific meeting or conference, but this approach can reach only the select few who are present. Instead, most scientists present their results in peer-reviewed manuscripts that are published in scientific journals. Peer-reviewed manuscripts are scientific papers that are reviewed by a scientist’s colleagues, or peers. These colleagues are qualified individuals, often experts in the same research area, who judge whether or not the scientist’s work is suitable for publication. The process of peer review helps to ensure that the research described in a scientific paper or grant proposal is original, significant, logical, and thorough. Grant proposals, which are requests for research funding, are also subject to peer review. Scientists publish their work so other scientists can reproduce their experiments under similar or different conditions to expand on the findings.

A scientific paper is very different from creative writing. Although creativity is required to design experiments, there are fixed guidelines when it comes to presenting scientific results. First, scientific writing must be brief, concise, and accurate. A scientific paper needs to be succinct but detailed enough to allow peers to reproduce the experiments.

The scientific paper consists of several specific sections—introduction, materials and methods, results, and discussion. This structure is sometimes called the “IMRaD” format. There are usually acknowledgment and reference sections as well as an abstract (a concise summary) at the beginning of the paper. There might be additional sections depending on the type of paper and the journal where it will be published for example, some review papers require an outline.

The introduction starts with brief, but broad, background information about what is known in the field. A good introduction also gives the rationale of the work it justifies the work carried out and also briefly mentions the end of the paper, where the hypothesis or research question driving the research will be presented. The introduction refers to the published scientific work of others and therefore requires citations following the style of the journal. Using the work or ideas of others without proper citation is considered plagiarism .

The materials and methods section includes a complete and accurate description of the substances used, and the method and techniques used by the researchers to gather data. The description should be thorough enough to allow another researcher to repeat the experiment and obtain similar results, but it does not have to be verbose. This section will also include information on how measurements were made and what types of calculations and statistical analyses were used to examine raw data. Although the materials and methods section gives an accurate description of the experiments, it does not discuss them.

Some journals require a results section followed by a discussion section, but it is more common to combine both. If the journal does not allow the combination of both sections, the results section simply narrates the findings without any further interpretation. The results are presented by means of tables or graphs, but no duplicate information should be presented. In the discussion section, the researcher will interpret the results, describe how variables may be related, and attempt to explain the observations. It is indispensable to conduct an extensive literature search to put the results in the context of previously published scientific research. Therefore, proper citations are included in this section as well.

Finally, the conclusion section summarizes the importance of the experimental findings. While the scientific paper almost certainly answered one or more scientific questions that were stated, any good research should lead to more questions. Therefore, a well-done scientific paper leaves doors open for the researcher and others to continue and expand on the findings.

Review articles do not follow the IMRAD format because they do not present original scientific findings, or primary literature instead, they summarize and comment on findings that were published as primary literature and typically include extensive reference sections.


The theory supporting psychodynamic therapy originated in and is informed by psychoanalytic theory. There are four major schools of psychoanalytic theory, each of which has influenced psychodynamic therapy. The four schools are: Freudian, Ego Psychology, Object Relations, and Self Psychology.

Freudian psychology is based on the theories first formulated by Sigmund Freud in the early part of this century and is sometimes referred to as the drive or structural model. The essence of Freud's theory is that sexual and aggressive energies originating in the id (or unconscious) are modulated by the ego, which is a set of functions that moderates between the id and external reality. Defense mechanisms are constructions of the ego that operate to minimize pain and to maintain psychic equilibrium. The superego, formed during latency (between age 5 and puberty), operates to control id drives through guilt (Messer and Warren, 1995).

Ego Psychology derives from Freudian psychology. Its proponents focus their work on enhancing and maintaining ego function in accordance with the demands of reality. Ego Psychology stresses the individual's capacity for defense, adaptation, and reality testing (Pine, 1990).

Object Relations psychology was first articulated by several British analysts, among them Melanie Klein, W.R.D. Fairbairn, D.W. Winnicott, and Harry Guntrip. According to this theory, human beings are always shaped in relation to the significant others surrounding them. Our struggles and goals in life focus on maintaining relations with others, while at the same time differentiating ourselves from others. The internal representations of self and others acquired in childhood are later played out in adult relations. Individuals repeat old object relationships in an effort to master them and become freed from them (Messer and Warren, 1995).

