Problem Set 5

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library(tidyverse); theme_set(theme_classic())
library(readxl)
library(emmeans)
set.seed(2026)

T-tests, ANOVA, and regression

For each scenario, select an appropriate analysis given the dataset. Follow the workflow illustrated in the practical and in the lectures, checking assumptions and applying transformations as needed.

Scenario 1

Research question: Do critical thermal limits change with repeated heatwave exposure in kelp?

In an experiment similar to King et al. 2024, a (hypothetical) H4 student measured critical thermal maxima (CT_max) on the kelp species Laminaria hyperborea under 1) no previous heat exposure, 2) recent moderate heat exposure, and 3) recent extreme heat exposure.

Identify the response and predictor variables, as well as what type of variable each is.

Next, load the data from the “MHW” sheet in “H2SMS_practicalData.xlsx” and perform appropriate checks.

Which analysis is most appropriate?

What is the null hypothesis?

Perform the analysis, including assumption checks. Calculate appropriate confidence intervals, make appropriate comparisons, and summarise results concisely in one short paragraph including key statistics.

Scenario 2

Research question: Is the average concentration of Alexandrium spp in an area greater than 40 cells per litre?

In the UK, shellfish cannot be harvested on aquaculture farms if densities of harmful algal species exceed certain levels. For example, Alexandrium spp release paralytic shellfish toxins, and growers are not allowed to harvest when Alexandrium spp exceeds 40 cells per litre.

I’ve collected 13 water samples and enumerated the number of Alexandrium spp cells.

NB: This is not quite how the regulatory monitoring works!

Identify the response and predictor variables, as well as what type of variable each is.

Next, load the data from the “Alexandrium” sheet in “H2SMS_practicalData.xlsx” and perform appropriate checks.

Which analysis is most appropriate?

What is the null hypothesis?

Perform the analysis, including assumption checks. Calculate appropriate confidence intervals, make appropriate comparisons, and summarise results concisely in one short paragraph including key statistics.

Scenario 3

Research question: Does mean seagrass shoot density differ among patches?

The data consists of seagrass shoot density measured by snorkelers in 20 randomly located quadrats in each of 3 lochs in western Scotland.

Identify the response and predictor variables, as well as what type of variable each is.

Next, load the data from the “Seagrass” sheet in “H2SMS_practicalData.xlsx” and perform appropriate checks.

Which analysis is most appropriate?

What is the null hypothesis?

Perform the analysis, including assumption checks. Calculate appropriate confidence intervals, make appropriate comparisons, and summarise results concisely in one short paragraph including key statistics.

Scenario 4

Research question: Does egg hatching success rate of Acartia tonsa depend on temperature?

A (hypothetical) H4 student has decided to replicate one of the experiments of Holste and Peck (2006) to test the effect of temperature on egg hatching success of the copepod Acartia tonsa. Their data are in the “HatchTemp” sheet in “H2SMS_practicalData.xlsx”, containing the temperature (C) and hatching success rate (%) for 3 replicates at each temperature.

Identify the response and predictor variables, as well as what type of variable each is.

Next, load the data from the “HatchTemp” sheet in “H2SMS_practicalData.xlsx” and perform appropriate checks.

Which analysis is most appropriate?

What is the null hypothesis?

Perform the analysis, including assumption checks. Calculate appropriate confidence intervals, make appropriate comparisons, and summarise results concisely in one short paragraph including key statistics.