3. Fundamental Statistics

What is a variable?

A defined characteristic that varies from one biological entity to another.

What is a factor variable?

A qualitative variable representing categories (e.g., Sex, Diet, Pesticide type).

What is a covariate?

A quantitative variable measured numerically (e.g., Rainfall, Temperature, Density).

What is a continuous variable?

A variable with infinite values within a possible range.

What is a discrete variable?

A variable with countable values, often whole numbers.

What is a nominal variable?

An unordered categorical variable.

What is an ordinal variable?

An ordered categorical variable.

What is a binary variable?

A variable with only two mutually exclusive outcomes.

When should you use the mean?

When the data is normally distributed.

When should you use the median?

When the data is skewed or not normally distributed.

What does the range measure?

The spread between the lowest and highest values.

Why use interquartile range (IQR)?

To reduce the influence of outliers by focusing on the middle 50% of data.

What plot visualizes the IQR?

A boxplot.

What test and plot assess if two covariates vary together?

Correlation analysis (Spearman or Pearson); Scatterplot.

What test and plot assess the effect of one covariate on another?

General Linear Model (regression); Scatterplot.

What test and plot assess the effect of a factor on a covariate?

General Linear Model (ANOVA); Boxplot.

What test and plot assess association between two factor variables?

Chi-square test; Bar plot.

What test and plot assess if a covariate differs between two factor levels?

T-test (or paired t-test); Boxplot.

What does y ~ x represent in R?

A model where variable y is explained by variable x.

What does a significant p-value in R output suggest?

There is statistical evidence of an effect or association.

What are the two things you must know before analysis?

1. What is your question? 2. What are the types of variables in your dataset?

What are the key measures of centrality in descriptive statistics?

Mean, Median, Mode

What are the key measures of variation?

Range, Interquartile Range, Sums of Squares, Variance, Standard Deviation

What is the purpose of calculating the sum of squares?

To quantify variation within a dataset and form the basis for calculating variance and standard deviation.

In a General Linear Model (GLM), what are the response and explanatory variables?

Response variable: the outcome being measured; Explanatory variable: the factor believed to influence the outcome

What does a GLM help you test?

Whether the explanatory variable significantly affects the response variable

How is total variation partitioned in a GLM?

Total Sum of Squares (TSS) = Explained Sum of Squares (ESS) + Residual Sum of Squares (RSS)

What does R-squared represent in a GLM?

The proportion of total variation in the response variable explained by the model

What is the null hypothesis in a GLM?

The explanatory variable does not account for variation in the response variable

What does a p-value < 0.05 indicate?

Reject the null hypothesis; the explanatory variable likely affects the response variable

What types of models fall under GLMs?

T-test, ANOVA (one-way, two-way, n-way), Regression, ANCOVA, Mixed models