i.intro to statistics ii.various variables. i.intro to statistics a. definitions -

I. Intro to StatisticsII. Various Variables

I. Intro to Statistics

A. Definitions

-

-


A. Definitions

-

- “ a collection of numerical data”


A. Definitions

-


can be measured quantities, or the frequency of occurrence of qualitative attributes…


A. Definitions

-


- “the mathematics of the collection, organization, and interpretation of numerical data and the analysis of population characteristics by inference from sampling”

- “the mathematics of the collection, organization, and interpretation of numerical data and the analysis of population characteristics by inference from sampling”

- there’s a mathematics of collection? (sampling)

- inference … inductive reasoning …


A. Definitions

- “the science of uncertainty, assigning probabilities to the reliability of estimates, to the reliability of conclusions, and to the likelihood of outcomes of future events.”


A. Definitions

B. Populations and Samples


A. Definitions


- What is “a population” in the statistical sense?


A. Definitions


- What is “a population” in the statistical sense?

def: “all objects of a particular kind in the universe, or in some designated subdivision of the universe”


A. Definitions


- What is “a population” in the statistical sense? - sample: “the portion of a population for which data is collected”


A. Definitions


- What is “a population” in the statistical sense? - sample: “the portion of a population for which data is collected” - “the mathematics of the collection, organization, and interpretation of numerical data and the analysis of population characteristics by inference from sampling”


A. Definitions


C. An Important Issue

- Is the sample truly representative of the population? If not, it is biased and inferences about the population may be incorrect.


A. Definitions



- Is the sample truly representative of the population? If not, it is biased and inferences about the population may be incorrect.

- example: medical research on animals and humans


A. Definitions



Your conclusion about a population is immediately circumspect if your sample is not representative of that population. (It may still be legitimate for a different population for which the sample IS representative.)


A. Definitions



D. Defining the Population



- problem: don’t want a biased sample, but want to be able to generalize to a group larger than your sample.

- example: biological populations…



- it is probably impossible to have a truly representative sample of an entire population. So, you want your sample to be representative of the population with respect to characteristics that might influence your dependent variable.



E. Sampling


E. Sampling

The goal is to have a representative sample from your population, particularly with respect to the variables that you think might be influential.

What would the most representative sample of a population include?


E. Sampling - sample size

Larger samples are more representative, on average, than smaller samples, because they include a greater fraction of the population.


E. Sampling - sample size - “random” sampling

We know individuals in a population vary, but we don’t necessarily know how, and we probably don’t know the distribution of that variability.



In a “random” sample, each individual in the population has the same probability of being included in the sample. So, rare things in the population will be relatively rare in the sample, and the sample should be “reasonably” representative as sample size increases… - example

A

B

CD E F

Letter Observed Expected

A

B

C

D

E

F



“randomness is not casual, haphazard, or unplanned” – it is a purposeful process



“randomness is not casual, haphazard, or unplanned” – it is a purposeful process

- random draw (chits in a hat, bingo balls, lottery)- random number table- computerized random draw



No? yes


E. Sampling - sample size - “random” sampling - sample units should be independent



- sampling without replacement… do you want to go first or second in a game of “Russian Roulette?”(not bad if sample is small relative to population, but important if population is small… like 9 chambers.)



- Lack of independence is common when measuring same organisms multiple times

“pooling fallacy”



- assignment of sampling units to treatments should be random and independent.

- our experiment?


A. Terms: - variable: characteristics that may differ from one member of a population to another. - datum: the value of a variable for one member of the population. (“data” is a plural noun).


A. Terms:B. Types of Variables: - “measurement” variables have states that are distinguished numerically; consistency of intervals between values is assumed.


A. Terms:B. Types of Variables: - “measurement” variables have states that are distinguished numerically; consistency of intervals between values is assumed.

- continuous: theoretically, can assume any value between any two points (length, volume, temperature, weight, time, etc.)

- discontinuous (discrete, meristic): numerical states that only assume particular values; like counts… number of offspring.


A. Terms:B. Types of Variables: - “measurement” variables - “ranked” variables are quantified and ordered by relative magnitude or sequence (largest, fastest, first, most dominant = 1).


A. Terms:B. Types of Variables: - “measurement” variables - “ranked” variables - “attributes” are qualitative, “categorical” variables. The frequencies can be analyzed, but there is no quantitative relationship between variable states.

male or female. Red or white. These aren’t rankable.


A. Terms:B. Types of Variables: - “measurement” variables - “ranked” variables - “attributes”

These aren’t necessarily independent; the same “thing” can be measured different ways. COLOR could be an attribute, or a measured wavelength, or ranked wavelengths or intensity.


A. Terms:B. Types of Variables: - “measurement” variables - “ranked” variables - “attributes” - “derived” variables are computed from two continuous measurements: rates, percentages, etc.


A. Terms:B. Types of Variables: - “measurement” variables - “ranked” variables - “attributes” - “derived” variables - “transformed” variables – these are variables that have had a particular mathematical operation performed on them. pH = - log[H+] … hydrogen ion concentration is measured, but it is reported as the negative log.


A. Terms:B. Types of Variables: - “measurement” variables - “ranked” variables - “attributes” - “derived” variables - “transformed” variables – these are variables that have had a particular mathematical operation performed on them. square-root and log transformations are common; they reduce the effect of outliers and may make the data normally distributed.


A. Terms:B. Types of Variables: - “measurement” variables - “ranked” variables - “attributes” - “derived” variables

These aren’t necessarily independent; the same “thing” can be measured different ways. COLOR could be an attribute, or a measured wavelength, or ranked wavelengths or intensity.


A. Terms:B. Types of Variables: - “measurement” variables - “ranked” variables - “attributes” - “derived” variables - experimental variables:



- what do you purposefully change?



- what do you purposefully change? Independent or ‘predictor’ variable

- what do your measure?



- what do you purposefully change? Independent or ‘predictor’ variable

- what do your measure?Dependent or ‘response’ variable

- experimental variables: - what do you purposefully change?

Independent or ‘predictor’ variable - what do your measure?

Dependent or ‘response’ variable- what do you regulate, holding constant or

allowing to vary in a narrow range?




allowing to vary in a narrow range?Controlled Variable

- what do you randomize?





- what do you randomize?Randomized Variable

- what do you allow to vary naturally?






- what do you allow to vary naturally?Uncontrolled variable

- what variable correlate with your independent variable?






- what do you allow to vary naturally?Uncontrolled variable

- what variable correlate with your independent variable? CONFOUNDING VARIABLE – BOOOOO!

TYPE OF VARIABLE VARIABLE IN OUR EXPERIMENT

INDEPENDENT VARIABLES

DEPENDENT VARIABLESS

CONTROLLED VARIABLES

RANDOMIZED VARIABLES

UNCONTROLLED VARIABLES

CONFOUNDING VARIABLES

i.intro to statistics ii.various variables. i.intro to statistics a. definitions -

Documents

population problem

different population

mathematics of collection

statistical sense

biased sample

sampling theres

important issueyour

reliability of estimates