Self Psychology was founded by Heinz Kohut, M.D., in Chicago during the 1950s. Kohut observed that the self refers to a person's perception of his experience of his self, including the presence or lack of a sense of self-esteem. The self is perceived in relation to the establishment of boundaries and the differentiations of self from others (or the lack of boundaries and differentiations). "The explanatory power of the new psychology of the self is nowhere as evident as with regard to the addictions" (Blaine and Julius, 1977, p. vii). Kohut postulated that persons suffering from substance abuse disorders also suffer from a weakness in the core of their personalities--a defect in the formation of the "self." Substances appear to the user to be capable of curing the central defect in the self.

[T]he ingestion of the drug provides him with the self-esteem which he does not possess. Through the incorporation of the drug, he supplies for himself the feeling of being accepted and thus of being self-confident or he creates the experience of being merged with the source of power that gives him the feeling of being strong and worthwhile (Blaine and Julius, 1977, pp. vii-viii).

Each of the four schools of psychoanalytic theory presents discrete theories of personality formation, psychopathology formation, and change techniques by which to conduct therapy and indications and contraindications for therapy. Psychodynamic therapy is distinguished from psychoanalysis in several particulars, including the fact that psychodynamic therapy need not include all analytic techniques and is not conducted by psychoanalytically trained analysts. Psychodynamic therapy is also conducted over a shorter period of time and with less frequency than psychoanalysis.

Several of the brief forms of psychodynamic therapy are considered less appropriate for use with persons with substance abuse disorders, partly because their altered perceptions make it difficult to achieve insight and problem resolution. However, many psychodynamic therapists work with substance-abusing clients, in conjunction with traditional drug and alcohol treatment programs or as the sole therapist for clients with coexisting disorders, using forms of brief psychodynamic therapy described in more detail below.

Missing Data Analysis: Making It Work in the Real World

This review presents a practical summary of the missing data literature, including a sketch of missing data theory and descriptions of normal-model multiple imputation (MI) and maximum likelihood methods. Practical missing data analysis issues are discussed, most notably the inclusion of auxiliary variables for improving power and reducing bias. Solutions are given for missing data challenges such as handling longitudinal, categorical, and clustered data with normal-model MI including interactions in the missing data model and handling large numbers of variables. The discussion of attrition and nonignorable missingness emphasizes the need for longitudinal diagnostics and for reducing the uncertainty about the missing data mechanism under attrition. Strategies suggested for reducing attrition bias include using auxiliary variables, collecting follow-up data on a sample of those initially missing, and collecting data on intent to drop out. Suggestions are given for moving forward with research on missing data and attrition.

Sequential Explanatory Design

The sequential explanatory approach is characterized by two distinct phases: an initial phase of quantitative data collection and analysis followed by a second qualitative data-collection and analysis phase (see Figure 1A). Findings from both phases are integrated during the data-interpretation stage. The general aim of this approach is to further explain the phenomenon under study qualitatively or to explore the findings of the quantitative study in more depth (Tashakkori and Teddlie, 2010). Given the sequential nature of data collection and analysis, a fundamental research question in a study using this design asks, “In what ways do the qualitative findings explain the quantitative results?” (Creswell et al., 2003). Often, the initial quantitative phase has greater priority over the second, qualitative phase. At the interpretation stage, the results of the qualitative data often provide a better understanding of the research problem than simply using the quantitative study alone. As such, the findings in the quantitative study frequently guide the formation of research questions addressed in the qualitative phase (Creswell et al., 2003), for example, by helping formulate appropriate follow-up questions to ask during individual or focus group interviews. The following examples from the extant literature illustrate how this design has been used in the BER field.

