1. What do we know about the sample? (Describe and Explore)

Suggestion: 2 pages

Prior to conducting the main analyses, the researchers would like some descriptive statistics on the participants in the study. In addition, they would like you to test that giving the participants the choice of instrument to listen to has not led to different sorts of participants listening to different types of solos. They would like you to test and report on:

1. Whether there’s any difference in tempos of pieces listened to between those who are musicians vs those who aren’t.
   
2. Whether there is an association between age and the tempo of piece played to them, and, if so, in what direction (e.g., the orchestra might have unintentionally played slower pieces for older people!).
   
3. Whether there is a balance such that musicians and non-musicians were equally likely to choose to listen to instruments from the different orchestral groups.

Provide a suitable brief description of the dataset, and then answer each of the questions above using an appropriate statistical test.

Hint:
When providing a description of your sample, think about the tradeoff between space used (by, for example, a figure or table) and detail (in writing). There’s no right way to describe the sample, but readers will want to understand the basic “shape” of the data.

descriptives

• mean and sd age

• count (and %) musicians vs non-musicians

• instrument to family mapping?

• counts (and %) family chosen

• mean bpm (possibly split by family)

• count and % enjoyed

summary(orchestra)

##    pptname               age                musician    instrument       
##  Length:394         Min.   :24.00   non-musician:212   Length:394        
##  Class :character   1st Qu.:40.00   musician    :182   Class :character  
##  Mode  :character   Median :44.00                      Mode  :character  
##                     Mean   :44.36                                        
##                     3rd Qu.:50.00                                        
##                     Max.   :75.00                                        
##       bpm             ERS            enjoyed             family         
##  Min.   : 20.0   Min.   :-10.250   Length:394         Length:394        
##  1st Qu.: 85.0   1st Qu.:  3.692   Class :character   Class :character  
##  Median :110.0   Median :  5.920   Mode  :character   Mode  :character  
##  Mean   :107.8   Mean   :  5.299                                        
##  3rd Qu.:130.0   3rd Qu.:  7.615                                        
##  Max.   :180.0   Max.   : 13.290                                        
##    isinf        
##  Mode :logical  
##  FALSE:394      
##                 
##                 
##                 
## 

table(orchestra$musician) |> print() |> prop.table()

## 
## non-musician     musician 
##          212          182

## 
## non-musician     musician 
##    0.5380711    0.4619289

1a

• t.test.
• if they just use welch (default) then fine. If they assume equal variances, then would be nice to be also shown a var.test.
• i’m pretty sure almost all groups will have this as non-significant

with(orchestra, t.test(bpm ~ musician))

## 
##  Welch Two Sample t-test
## 
## data:  bpm by musician
## t = -0.42985, df = 391.41, p-value = 0.6675
## alternative hypothesis: true difference in means between group non-musician and group musician is not equal to 0
## 95 percent confidence interval:
##  -7.199780  4.616326
## sample estimates:
## mean in group non-musician     mean in group musician 
##                   107.1698                   108.4615

with(orchestra, boxplot(bpm ~ musician))

1b

• a correlation, but ideally with a plot as it will highlight some weird people that don’t fit.
• if they frame as lm() then they might justify removing these people based on influence, which is fine. could also just do it from plot though.
• some might have already discussed removing these at the outset
• if they don’t remove them it will probably be non-signif
• if they do remove them, it will probably be signif

with(orchestra, cor.test(age, bpm))

## 
##  Pearson's product-moment correlation
## 
## data:  age and bpm
## t = -5.2226, df = 392, p-value = 2.87e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3451564 -0.1603007
## sample estimates:
##        cor 
## -0.2550577

with(orchestra, plot(age, bpm))

1c

• chisquare test of independence
• probably signif for every group
• ideally a table too, or discussion of relative counts.
  • something that highlights that it’s percussion that has biggest impact here (musicians much less likely to choose to listen to percussion solos)

with(orchestra, table(family,musician)) |> 
  print() |>
  chisq.test()

##             musician
## family       non-musician musician
##   brass                53       64
##   percussion           31        2
##   string               65       44
##   woodwind             63       72

## 
##  Pearson's Chi-squared test
## 
## data:  print(with(orchestra, table(family, musician)))
## X-squared = 29.049, df = 3, p-value = 2.187e-06

2. Sound & Sentiment

Suggestion: 2 pages

The first major research aim is to investigate the question about emotional response. Recall that the researchers are interested in whether the tempo of a musical piece is associated with eliciting more or less emotional response, and whether this might differ between the broad categories of instruments (strings/woodwind/brass/percussion).
Conduct and write up appropriate analysis/analyses to address this question.

Hint: Neither this analysis nor the one below need be very complex. Think about the background-&-study-aims, and what the researchers already “know” to be true; what they suspect might affect things (but aren’t necessarily interested in); and what the focus of their research is.

3. Enjoyment in every note

Suggestion: 2 pages

The second research aim is to explore what factors led to being more likely to report enjoyment of the solo piece.
from background: “but the experimenters were also interested in what types of music people find enjoyable.”

Note: The researchers are pretty sure that nobody enjoys percussion solos, so for this question specifically they are happy if you want to exclude all percussion solos in order to make the analysis more straightforward. (This doesn’t mean you have to, but it may make things easier).