128 lines
3.0 KiB
Plaintext
128 lines
3.0 KiB
Plaintext
---
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title: "Assignment 5"
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subtitle: "STAT3373"
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author: "Isaac Shoebottom"
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date: "Oct 23th, 2025"
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output:
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pdf_document: default
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html_document:
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df_print: paged
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---
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```{r message=FALSE, warning=FALSE}
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library(tidyverse)
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```
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# Question 1
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## a)
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```{r}
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latin_data <- tribble(
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~sunlight, ~soil, ~treatment, ~growth,
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"Sunny", "Sandy", "C", 45,
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"Sunny", "Loamy", "A", 52,
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"Sunny", "Clay", "B", 48,
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"Sunny", "Sandy", "B", 43,
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"Sunny", "Loamy", "C", 50,
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"Sunny", "Clay", "A", 49,
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"Sunny", "Sandy", "A", 47,
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"Sunny", "Loamy", "B", 51,
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"Sunny", "Clay", "C", 46,
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"Partial Sun", "Sandy", "A", 41,
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"Partial Sun", "Loamy", "B", 44,
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"Partial Sun", "Clay", "C", 38,
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"Partial Sun", "Sandy", "B", 39,
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"Partial Sun", "Loamy", "C", 42,
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"Partial Sun", "Clay", "A", 40,
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"Partial Sun", "Sandy", "C", 40,
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"Partial Sun", "Loamy", "A", 43,
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"Partial Sun", "Clay", "B", 41,
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"Shade", "Sandy", "B", 32,
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"Shade", "Loamy", "C", 35,
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"Shade", "Clay", "A", 33,
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"Shade", "Sandy", "C", 31,
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"Shade", "Loamy", "A", 36,
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"Shade", "Clay", "B", 34,
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"Shade", "Sandy", "A", 30,
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"Shade", "Loamy", "B", 33,
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"Shade", "Clay", "C", 32
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)
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latin_data
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```
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## b)
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```{r}
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treatment_means <- latin_data %>%
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group_by(treatment) %>%
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summarise(mean_growth = mean(growth))
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treatment_means
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```
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## c)
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Mean Growth by Sunlight Level
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```{r}
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sunlight_means <- latin_data %>%
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group_by(sunlight) %>%
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summarise(mean_growth = mean(growth))
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sunlight_means
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```
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Mean Growth by Soil Type
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```{r}
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soil_means <- latin_data %>%
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group_by(soil) %>%
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summarise(mean_growth = mean(growth))
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soil_means
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```
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## d)
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From the descriptive statistics:
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Sunlight effects: Growth is highest under Sunny, moderate under Partial Sun, and lowest under Shade. This suggests sunlight has a strong positive effect on growth.
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Soil effects: Loamy soil consistently produces higher growth than Sandy or Clay, indicating soil type is an important blocking factor.
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Treatment effects: If the treatment means differ noticeably:
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- The watering schedule with the highest mean appears most effective.
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- Smaller differences suggest weaker treatment effects relative to blocking factors.
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- Because the Latin square controls for sunlight and soil, observed treatment differences are less confounded.
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## e)
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A Latin square ANOVA partitions variation into:
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- Sunlight (row effect)
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- Soil type (column effect)
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- Treatment effect
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- Error
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Expected Findings:
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- Sunlight effect: Likely highly significant, given the strong gradient from Sunny to Shade.
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- Soil effect: Likely significant, especially if Loamy soil dominates.
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- Treatment effect:
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- Possibly significant if Daily watering shows consistently higher growth.
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- Could be marginal if differences among watering schedules are small compared to sunlight and soil.
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- Error variance: Expected to be relatively small due to strong blocking.
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