In an interventional study with an overtly described two-phase sequential explanatory design, Buchwitz et al. (2012) assessed the effectiveness of the University of Washington’s Biology Fellows Program, a premajors’ course that introduced incoming biology majors to the rigor expected of bioscience majors and assisted them in their development as science learners. The program emphasized the development of process skills (i.e., data analysis, experimental design, and scientific communication) and provided supplementary instruction for those enrolled in introductory biology courses. To assess the effectiveness of the program, the authors initially used nonhierarchical linear regression analysis with six explanatory variables inclusive of college entry data (high school grade point average and Scholastic Aptitude Test scores), university-related factors (e.g., economically disadvantaged and first-generation college student status), program-related data (e.g., project participation), and subsequent performance in introductory biology courses. Analysis showed that participation in the Biology Fellows Program was associated with higher grades in two subsequent gateway biology courses across multiple quarters and instructors. To better understand how participating in the Biology Fellows Program may be facilitating change, the authors asked two external reviewers to conduct a focus group study with program participants. Their goal was to gather information from participants retrospectively (2 to 4 years after their participation in the program) about their learning experiences in and beyond the program and how those experiences reflected program goals. Students’ responses in the focus group study were used to generate themes and help explain the quantitative results. The manner in which the quantitative and qualitative data were collected and analyzed was described in detail. The authors justified the use of this design by stating, “A mixed-methods approach with complementary quantitative and qualitative assessments provides a means to address [their research] question and to capture more fully the richness of individuals’ learning” (p. 274).

In a similar study, Fulop and Tanner (2012) administered written assessments to 339 high school students in an urban school district and subsequently interviewed 15 of the students. The goal of this two-phased sequential study was to examine high school students’ conceptions about the biological basis of learning. To address their research problem, they used two questions to guide their study: 1) “After [their] mandatory biology education, how do high school students conceptualize learning?,” and 2) “To what extent do high school students have a biological framework for conceptualizing learning?” The authors used statistical analysis (post hoc quantitative analysis and quantification of open-ended items) to score the written assessment and used thematic analysis to interpret the qualitative data. Although the particular design of the sequential explanatory model is not mentioned in the article, the authors make it clear that they used a mixed-methods approach and particularly mention how the individual interviews with a subset of students drawn from the larger study population were used to further explore how individual students think about learning and the brain. In drawing their conclusions about students’ conceptualization of the biological basis of learning, the authors integrated analysis of the quantitative and qualitative data. For example, on the basis of the written assessment, the authors concluded that 75% of the study participants demonstrated a nonbiological framework for learning but also determined that 67% displayed misconceptions about the biological basis of learning during the interviews.

Topics and Ideas for Ethics Research Paper

1. Moral Relativism in a Globalized World

The concepts of Moral Relativism deals with the diversity of ethical principles resulted from a diversity of cultures. When researching this topic, you can refer to the ideas of normative moral relativism about tolerating the values of other cultures, even in case they contradict the widely accepted standards. Moreover, it will be interesting to discuss these ideas within the framework of globalization, reviewing the examples of international toleration.

2. The Role of Applied Ethics in the Contemporary World

Since Applied Ethics involves itself into the research and analysis of the controversial issues, such as abortion, capital punishment, and some others, it is critically important to analyze the background of this approach, as well as its place in the contemporary world. Namely, you can research the critical principles driving the theorists working towards this direction, as well as the significant contribution of the applied ethics to the practical study of the modern dilemmas.

3. The Contribution of William Ockham to the Development of Voluntarism

To understand better the ideas of the divine command theory or voluntarism, it is reasonable to research the life and work of William Ockham, the proponent of this theory. Although there is a list of widely known principles of voluntarism, you can research which of them have appeared due to the contribution of William Ockham and make a conclusion regarding the importance of the insights expressed by him, especially in relation to the other authors.

4. Skepticism as the Alternative to Divine Nature of Ethics

Although skeptics acknowledge the moral values, they reject the divine nature of ethics, or, in other words, the ideas of voluntarism. Instead, they insist on the human ground of morality. You can move on and research moral skepticism in relation to how it differs from the divine command theory.

5. The Differences and Similarities between Male and Female Morality

Since gender issues are of high importance in the contemporary world, it will be reasonable to research and compare male and female moral values. To complete this task, you can analyze the scholarly articles containing surveys and experiments to figure out how those values differ, basing on quantitative data. Besides, you can employ theoretical insights and universal ethical theories to explain the results of the first part of the research.

6. The Basics of Consequentialist Justification

Consequentialism is among the most widely discussed ethical approaches because of its definition of morality. Namely, it states that morality is determined by the outcomes of the action. In this research, you can go into details of this approach, as well as review the example of the application of consequentialism taken from real life.

7. Contradictory Aspects of the Principle of Lawfulness

The principle of lawfulness is among the basic principles of ethics, which state that one should not violate the law to act ethically. Research this principle and discuss, providing real-world examples, and how it can contradict other essential ideas of ethics, such as the principle of personal benefit or principle of paternalism.

