Statistical Tests

Background

I will be using the cod and trout analogy. Which statistical test depends upon:

1. Number of cohorts analysed

2. Number of variable analysed

3. Variable characteristics:

   1. 1. 1. 1. Normally distributed

            2. Continuous, nominal or categorical

Definitions

Normal distribution: (figure 1 below) this is where the median value (middle) = mean (average) and the mode (most common value). Secondly 95% of the values lie within two standard deviations of the mean, black lines shown. Most attributes in nature are normally distributed, like height and weight. 

Note if you were to take the tallest 10% of individuals this would no longer be normally distributed, 

Variable Definition Examples

Continuous variable: Defined by  number that can be less than 1 Height, weight

Nominal variable Defined in multiples of 1 Number of people on a plane (can't have half a person!)

Categorical variables Description variables Eye colour

Common Tests (6)

Pearson Ranking Co-efficient

• One cohort

• Two variables: normally distributed & continuous

• Example: comparing the height vs the weight of cod

T Test Paired

• One cohort compared against itself, e.g. 10 years later

• One variable: normally distributed & continuous

• Example: comparing weight of cod in 1980 vs 1990

T Test Unpaired

• Two cohorts

• One variable: normally distributed & continuous

• Example: comparing weight of cod vs weight of trout

Mann Whitney Test

• Two cohorts

• One variable with nominal distribution

• Example: comparing the number of spots on cod vs trout

• Also called Wilcoxon Rank Sum Test

ANOVA Test

• Multiple cohorts (greater than two)

• One variable, normally distributed

• Example: comparing the weight of cod, trout, sharks, lobsters and herring

Chi- square Test

• Comparing differences in proportions between two groups

• For example: rates of lice in treated cod vs rates of lice in untreated cod

Rarer tests

Spearman's Rank Test

• Assesses whether there is causation between two variables within a population

• For example, if the number of fishing boats increases does the size of cod decrease

• Similar to Pearson's- Pearson looks at the strength of association whereas Spearman looks at probability of causation

Tukey's Range Test

• Compare means of different populations

• For example the weight of cod vs weight of trout

• T-test would be able to compare the weight within a sample of cod and sample of trout, but less useful for a population based comparison

Wilcoxon Signed Rank Test

• Compare one variable, two cohorts

• Nominal value, non -normal distribution, e.g. pain score / 10

• Compares median of a set of numbers against a hypothetical median

• Similar in name to the Mann Whitney U Test, Wilcoxon Rank Sum Test

Written 2024.