## Advanced Statistics - Biology 6030 |

## Bowling Green State University, Fall 2019 |

**Initial Observation**tickles your interest in a particular topic- Phrase a
**Question**that can be addressed with an experiment - Phrase
**Null Hypothesis**as an explicit claim about the value of a specific parameter. What would you predict if the decision to turn left/right is random? In our example, the probability to turn right P(R) must equal the probability of turning left P(L). Because subjects have two mutually exclusive choices at the decision point we know that the probability of turning either left or right P(R or L) = P(R) + P(L) = 1, or P(R) = P(L) = 0.5. Thus, we can make an explicit claim about the probability that a subject turns right or left at the decision point given the choice is random. Our null hypothesis is that P(R) = 0.5 (or, equivalently, that P(L) = 0.5).- Directional vs. non-directional hypotheses
- Rejection regions and one-tailed vs. two-tailed tests

- Phrase
**Alternate Hypothesis**which simply states that our null hypothesis is not true, or P(R) 0.5 (or, equivalently, P(L) 0.5). - Consider issues relating to the
**Treatment Effect**- Decide what
**size**of a treatment effect would be considered "significant" - Decide on
**sample size**needed to detect a treatment effect of this size (i.e., power)

- Decide what
- Decide on
**framework**(experiment) for distinguishing between the two hypotheses. This allows us to attach a sense of likelihood to the outcomes associated with a particular outcome under the null hypothesis. Scientists must minimize their own biases with respect to a specific outcome and their preferences may not bias the results or their interpretation.- Choose
**statistical test**which involves the computation of a test statistic. You are bound to retain the null hypothesis unless you have good evidence that it is not compatible with the outcome of the experiment. A comparison of the test statistic to a critical value allows us to either retain our null hypothesis or reject it in favor of the alternative hypothesis. - Choose acceptable level for falsely rejecting the null hypothesis (i.e.,
**p-value**) - Determine
**critical values**for the sample statistic. We accept the null hypothesis if our test statistic does not exceed the critical value and we reject the null hypothesis in favor of the alternative if the test statistic exceeds the critical value.

- Choose
- Conduct Experiment in
**randomized**,**double-blind**fashion with the inclusion of appropriate controls **Un-blind**samples. Match each particular outcome with their respective treatments- During
**Data Analysis**all data must be handled in the same way. There is always the temptation to more closely inspect the validity of data points which do not support the scientist's expectations, while data which do agree with those expectations may not be checked as carefully. - Draw Conclusions
- Communicate Results

The general public often critically misinterprets terms used by scientists such as "hypothesis" "theory" and "scientific law". A **hypothesis** is any educated hunch phrased to explain an observed phenomenon so it becomes testable by an experiment. Even the most hair-brained ideas can be phrased into a hypothesis. **Model** or **principle** is reserved for situations that have at least limited validity. For example, Bohr's model of the atom is formed as an analogy to the solar system, where electrons move in circular orbits around the nucleus. This is not an accurate depiction of what an atom "looks like," but the model is to some degree able to represent the energies of electrons in a hydrogen atom. The term **Scientific Law** is reserved for a concise explanation of a simple set of actions that is accepted to be true and universal. Scientific laws are similar to mathematical postulates. The latter really no longer need complex external proofs or experimental verfication based upon the fact that they have always been observed to be true. Examples include the law of gravity, or the laws of thermodynamics. Both, laws and theories can be used to make predictions about the outcome of future events. Like a law, a **theory** is not any hair-brained idea that popped into somebody's head - it is rather an understanding of something that has been well documented, supported by overwhelming scientific evidence, has stood up to exhaustive rigorous testing, and is generally accepted as being true beyond reasonable doubt.. Whereas laws govern a single action, a series of related phenomena can only be represented by a theory that describes the fundamental properties and relationships in a complex system. As with an automobile used as a transportationd device, improvements are sometimes made to one or more component parts (e.g., a new set of spark plugs), but the function of the automobile as a whole remains unchanged. Similarly, individual components of a theory can be changed or improved upon, without changing the overall truth of the theory as a whole. Examples of scientific theories include the theory of evolution, the theory of relativity, and quantum theory. Although scientists continue to attempt to make its components more elegant, concise, or all-encompassing, they are seldom, if ever, entirely replaced.

**Tautological Arguments** are a needless repetition of an idea in different words or a logical statement that is necessarily true because it includes all possibilities. It is logically true regardless of whether the underlying statement is factually true or false because no alternate hypothesis is possible.

*Competitive Exclusion Principle*: When two ecologically identical species compete, one will exclude the other or they will coexist*Natural Selection*: If fitness is defined as survival. Which one survives? - "The fittest". Who are they? - Those that survive.

**Circular Arguments** assume the very thing it aims to prove. Statements may be logical consistent, but they do nothing to convince one of the truthfulness of the speaker. We take it for granted that proposition A implies proposition B. If we suppose that Proposotion A is correct, then proposition B has to be correct, right?

- "The Bible is the inspired Word of God because the Bible says so"
- "My arguments are correct because I am always right"

- Thomas Kuhn (1962) The Structure of Scientific Revolutions (Univ. of Chicago Press)

last modified: 7/1/19

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