8. The Legality of Prostitution

The issue of whether prostitution should be acknowledged legal is long lasting but still unresolved. The reason is the existence of pluralistic values and contradictory ethical approaches. Research the two ethical theories that justify and refute the legality of prostitution, and reveal which one has more proponents. To perform this research appropriately, you can use academic literature to provide relevant facts about two approaches, as well as other sources to get an insight into the question of what theory is more promising.

9. Obligatory Status of Vaccination

Immunization programs become more and more popular in the contemporary world, while still being actively criticized by those arguing that obligatory vaccination violates the principle of autonomy. You can research different ethical approaches to this issue, including the one mentioned above, and after comparing them with the real-world facts, figure out the relevant conclusions regarding which theory should be accepted universally.

10. National Security vs. Individual Privacy: An Ethical Approach

This research should focus on the controversies that appear when one is trying to combine the goals of national security and individual right to privacy. You can study different ethical interpretations of this issue to find out the most convenient one. Also, highlight what situations require taking into account the individual interests over national security and vice versa. For this purpose, you can review the real-world case showing the process of balancing between national and individual interests.

11. Utilitarian Approach to Population Control

Use the contribution of Utilitarianism to research the issue of population control. Although non-interference in relation to the matter of constantly growing population protects people right to decide on the size of their families by their own, it creates significant threats for future generations, such as those challenges that relate to overpopulation. Using the utilitarian approach, ensure to research the advantages and costs of population control to figure out the position of the supporters of this theory regarding this matter.

12. Utilitarian Interpretation of Armed Conflict

In this research, it seems reasonable to include both theoretical and applied parts. Namely, after researching the major ideas of Utilitarianism, you can study how they apply to the matter of armed conflict and well-known examples of such conflicts. Besides, you can cover the appearance of terrorism, including the real-world cases, and conclude whether it can be ethically justified.

Spencer and the Wider World of Work

Aspects of work and employment which impinge on professional activities, in particular the trades unions, working conditions in general and unpaid work, attracted Spencer's attention. His critical comments derive from his equal freedom principle (justice). Trades unions can resort to coercion to demand obedience from their members and obstruct piece-work practices (Spencer, 1910, ii, p. 279� Offer, 2010), and in their name strikers had resorted to violence and hence injustice against employers (Spencer, 1910, ii, p. 294�). However, justice is also a weapon on the side of unions. “Judging from their harsh and cruel conduct in the past,” Spencer writes, “it is tolerable certain that employers are now prevented from doing unfair things which they would else do” (Spencer, 1896, p. 542). Clearly pertaining to wages and health at work, these are remarks seldom credited to Spencer: Wiltshire, for example, accused him of “inveterate hostility” to trade unions (Wiltshire, 1978, p. 141 161).

On some general working conditions Spencer's condemnation is unequivocal (as Peel noted, 1971, p. 216). The advances in machinery in factories “has proved extremely detrimental” in mental and physical respects for the health of the operatives (Spencer, 1896, p. 515). The wage-earning mill worker may exemplify free labor, but “this liberty amounts in practice to little more than the ability to exchange one slavery for another” …. “The coercion of circumstances often bears more hardly on him than the coercion of a master does on one in bondage” (Spencer, 1896, p. 516. Spencer's misgivings about wage labor and injustice, and his support for trade unionism, receive further discussion in Weinstein, 1998, p. 201�).

Spencer was well-aware that, in ordinary social interaction, there was much activity showing the �llow feeling” which was integral to social life, as opposed to the perspective of 𠇊tomic individualism” of which, as has been noted earlier, some critics have charged him:

Always each may continue to further the welfare of others by warding off from them evils they cannot see, and by aiding their actions in ways unknown to them or, conversely putting it, each may have, as it were, supplementary eyes and ears in other persons, which perceive for him things he cannot perceive himself: so perfecting his life in numerous details, by making its adjustments to environing actions complete (Spencer, 1910, p. i, 254).

