R Lab: One-Way ANOVA and Kruskal-Wallis

# use this code chunk to call in all packages the document will need
library(tidyverse)
library(ssstats)

King Triton is concerned that the different sea creatures in Atlantica are not equally loud during musical rehearsals, which might be affecting the harmony of their performances. To investigate, Sebastian conducts a study (singing_data) measuring the average decibel level (volume) of singing during rehearsals from three types of performers: mermaids, fish chorus, and crustaceans.

Each group (performer) includes 25 randomly selected performers, and their peak singing volumes (volume_db) are recorded during a standard song.

1a. Use ANOVA to determine if the average peak singing volume (volume_db) differs between performance groups (performer).

• Hypotheses:
  • H_0:
  • H_1:
• Test Statistic and p-Value
  • F_0 =, p =
• Rejection Region
  • Reject H_0 if p < \alpha; \alpha =
• Conclusion and interpretation
  • Reject or Fail to reject H_0 (p \text{ vs } \alpha \to). There is or is not sufficient evidence to suggest (the alternative hypothesis in words, not math).

1b. Perform the appropriate posthoc test to determine what pairwise differences exist. Test at the \alpha=0.05 level. Assume that this is an exploratory study; do not adjust for \alpha.

Pairwise differences:

• List
• Them
• Here

1c. Perform the appropriate posthoc test to determine what pairwise differences exist. Test at the \alpha=0.05 level. Assume that this is a confirmatory study; adjust for \alpha.

Pairwise differences:

• List
• Them
• Here

2a. Use the Kruskal-Wallis to determine if the median peak singing volume (volume_db) differs between performance groups (performer).

• Hypotheses:
  • H_0:
  • H_1:
• Test Statistic and p-Value
  • \chi^2_0 =, p =
• Rejection Region
  • Reject H_0 if p < \alpha; \alpha =
• Conclusion and interpretation
  • Reject or Fail to reject H_0 (p \text{ vs } \alpha \to). There is or is not sufficient evidence to suggest (the alternative hypothesis in words, not math).

2b. Perform the appropriate posthoc test to determine what pairwise differences exist. Test at the \alpha=0.05 level. Assume that this is an exploratory study; do not adjust for \alpha.

Pairwise differences:

• List
• Them
• Here

2c. Perform the appropriate posthoc test to determine what pairwise differences exist. Test at the \alpha=0.05 level. Assume that this is a confirmatory study; adjust for \alpha.

Pairwise differences:

• List
• Them
• Here

3a. Construct the graph for assessing ANOVA assumptions.

3b. Formally test for the variance assumption. Test at the \alpha=0.05 level.

• Hypotheses:
  • $H_0: $
  • $H_1: $
• Test Statistic and p-Value
  • F_0 =, p =
• Rejection Region
  • Reject H_0 if p < \alpha; \alpha =
• Conclusion and interpretation
  • Reject or Fail to reject H_0 (p \text{ vs } \alpha \to). There is or is not sufficient evidence to suggest (the alternative hypothesis in words, not math).

3c. Do we meet the assumptions? Why or why not?

Replace with your answer

3d. Which test should we use to look for differences among the performer groups? Why?

Replace with your answer