Sampling and Randomization
Tuesday, January 17th, 2023
Midterms
- Due January 31 (two weeks from now!).
- 5-7 pages.
- construct a literature review of the topic you’re interested in writing about, culminating in a hypothesis section.
- Feel free to meet with me if you have any questions.
Midterms
- Be sure to include an overview of previous research related to the topic. This should include both empirical and non-empirical work. So if you’re focusing on the memory for jazz licks, for example, research on improvisational styles should be included alongside work on memory for musical ideas. It need not be all-encompassing, but it should try to cover as much ground as possible.
Midterms
Address a gap in the current literature, or that between theory and research. End with a discussion of your study, and how it hopes to fill in these gaps.
Populations
- A population is everything or everyone that you’re interested in.
- e.g. all the world’s people
- all the world’s people including living and deceased
- all Western-enculturated people
- all people who enjoy listening to music
- all clarinet players
Populations (continued)
A “population” does not refer only to people: Other examples:
- all of the music written by Vivaldi
- all solo flute music (both with and without accompaniment)
- all music in the minor mode
- all of the jazz scores available in the New York Public Library
- all performances of Rachmaninov’s 2nd piano concerto
Sample
- Sample: a subset of the population that you hope closely resembles the population as a whole.
Sample (Continued)
- A sample is said to be representative when the property of interest is identical in both the sample and the population.
Bias
- A sample is said to be biased when the property of interest differs between the sample and the population.
Defining Your Population
You can’t sample a population unless you have a clear idea of what constitutes the population of interest.
Suppose, for example, that you are a political pollster. Your aim is to predict the likely election results for a national election in Denmark. What, precisely, is the population you are interested in?
Defining Your Population (continued)
- All Danish citizens?
- All people living in Denmark?
- All people living in Denmark eligible to vote?
- All people eligible to vote in Danish elections?
- All people likely to vote in Danish elections?
Sampling Method
- Sampling method: the way you recruit or assemble your sample. When your population consists of people, sampling methods might include soliciting information by telephone (telephone sampling), street sampling, mail sampling, web sampling, classroom sampling, concert sampling, etc.
Sampling Bias
- Sampling bias: when the sampling method introduces differences that cause the sample not to be representative. We try to avoid or minimize sampling bias.
Sampling Bias (continued)
- When conducting a telephone survey, a pollster may be tempted to ask to speak to a respondent’s spouse. However, spouses are likely to share many things in common (such as political views) so the sampling method will introduce a bias.
Simple Random Sampling
- Simple Random Sampling. Suppose we want to know about musical instrument sales in the City of Nashville. We could use the phone book to identify all of the shops within the city boundaries that sell musical instruments. Perhaps we discover that there are 131 retailers. From this list, we might randomly select 25 retailers in order to carry out our survey.
Systematic Sampling
Suppose that we have a questionnaire we want to distribute to people who attended a concert. There might be 500 audience members, but we have only 50 surveys to distribute. One approach would be to distribute the questionnaires to the first 50 people leaving the concert hall.
Matched Random Sampling
- A way of linking members from two or more samples. For example, a study might involve matching each professional musician with an amateur musician who plays the same instrument.
Convenience Sampling
- Convenience Sampling. A convenience sample simply takes advantage of whatever might be available. For example, a sample of organ music by Gabriel Fauré might simply consist of all of the scores available in a music library. Similarly, we might stand on a street corner and ask whoever passes by to answer questions on a survey.
Stratified Sampling
- When we have reason to suspect that difference in sub-populations might influence the results, it is common to sample in such a way to ensure that each of the main sub-populations are represented.
Stratified Sampling (Continued)
- Post and Huron (2009) were interested in common-practice era tonal classical music. So we decided to use a stratified sample consisting of music from three periods: Baroque, Classical and Romantic. Our overall sample consisted of equivalent numbers of works from each of these historical eras.
Quota Sampling
- A type of stratified sampling in which sub-samples are weighted according to their prevalence in the population.
Quota Sampling
- Suppose that we find that 52% of instrumentalists are most accomplished on guitar, 33% are most accomplished on keyboards, 12% on flute, 9% on trumpet, 8% on violin, etc. In quota sampling, we would aim to sample the same proportions for each instrument.