Moreover, he captured for his readers in some sympathetic detail the intricate dynamics of “private beneficence,” or informal care, arising when families or neighbors undertake to tend or nurse ill or frail family members or acquaintances. Private beneficence had moral qualities that made it preferable to state beneficence, but he was disquieted by the disproportionate burdens of care which were performed by women and the restricted opportunities which followed in its wake (on Spencer on this aspect see Offer, 1999). Spencer's comments on unpaid work pivot around �neficence” in the Principles of Ethics. Beneficence is altruism over and above the demands of “justice.” Spencer's concern with �neficence” as against “justice” and its demands here signified that he was continuing a tradition familiar from The Theory of Moral Sentiments by Adam Smith 16 .

Voluntariness in the shape of voluntary organizations conformed to Spencer's ideas about social development. He welcomed the organized but spontaneous voluntary action (the “provident beneficence”) which was forthcoming when ordinary persons, who had acquired surgical and medical knowledge, stepped in to provide help to sufferers before the arrival of professional help (Spencer, 1910, ii, p. 361). Hiskes (1983) traces the treatment of Spencer's idea of social individuals and his liberal idea of community since his day, criticizing some libertarian sources, including Robert Nozich's Anarchy, State, and Utopia (1974), for ignoring the altruistic attitudes and motivations of people in social life which Spencer had described in detail. In addition, Spencer's familiarity with The History of Cooperation in England of 1875 by G J Holyoake and The Cooperative Movement in Great Britain of 1891 by Beatrice Potter made him amiably disposed toward organized cooperative ventures in production: we were witnessing the “germ of a spreading organization” (1896, p. 564) 17 .

Any discussion of Spencer and the wider world of work has to consider at least briefly Spencer's reference to a “third” type of society beyond his distinction between “militant” and industrial' types of societies. In the first and subsequent editions of the first volume of the Principle of Sociology (Spencer, 1876) he predicted that when the industrial form was more fully developed, societies will use the results not exclusively for material aggrandizement, but for carrying on “higher activities” as well. The new type is indicated by “inversion of the belief that life is for work into the belief that work is for life” (Spencer, 1893, p. 563). The changes to be expected are “the multiplication of institutions and appliances for intellectual and aesthetic culture” (Spencer, 1893, p. 563). In 1882, the third type became the theme of his speech delivered in New York, warning his audience of the barrenness of an obsession with work (Spencer, 1904 Shapin, 2007 Werth, 2009, ii, p. 387�). Again, it is significant that Spencer frowned on laissez-faire without boundaries.

In theory, we could always capitalize “Normal” to emphasize its role as the name of a distribution, not a reference to “normal”, meaning usual or typical. However, most texts don't bother and so we won't either.

A useful addendum: Four SDs captures the range of most (here, formally 95%) data values it turns out this is casually true for the distribution for most real-life variables (i.e., not only those that are normally distributed). Most (but not quite all) of the values will span a range of approximately four SDs.

For example, in many instances, data values are known to be composed of only non-negative values. In that instance, if the coefficient of variation (SD/mean) is greater than 𢏀.6, this would indicate that the distribution is skewed right.

Indeed the data from Panel B was generated from a normal distribution. However, you can see that the distribution of the sample won't necessarily be perfectly symmetric and bell-shape, though it is close. Also note that just because the distribution in Panel A is bimodal does not imply that classical statistical methods are inapplicable. In fact, a simulation study based on those data showed that the distribution of the sample mean was indeed very close to normal, so a usual t-based confidence interval or test would be valid. This is so because of the large sample size and is a predictable consequence of the Central Limit Theorem (see Section 2 for a more detailed discussion).

We note that the SE formula shown here is for the SE of a mean from a random sample. Changing the sample design (e.g., using stratified sampling) or choosing a different statistic requires the use of a different formula.

Our simulation had only ten random samples of size six. Had we used a much larger number of trials (e.g., 100 instead of 10), these two values would have been much closer to each other.

This calculation (two times the SE) is sometimes called the margin of error for the CI.

Indeed, given the ubiquity of �%” as a usual choice for confidence level, and applying the concept in Footnote 2, a quick-and-dirty “pretty darn sure” (PDS) CI can be constructed by using 2 times the SE as the margin of error. This will approximately coincide with a 95% CI under many circumstances, as long as the sample size is not small.

The requirement for normality in the context of various tests will be discussed in later sections.

Here meaning by a statistical test where the P-value cutoff or 𠇊lpha level” (α) is 0.05.

R.A. Fisher, a giant in the field of statistics, chose this value as being meaningful for the agricultural experiments with which he worked in the 1920s.

