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Statistics

Science of collecting, summarizing, and interpreting biological data.

Population

All individuals in a study.

Sample

A subset of the population used to estimate the population parameters.

Parameter

A value summarizing a population (e.g., true mean \( \mu \), true proportion \( p \)).

Estimate (Statistic)

A value summarizing a sample (e.g., sample mean \( \bar{x} \), sample proportion \( \hat{p} \)).

Sampling Error

Random deviation between a sample estimate and the true population parameter.

Bias

Systematic deviation from the true population parameter due to flawed sampling methods.

Sample Mean

sum of terms / number of terms

Precision

Related to the consistency of repeated estimates.

Accuracy

How close an estimate is to the true population parameter.

Categorical Data

Divides observations into groups.

Nominal Data

Categories with no natural order (e.g., species names).

Ordinal Data

Categories with a natural order (e.g., size:small, medium, large).

Numerical Data

Values that can be measured.

Continuous Data

Can take any value (e.g., weight).

Discrete Data

Takes specific integer values (e.g., number of eggs).

Frequency Table

A table that shows how often each category or value occurs.

Bar Graph

A graphical representation for categorical data.

Histogram

A graphical representation for numerical data; displays the distribution of values; continuous numerical data

Box Plot

Shows the spread of data, including median, quartiles, and outliers.

Skewness

Measures asymmetry in data.

Right-skewed

Tail on the right.

Left-skewed

Tail on the left.

Outliers

Data points that are far from the rest of the observations.

Mean \( \bar{x} \)

Average of data.

Median

Middle value when data are ordered.

Mode

Most frequent value in the dataset.

Variance \( s^2 \)

Average of the squared differences from the mean.

Standard Deviation \( s \)

Square root of variance.

Interquartile Range (IQR)

Difference between the third quartile \( Q_3 \) and the first quartile \( Q_1 \).

Coefficient of Variation (CV)

ratio of standard deviation to the mean

Sampling Distribution

The distribution of sample statistics across many samples.

Standard Error (SE)

Reflects the variability of a sample estimate.

Standard Error of the Mean

Confidence Intervals (CI)

A range that likely contains the population parameter.

95% Confidence Interval

range of values that describes the possible the mean of population based on a sample

Margin of Error

The range added to and subtracted from a point estimate to create a confidence interval.

Probability

The chance of an event occurring in the long run, expressed as a number between 0 and 1.

Discrete Probability Distribution

Describes probabilities for discrete random variables.

Continuous Probability Distribution

Describes probabilities for continuous variables.

Addition Rule

general law of addition is used to find the probability of the union of two events

Independent Events

The outcome of one event does not influence the outcome of another.

Conditional Probability (Bayes’ Theorem)

possibility of an event or outcome happening, based on existence of a previous event or outcome

Bar Graph

used for categorical data

Histogram

used for visualizing the distributions of continuous numerical data

Box Plot

summarizes the spread and central tendency of numerical data (includes outliers)

Scatter Plot

shows relationships between two continuous variables

Dot Plot

displays individual data points fro small datasets

Error Bars

used in bar graph and line graphs to show uncertainty (standard error, confidence intervals)

Probability Distribution (Discrete)

displays the probabilities of each outcome for a discrete variable

Normal Distribution Curve

bell-shaped curve representing a continuous normal distribution