BioStatistics

Fisher Exact Test

- Used when doing a 2 by 2 table analysis for independence (test of association)
- This test is reliable when sample size is small
- conclude that there is or is not statistical association with rows and columns
- used to determine two categorical variables are independent
- the alternative hypothesis is dependent

Chi Square Test Assumptions

- Expected (not observed) counts for each group are greater than five
- Low sample size can result in an unreliable chi square test

Inferential Statistics

- A set of procedures used to test hypotheses about a population of populations using data from a sample collected from a sample collected from that population

Statistical Test

- You need a null hypothesis (NH) and its converse, the alternative hypothesis (AH)
- Reject the NH (decide it isn't true)
- Fail to reject the NH (which is not the same as accepting the NH)

Rejecting the null hypothesis

- occurs when the value of the test statistic you calculate from your data is very different from the predicted values of the test statistic assuming the NH is true
- if the observed value of the test statistic is very unlikely to be seen when the NH is true then we should reject the NH and therefore accept the AH

Null Hypothesis

- there is no difference in the mean value of a variable in two different populations
- two variables are independent
- if __ true we fail to reject __ with a probability of 1 - alpha
- if __ is wrong we fail to reject with a probability of beta

Alpha

- 0.05
- likelihood that the null hypothesis is rejected when it was actually true

Frequency distribution

- we can use the binomial distribution

Chi square test

- the null hypothesis is the observed counts were obtained from a population with some specified hypothetical frequencies
- fail to reject if over 0.05
- reject if under 0.05

Goodness of fit test

- we want to test the null hypothesis that the counts are consistent with some expected set of frequencies
- we want to compare observed frequencies with hypothetical frequencies that are generated by biological information

Chi square test for independence

- Pa&b = Pa X Pb
- row sum * column sum / total

T-Test

- number calculated from the data with a known probability distribution when the null hypothesis is true
- test statistic is called t
- t=(difference between the two means)/(standard error of this difference)
- we assume that the population from which our sample were collected were normally distributed
- in some we assume the two populations have equal variances
- has a mean (average)

degrees of freedom

- influence of sample size is reflected in the quantity
- total sample size - two

Parametric test

- we make assumptions about the parameters of the populations we study

nonparametric test

- do not depend on making assumptions about population parameters

p-value

- gives the probability of getting a calculated value for the test statistic as extreme or even more extreme if the null hypothesis is true
- we reject the null hypothesis if it is less than 0.05
- cannot be greater than 1.0

Beta

- cannot be greater than1.0
- type 2 error

Type 1 error

Alpha

Chi square test

observed total equals expected total

null hypothesis

there is no association between two variables

science

the systematic organization of knowledge about the universe on the basis of explanatory principles that are subject to the possibility of empirical falsifiability

the logic of scientific info

1. the methodology of science in unique and definable
2. scientific ideas are explanatory and predictive
3. there is no single "scientific" method
4. experimental approach is preferred, not always practical
5. scientific ideas are subject to disproof (falsification), but not absolute proof
6. scientific conclusions are always provisional, tentative

systematic

- by subject matter
- i.e. disciplines, subdisciplines of natural science: physics, chem., bio.

explanatory

- cause/effect relationships between observations
- hypotheses, theories
- predictive - explains known facts, also suggest what will happen in unobserved situations

empirical falsifiability

- explanations must be potentials disprovable by observation (collection of data)

Karl Popper

- empirical falsifiability is the "criterion of demarcation" between science and other methods
- defining characteristic of science
- an explanation that is not subject to empiricism (observation, measurement) or falsifiability is not scientific

falsifiability

- an assertion is falsifiable if it can be refuted by data (observation)

constraints on falsifiability

- falsification is never completely conclusive (absolute) because explanations are tested in specific, limited situations
- falsification may occur because the explanation is wrong or because of faulty assumptions involved in testing the explanation

non-defining characteristics of science

experimentation, controls, replicability statistical analysis

The scientific method

- there is no such thing as a single "scientific method." Rather there are general methods that are applied to all scientific studies, including: empiricism and logical techniques to derive conclusions

hypothetico-deductive model of science

- take a hypothesis, make predictions about the world based on that hypothesis using logic (deduction)
- if the data indicates the prediction is correct , the hypothesis is supported
- if the data indicates the prediction is wrong, then it is evidence against the hypothesis (falsification)

Characteristics of a Good hypothesis

- predictive, testable - makes specific predictions - falsifiable
- generality - can be applied to many specific situations
- simplicity - parsimony (Occam's razor)
- internal and external consistency - fits into the accepted state of knowledge in a field

Methods of Evaluating Hypothesis

1. observational - measurement, quantification of the phenomenon of interest in the real world
- unmanipulated
2. experimental - manipulation of one or more variables thought to affect phenomenon you are interested in
- researcher manipulates levels of one or more variables
- test subjects are randomly assigned to groups before the manipulation begins

Theory

- indicates great amount of empirical support

type two error

the probability that you fail to reject the null hypothesis when in reality it is false

parametric test

general term for a statistical test that makes assumptions the way the data are distributed

t-test

mean1 = mean2 is the null hypothesis for

Chi square for goodness of fit test

comparing a set of counts from a data set to a hypothetical ratio or set of frequencies

inferential statistical test

involve the calculation of a statistic with known probability distribution when the null hypothesis is true

null hypothesis

- usually a specific statement rather than a vague statement
- committed type 2 error it was in reality false