Although one of us is in favor of 0.056, as it coincides with his age (modulo a factor of 1000).

The term “statistically significant”, when applied to the results of a statistical test for a difference between two means, implies only that it is plausible that the observed difference (i.e., the difference that arises from the data) likely represents a difference that is real. It does not imply that the difference is 𠇋iologically significant” (i.e., important). A better phrase would be “statistically plausible” or perhaps “statistically supported”. Unfortunately, “statistically significant” (in use often shortened to just “significant”) is so heavily entrenched that it is unlikely we can unseat it. It's worth a try, though. Join us, won't you?

When William Gossett introduced the test, it was in the context of his work for Guinness Brewery. To prevent the dissemination of trade secrets and/or to hide the fact that they employed statisticians, the company at that time had prohibited the publication of any articles by their employees. Gossett was allowed an exception, but the higher-ups insisted that he use a pseudonym. He chose the unlikely moniker “Student”.

These are measured by the number of pixels showing fluorescence in a viewing area of a specified size. We will use 𠇋illions of pixels” as our unit of measurement.

More accurately, it is the distribution of the underlying populations that we are really concerned with, although this can usually only be inferred from the sample data.

For data sets with distributions that are perfectly symmetric, the skewness will be zero. In this case the mean and median of the data set are identical. For left-skewed distributions, the mean is less than the median and the skewness will be a negative number. For right-skewed distributions, the mean is more than the median and the skewness will be a positive number.

Kurtosis describes the shape or “peakedness” of the data set. In the case of a normal distribution, this number is zero. Distributions with relatively sharp peaks and long tails will have a positive kurtosis value whereas distributions with relatively flat peaks and short tails will have a negative kurtosis value.

A-squared (A2) refers to a numerical value produced by the Anderson-Darling test for normality. The test ultimately generates an approximate P-value where the null hypothesis is that the data are derived from a population that is normal. In the case of the data in Figure 5, the conclusion is that there is < 0.5% chance that the sample data were derived from a normal population. The conclusion of non-normality can also be reached informally by a visual inspection of the histograms. The Anderson-Darling test does not indicate whether test statistics generated by the sample data will be sufficiently normal.

The list is long, but it includes coefficients in regression models and estimated binomial proportions (and differences in proportions from two independent samples). For an illustration of this phenomenon for proportions, see Figure 12 and discussion thereof.

There are actually many Central Limit Theorems, each with the same conclusion: normality prevails for the distribution of the statistic under consideration. Why many? This is so mainly because details of the proof of the theorem depend on the particular statistical context.

And, as we all know, good judgment comes from experience, and experience comes from bad judgment.

Meaning reasons based on prior experience.

Also see discussion on sample sizes (Section 2.7) and Section 5 for a more complete discussion of issues related to western blots.

This is due to a statistical “law of gravity” called the Central Limit Theorem: as the sample size gets larger, the distribution of the sample mean (i.e., the distribution you would get if you repeated the study ad infinitum) becomes more and more like a normal distribution.

Estimated from the data again, this is also called the SEDM.

In contrast, you can, with data from sample sizes that are not too small, ask whether they (the data and, hence, the population from whence they came) are normal enough. Judging this requires experience, but, in essence, the larger the sample size, the less normal the distribution can be without causing much concern.

This discussion assumes that the null hypothesis (of no difference) is true in all cases.

Notice that this is the Bonferroni critical value against which all P-values would be compared.

If the null hypothesis is true, P-values are random values, uniformly distributed between 0 and 1.

The name is a bit unfortunate in that all of statistics is devoted to analyzing variance and ascribing it to random sources or certain modeled effects.

These are referred to in the official ANOVA vernacular as treatment groups.

This is true supposing that none are in fact real.

Proofs showing this abound on the internet.

Although this may seem intuitive, we can calculate this using some of the formulae discussed above. Namely, this boils down to a combinations problem described by the formula: Pr(combination) = (# permutations) (probability of any single permutation). For six events in 20, the number of permutations = 20!/6! 14! = 38,760. The probability of any single permutation = (0.08)6 (0.92)14 = 8.16e-8. Multiplying these together we obtain a value of 0.00316. Thus, there is about a 0.3% chance of observing six events if the events are indeed random and independent of each other. Of course, what we really want to know is the chance of observing at least six events, so we also need to include (by simple addition) the probabilities of observing 7, 8, � events. For seven events, the probability is only 0.000549, and this number continues to decrease precipitously with increasing numbers of events. Thus, the chance of observing at least six events is still π.4%, and thus we would suspect that the Poisson distribution does not accurately model our event.

