Research in Music Teaching

1
Research in Music Teaching

• Miksza - Fall 08
• WEEK FOUR
• PART I - Descriptive Statistics
• PART II - Survey Research

2
Descriptive Statistics

• Some basic nomenclature
• Statistics and Parameters
• Sample and population indices
• Quantitative/Continuous vs. Categorical
• Levels of Measurement
• This becomes more important when deciding what
  types of statistical summaries and methods of
  analysis to use
• NOIR
• Nominal
• Ordinal
• Interval
• Ratio

3
Visual Summaries of Data

• Frequencies
• Distribution
• Grouped-Distribution
• Polygon
• Stem-leaf Plot
• Numerical arrangement to show shape of data
  distribution
• Shows all individual values
• Histogram
• Versus a bar graph?
• Bar graph categorical data, Histogram
  quantitative/continuous data
• Boxplot
• Shows range, median, and where the majority of
  the subjects scored with respect to the median
• Based on quartiles, 25, 50, 75, 100

4
Central Tendency

• Mode
• Most frequently occurring
• Median
• Point at which half fall below, half fall above
• Mean
• Sum of all scores divided by number of scores
  (average)
• X --- single score (your test grade)
• ? --- sum (add it all up!)
• ?X --- mean (class average on test)
• n --- number of individuals/entities (number of
  people in class)
• ?X ?X/n

5
Variability (spread)

• Range
• Distance between lowest and highest score
• Standard Deviation
• A single number which describes the entire
  distribution of scores in terms of a relationship
  to the mean
• SD SquareRoot of ?(X-?X)2/n
• Variance
• A single number that describes the amount of
  variability among the scores although with less
  overt reference to the mean, more abstract - good
  for comparing groups on similar characteristics

6
Altogether.. describes the shape of a distribution

• More on distributions..
• Normal Curve (bell curve)
• Most scores clustered at the middle with fewer
  scores falling at the extreme highs and lows
• Skewness - When the scores tend to bunch up
• on the HIGH END Negative Skew less than -1
• on the LOW END Positive Skew greater than 1
• Kurtosis - When the distribution is
• PEAKED positive kurtosis leptokurtic
  greater than 1 or 2 depending on who you ask
• SMALLER PEAK THAN IN NORMAL CURVE negative
  kurtosis less than -1
• Bi-Modal
• When there are two humps in the curve, more than
  one mode

7
More on the normal curve and variability...

• Mean, median, mode are equal
• 50 of scores lie above mean, 50 lie below
• 68 of scores are between one SD above the mean
  and one SD below the mean
• 95 of the scores are within two SDs above and
  below the mean
• 99.7 of the scores are within three SDs above
  and below the mean

8
Standard Scores and Their Relationships to the
Normal Curve

• Raw score vs. Standard Score
• As is vs. computed to reflect the scores place
  with respect to the sample mean and standard
  deviation
• z scores
• Allow raw scores on various measures to be
  compared
• z (Raw - Mean)/Standard Deviation
• T scores
• A way to avoid negative scores and therefore
  increase interpretability
• T (z X 10) 50
• SAT/GRE scores
• SAT/GRE (z X 100) 500
• CAVEAT - Standard scores are most beneficial when
  distribution resembles normal curve

9
Survey Design

• A purpose/problem is stated
• A population is selected
• A mode of data collection is selected
• A sample is selected
• The instrument is constructed/adapted
• Information related to the purpose/problem is
  collected from a group of individuals
• The information is summarized and analyzed
• From the results, generalizations are made about
  the population in question

10
Survey/Interview Types

• Cross-sectional
• Information collected at one point in time
• Longitudinal
• Information collected at MORE than one point in
  time
• Trend
• Members of a population differ over time
• Cohort
• Population is constant, individuals selected may
  differ
• Panel
• Individuals are constant
• Interview
• Standardized/structured, semi-structured,
  open-ended

11
Uses of Survey Research

• Tend to be descriptive
• May be associational
• Correlations among items
• Comparisons between groups on items
• Comparisons within groups on items
• Rarely experimental

12
Defining the Problem/Purpose

• Questions need to be important and interesting
  enough to merit response
• Text suggests a hierarchical approach to question
  selection
• Also avoid asking for information to be reported
  when you can find it elsewhere (i.e.,
  unobtrusively)
• Whenever possible, make it clear that you intend
  to share the results and that it may be of
  benefit to them to consult the results

13
ID the Population and Sample

• Individuals vs. Units of Analysis
• Not just people things, places, events, etc.
• Define the population so that is clear who may or
  may not be considered in the sample
• Some form of random sampling is best once
  population is defined
• Consider sending to those in authority rather
  than simply the respondents (e.g., teachers to
  administer to their students)

14
Choose Mode of Data Collection

• Telephone interview
• Pro
• Cheaper and quicker than a personal interview
• Con
• Poor response rate
• Personal interview
• Pro
• Good for encouraging participation
• Can clarify on the spot
• Can probe for more info. or detail
• Con
• Very time consuming
• Very costly
• May require assistants - who then need extensive
  training
• Compromises anonymity

• Direct administration
• Pro
• When researcher has access
• Response rate often excellent
• Can clarify on the spot
• Con
• Intact groups may not be representative of
  population
• Mailed survey
• Pro
• Access to individuals who are hard to reach
• Con
• Response rate is often poor

15
Survey Items

• Close Ended
• Easier to score
• Harder to write
• May not include subjects desired responses

• Open Ended
• Harder to score
• Easier to write
• Subjects can say whatever they want

• Gateway/Contingency - good when items may only
  apply to some of the subjects
• May be best to consider a combination
• Some general tips when constructing items
• Avoid ambiguity, Focus on one issue at a time (no
  double barreled questions), Shorter is better,
  Use common language rather than jargon, Avoid
  triggers for bias, Avoid leading language,
  Avoid double negatives

16
Response Issues

• Problem those who do not respond may differ from
  those who do on some critical issue in some
  systematic way
• Ideas for increasing response rate
• Face-to-face best, Telephone 2nd, Mail 3rd
• Confidentiality, anonymity
• Organized survey/interview
• Business-like, conservative interviewer
  characteristics
• Multiple mailings
• Post-card ahead of time, survey and cover letter,
  reminder, 2nd mailing, reminder, 3rd mailing,
  etc.
• Call specific individuals
• Call-backs, appointments
• Tangible rewards