PPT 1: Descriptive Statistics

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.