Given that Table 4 indicates that the optimal number of F2s is between 2 and 3.

Calculating the probability that a medical patient has a particular (often rare) disease given a positive diagnostic test result is a classic example used to illustrate the utility of Baye's Theorem. Two complimentary examples on the web can be found at: http://vassarstats ​.net/bayes.html and http://www ​ ​/sbrown/stat/falsepos.htm.

This will often be stated in terms of a margin of error rather than the scientific formalism of a confidence interval.

The reasons for this are complex and due in large part to the demonstrated odd behavior of proportions (See Agresti and Coull 1998, Agresti and Caffo 2000 and Brown et al., 2001).

A more precise description of the A-C method is to add the square of the appropriate z-value to the denominator and half of the square of the z-value to the numerator. Conveniently, for the 95% CI, the z-value is 1.96 and thus we add 1.962 = 3.84 (rounded to 4) to the denominator and 3.84/2 = 1.92 (rounded to 2) to the numerator. For a 99% A-C CI, we would add 6.6 (2.5752) to the denominator and 3.3 (6.6/2) to the numerator. Note that many programs will not accept anything other than integers (whole numbers) for the number of successes and failures and so rounding is necessary.

Other assumptions for the binomial include random sampling, independence of trials, and a total of two possible outcomes.

Card counters in Las Vegas use this premise to predict the probability of future outcomes to inform their betting strategies, which makes them unpopular with casino owners.

Note that the numbers you will need to enter for each method are slightly different. The binomial calculators will require you to enter the probability of a success (0.00760), the number of trials (1,000), and the number of successes (13). The hyper-geometric calculator will require you to enter the population size (20,000), the number of successes in the population (152), the sample size (1,000), and the number of success in the sample (13). Also note that because of the computational intensity of the hyper-geometric approach, many websites will not accommodate a population size of ϡ,000. One website that will handle larger populations (http://keisan ​ ​.cgi?id=system ​/2006/1180573202) may use an approximation method.

Admittedly, standard western blots would also contain an additional probe to control for loading variability, but this has been omitted for simplification purposes and would not change the analysis following adjustments for differences in loading.

A similar, although perhaps slightly less stringent argument, can be made against averaging cycle numbers from independent qRT-PCR runs. Admittedly, if cDNA template loading is well controlled, qRT-PCR cycle numbers are not as prone to the same arbitrary and dramatic swings as bands on a western. However, subtle differences in the quality or amount of the template, chemical reagents, enzymes, and cycler runs can conspire to produce substantial differences between experiments.

This Excel tool was developed by KG.

The maximum possible P-values can be inferred from the CIs. For example, if a 99% CI does not encompass the number one, the ratio expected if no difference existed, then you can be sure the P-value from a two-tailed test is π.01.

Admittedly, there is nothing particularly “natural” sounding about 2.718281828…

An example of this is described in Doitsidou et al., 2007

In the case of no correlation, the least-squares fit (which you will read about in a moment) will be a straight line with a slope of zero (i.e., a horizontal line). Generally speaking, even when there is no real correlation, however, the slope will always be a non-zero number because of chance sampling effects.

For example, nations that that supplement their water with fluoride have higher cancer rates. The reason is not because fluoride is mutagenic. It is because fluoride supplements are carried out by wealthier countries where health care is better and people live longer. Since cancer is largely a disease of old age, increased cancer rates in this case simply reflect a wealthier long-lived population. There is no meaningful cause and effect. On a separate note, it would not be terribly surprising to learn that people who write chapters on statistics have an increased tendency to become psychologically unhinged (a positive correlation). One possibility is that the very endeavor of a writing about statistics results in authors becoming mentally imbalanced. Alternatively, volunteering to write a statistics chapter might be a symptom of some underlying psychosis. In these scenarios cause and effect could be occurring, but we don't know which is the cause and which is the effect.

In truth, SD is affected very slightly by sample size, hence SD is considered to be a 𠇋iased” estimator of variation. The effect, however, is small and generally ignored by most introductory texts. The same is true for the correlation coefficient, r.

