Statistical Tests and Practical Skills

Flashcards covering Spearman's Rank Correlation, Simpson's Index of Diversity, Chi-Squared testing, and Standard Deviation/Confidence Limits based on the lecture notes.

Spearman's Rank Correlation ($r_s$)

A statistical test used to determine if two variables correlate, where the value determines if there is a strong negative (up to $-1$), no correlation ($0$), or strong positive (up to $+1$) relationship.

Null Hypothesis ($H_0$) [Spearman's]

The assumption that there is no correlation between the variables being tested.

$D^2$ [Spearman's]

The sum of the differences in ranked pairs used in the Spearman's Rank Correlation formula.

Significant Correlation

A result where the calculated $r_s$ is greater than the critical value ($r_s > \text{Critical value}$), meaning the null hypothesis can be rejected.

Significance Level of $5\%$ ($0.05$)

A statistical threshold indicating that we are $95\%$ sure of the correlation.

Simpson's Index of Diversity ($D$)

A formula used to determine biodiversity (Species Richness and Species Evenness) on a scale of $0\text{-}1$, calculated as $D = 1 - \left[ \sum \left( \frac{n}{N} \right)^2 \right]$.

$n$ [Simpson's Index]

The number of individuals of one specific species.

$N$ [Simpson's Index]

The total number of all individuals of all species.

Low Simpson's Index Value

Indicates low biodiversity, fewer species, an unstable or extreme environment, and a simple food web.

High Simpson's Index Value

Indicates high biodiversity, more species, a stable environment, more niches, and a complex food web.

Chi-Squared Test ($\chi^2$)

A test used to determine if there is a statistically significant relationship between variables, calculated using the formula $\chi^2 = \sum \frac{(O-E)^2}{E}$.

$O$ [Chi-Squared]

The observed value in a specific category.

$E$ [Chi-Squared]

The expected value in a specific category.

Degrees of Freedom [Chi-Squared]

A value used to find the critical value, calculated as the number of categories minus $1$.

Standard Deviation ($s$)

A measure of how much a sample mean differs (deviates) from the true mean, calculated as $s = \sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}$. Lower values indicate data is closer to the mean and more reliable.

Standard Error

A measure used to find confidence limits, calculated using the formula $\frac{s}{\sqrt{n}}$, where $s$ is standard deviation and $n$ is sample size.

$95\%$ Confidence Limits

Calculated as $\text{Mean} \pm 2 \times \text{Std. Error}$. These are represented as error bars on graphs.

Error Bar Overlap

When error bars on a graph overlap, it indicates the data is likely due to chance and is not trusted. No overlap indicates the data was not by chance and can be trusted.