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Lecture 1 Terms
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Terms in this set (27)
What are Statistics?
The study of the collection, organization and interpretation of data. They are involved in all stages of scientific research, from the planning of data collection (design of surveys and experiments) to the reporting and interpretation of results.
Why use Statistics?
To plan efficient sampling of patterns.
To rigorously quantify and compare observations.
To understand patterns by developing and evaluating models.
Step-by-step Data Analysis
Specify the biological question you are asking.
Phrase the question in form of a biological null / alternate hypotheses (the scientific hypothesis).
Phrase the question in form of a statistical null / alternate hypotheses.
Determine which variables are relevant to the statistical hypotheses (and the biological question).
Determine what kind of variables they are: numerical / categorical, discrete / continuous.
Design an experiment (or sampling approach) that controls or randomizes the confounding variables.
Choose the best statistical test to use, based on: the hypothesis being tested, the number and kinds of variables, and the expected fit to the assumptions.
If possible, do a power analysis to determine the sample size needed for good statistical power.
Do experiment (Take samples / Make measurements).
Examine data to see if they meet the assumptions of the selected statistical test (parametric statistics). If they do not, choose a non-parametric version of test.
Apply the statistical test, and interpret the results.
Communicate the outcome, with a graph(s) and table(s).
Biological Population
All organisms of the same species (interbreed) that live in the same geographical area (given time period).
Statistical Population
A defined set of entities concerning which statistical inferences are to be drawn, often based on a sample taken from the biological population.
Potential set of all measurements or observations in a sample, including not only the cases actually observed but also those that are potentially observable.
Null Hypothesis
No change in ocean productivity over time (No Trend)
Alternative Hypothesis
Decrease in ocean productivity due to deepening thermocline and increased stratification.
OR Increase in ocean productivity due to strengthening atmospheric pressure gradients and enhanced upwelling.
Inference Space
What are we measuring?
Where?
How often?
What time period are we considering?
Variables
Anything that can be measured and (potentially) can differ across entities or over time
Independent Variable
Variable denotes the cause (the driver of the pattern).
Termed: predictor variable
Dependent Variable
Variable denotes the effect (responds to the driver).
Termed: outcome variable
Types of Variables
measurement, nominal, and ranked (ordinal)
Numerical (Measurement) Variables
Properties: Variable takes on numerical values (e.g., ants, arm lengths). Can be ordered and ranked.
Subclasses: Discrete and Continuous
Discrete Variable (Numerical Variable)
Few possible values (integers)
Continuous Variable (Numerical Variable)
Measurements take any value within range
Subclasses: Interval variable and Ratio variable
Interval Variable (Continuous Variable)
Differences in one unit of measurement equal along entire measurement scale. There is not a real zero value.
e.g., Temperature (deg. C)
Ratio Variable (Continuous Variable)
Differences in one unit of measurement equal along entire measurement scale. There is a real zero value.
e.g., Salinity, Money
Categorical Variables
Properties: Variable takes on different categories (e.g., eye color). Only ordinal variables can be ordered and ranked.
Subclasses: Ordinal and Unordered
Ordinal Variable (Categorical Variable)
ordered (first, second, third...)
Nominal Variable (Categorical Variable)
unordered
Likert Items
A statement that the respondents evaluate by giving a quantitative value on any subjective or objective dimension, with the level of agreement / disagreement being the dimension most commonly used.
Validity
Refers to whether an instrument measures what it was designed to measure. The extent to which the scores from a measure represent the variable they are intended to.
Reliability
the ability of the measure to produce the same results under the same conditions.
Measurement Error
Discrepancy between the value we use to represent what we are measuring and the actual value of what we are measuring (i.e., the real value).
Monte Carol Approach
Makes no assumptions about underlying data distributions. Uses randomizations of the observed data for inference. Calculates probability that the pattern found in the sample occurred "by chance" (due to sampling).
Bayesian Approach
Makes assumptions about underlying data distributions. Uses the data to estimate parameters, augmented with additional "previous" knowledge. Assigns probabilities to these parameter estimates.
Fisherian Analysis (Parametric Statistics)
Makes assumptions about the underlying data distributions. Uses only the data from one experiment / study to estimate parameters. Calculates probability that the pattern found in the sample occurred "by chance" (sampling).
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