Rea et al. (2005) Nat. Genet. 37, 894-898. In this case, the investigators did not conclude causation but nevertheless suggested that the reporter levels may reflect a physiological state that leads to greater longevity and robust health. Furthermore, based on the worm-sorting methods used, linear regression was not an applicable outcome of their analysis.

The standard form of simple linear regression equations takes the form y = b1x + b0, where y is the predicted value for the response variable, x is the predictor variable, b1 is the slope coefficient, and b0 is the y-axis intercept. Thus, because b1 and b0 are known constants, by plugging in a value for x, y can be predicted. For simple linear regression where the slope is a straight line, the slope coefficient will be the same as that derived using the least-squares method.

Although seemingly nonsensical, the output of a linear regression equation can be a curved line. The confusion is the result of a difference between the common non-technical and mathematical uses of the term “linear”. To generate a curve, one can introduce an exponent, such as a square, to the predictor variable (e.g., x 2 ). Thus, the equation could look like this: y = b1x 2 + b0.

A multiple regression equation might look something like this: Y = b1X1 + b2X2 - b3X3 + b0, where X1-3 represent different predictor variables and b1-3 represent different slope coefficients determined by the regression analysis, and b0 is the Y-axis intercept. Plugging in the values for X1-3, Y could thus be predicted.

Even without the use of logistic regression, I can predict with near 100% certainty that I will never agree to author another chapter on statistics! (DF)

An online document describing this issue is available at: In addition, a recent critical analysis of this issue is provided by Bacchetti (2010).

The median is essentially a trimmed mean where the trimming approaches 100%!

More accurately, the tests assume that the populations are normal enough and that the sample size is large enough such that the distribution of the calculated statistic itself will be normal. This was discussed in Section 1.

Note that there are subtle variations on this theme, which (depending on the text or source) may go by the same name. These can be used to test for differences in additional statistical parameters such the median.

More accurately, nonparametric tests will be less powerful than parametric tests if both tests were to be simultaneously carried out on a dataset that was normal. The diminished power of nonparametric tests in these situations is particularly exacerbated if sample sizes are small. Obviously, if the data were indeed normal, one would hopefully be aware of this and would apply a parametric test. Conversely, nonparametric tests can actually be more powerful than parametric tests when applied to data that are truly non-Gaussian. Of course, if the data are far from Guassian, then the parametric tests likely wouldn't even be valid. Thus, each type of test is actually �tter” or �st” when it is used for its intended purpose.

For example, strains A and B might have six and twelve animals remaining on day 5, respectively. If a total of three animals died by the next day (two from strain A and one from strain B) the expected number of deaths for strain B would be twice that of A, since the population on day 5 was twice that of strain A. Namely, two deaths would be expected for strain B and one for strain A. Thus, the difference between expected and observed deaths for strains A and B would be 1 (2𢄡=1) and 𢄡 (1𢄢=𢄡), respectively.

The final calculation also takes into account sample size and the variance for each sample.

Note that, although not as often used, there are also parametric bootstrapping methods.

This is a bad idea in practice. For some statistical parameters, such as SE, several hundred repetitions may be sufficient to give reliable results. For others, such as CIs, several thousand or more repetitions may be necessary. Moreover, because it takes a computer only two more seconds to carry out 4,000 repetitions than it takes for 300, there is no particular reason to scrimp.

Note that this version of the procedure, the percentile bootstrap, differs slightly from the standard bootstrapping method, the bias corrected and accelerated bootstrap (BCa). Differences are due to a potential for slight bias in the percentile bootstrapping procedure that are not worth discussing in this context. Also, don't be unduly put off by the term 𠇋ias”. SD is also a 𠇋iased” statistical parameter, as are many others. The BCa method compensates for this bias and also adjusts for skewness when necessary.

A brief disclaimer. Like everything else in statistics, there are some caveats to bootstrapping along with limitations and guidelines that one should become familiar with before diving into the deep end.

Edited by Oliver Hobert. Last revised January 14, 2013, Published June 26, 2013. This chapter should be cited as: Fay D.S. and Gerow K. A biologist's guide to statistical thinking and analysis (June 26, 2013), WormBook, ed. The C. elegans Research Community, WormBook, doi/10.1895/wormbook.1.150.1, http://www ​

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26.5: Possible Theoretical and Practical Issues with Discussed Approach - Biology

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