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Why do we use statistics in biology?
Most things are probabilistic (data based on probabilities) rather than deterministic (data based on know facts)
What is the difference between observational and experimental populations?
Observational- A finite population, but is difficult to count
Experimental- An infinite amount in the population
Observational Population
A finite population that is difficult to count.
What is a sample survey (or an observational study)
A study of the individuals actually present in a population (under what the investigator can control)
What is a sample?
The amount of a population actually measured
Observation
Descriptions of patterns in data.
What is a sample unit?
An individual thing drawn from the population (e.g. an organism or a measurement)
What is inference?
A generalization of an observation (as samples do not always contain all of the population)
What is random sampling?
Truly random, all members of a population have a chance to be chosen
What is simple random sampling?
A random sample within the whole population
What is a stratified random sample?
A random sample within a group (males v females, age 1 age 2, etc)
What is continuous measurement of variables?
Any value between two extremes can be selected
What are discrete measurements of variables?
Fixed values are chosen between extremes (whole numbers)
What are rank variables?
Indicate more or less of variables based on their rank (e.g. smallest to greatest)
What are qualitative variables
Categorical variables (e.g. male/female, living/dead)
What is a rate?
The quantity per unit (eg. time, mass, births per year)
What are indices (or index)?
Complex derived variables (e.g. condition index: condition of body)
What is the difference between accuracy an precision?
Accuracy- How close a value is to the true value
Precision- How close repeated variables are
What is bias?
Departure from the true value
What can frequency distribution show?
Location, dispersion, and symmetry
What are examples of frequency distributions?
Symmetrical unimodal, Asymmetrical bimodal, Symmetrical uniform, Asymmetrical (skewed) unimodal, Symmetrical bimodal, Extremely skewed
What is the difference between absolute and relative frequencies?
Absolute- The vertical axis represents the real number of observations
Relative- The axis represents a percentage of observations
What does ∑ represent?
The sum of all of the variables
What is the statistics of location (or mean)?
The position of a sample along a given dimension representing a variable
What is the difference between an arithmetic mean and a weighted mean?
Arithmetic- The balance point of a distribution. All numbers are treated equally and have equal weight. Most commonly used
Weighted- The averages of the values are taken to find the mean (may be based on prevalence or the overall percentage of some variables)
Why do we transform our results?
We want to be able to shift the data to get a normal distribution
What is the geometric mean (GM)?
The back-transformed mean of a log-transformed variable (Y becomes logY, and then is changed back to Y)
What is a harmonic mean?
1/Y
When we take a (highly) skewed distribution and make it normal.
What is the median?
M or Y
It is the middle value of the distribution
What is mode?
The most frequent value. Can be bimodal or multimodal.
Where are the mode, median, and means in an asymmetric distribution?
Mode- Farthest from the tail
Median- in between
Mean- Closest to the tail
What is the mean deviation?
A measure of the average deviation from the mean
Standard Deviation
A measure of the amount of variation from the variables around the mean
The square root of the variance
σ
Variance
The overall deviation of observations from their mean.
Parameter
The true numerical value of a population.
Sample Statistic
An estimate of a parameter based on a sample.
μ
The population mean or expected value.
ȳ
The unbiased estimate of the population mean.
σ
The standard deviation of a population.
Covariance
A measure of how two numerical variables are related.
Positive Covariance
Indicates that large values of one variable correspond to large values of another.
Negative Covariance
Indicates that large values of one variable correspond to small values of another.
Zero Covariance
Indicates no relationship between two variables.
Standardized Covariance
The correlation coefficient, which scales variance between -1 and 1.
n
The number of possible outcomes in a probability scenario.
s
The number of successful outcomes in a probability scenario.
Probability of Success
The ratio of successful outcomes to total outcomes (s/n).
Simple Event
A single outcome in a sample space.
Event
A set of outcomes that meet a specific criterion.
Intersection
The common elements between two sets (A⋂B).
Union
The combined elements of two sets (A⋃B).
Independence
When the occurrence of one event does not affect the probability of another.
Replacement
A method where the sample space remains unchanged after an event.
Clumped Distribution
A distribution with excess in the tails.
Repulsed Distribution
A distribution with excess in the center.
Skewness
The asymmetry of a distribution.
Kurtosis
The shape and height of a distribution.
Standard Error of the Mean
The standard deviation of the sample mean.
Confidence Interval
The range of values expected to contain the population mean.
Central Limit Theorem
As sample size increases, the sample mean approaches a normal distribution.
Pr
The probability that a certain percentage of data falls within a specified range.
