Research in Music Teaching

1
Research in Music Teaching

• Miksza - Fall 08
• WEEK FIVE
• PART I - Correlational Research, Reliability and
  Validity

2
Correlational Research Basics

• Relationships among two or more variables are
  investigated
• The researcher does not manipulate the variables
• Direction (positive or negative) and degree (how
  strong) in which two or more variables are related

3
Uses of Correlational Research

• Clarifying and understanding important phenomena
• Explaining human behaviors
• Predicting likely outcomes
• Particular beneficial when experimental studies
  are difficult or impossible to design
• DOES NOT indicate causation
• Reciprocal effect
• Third (other) variable

4
Scatterplots

• Graph of subjects values on two variables
• Regression line a line drawn through the
  scatter plot which algebraically approximates the
  relationship between the variables
• Y1 a bX1
• Y1 is predicted score on the criterion variable
• X1 is the subjects score on the predictor
  variable
• Theoretical intercept - a
• Theoretical slope - b

5
Interpreting Correlations

• r
• Correlation coefficient (Pearson, Spearman)
• Can range from -1.00 to 1.00
• Direction
• Positive
• As X increases, so does Y and vice versa
• Negative
• As X decreases, Y increases and vice versa
• Degree or Strength (rough indicators)
• lt .30 small
• lt .65 moderate
• gt .65 strong
• gt .85 very strong
• r2
• Coefficient of determination
• Percentage of variance explained

6
Interpreting Correlations (cont.)

• Words typically used to describe correlations
• Direct, indirect
• Perfect,
• Strong, weak
• High, moderate, low
• Negative, inverse
• Correlations vs. Mean Differences
• Groups of scores that are correlated will nto
  necessarily have similar means

7
Statistical Assumptions

• The mathematical formulae used to determine
  various correlation coefficients carry with them
  certain assumptions about the nature of the data
  used
• Independence (all)
• Level of data (all)
• Normality (Pearson, Alpha)
• Linearity (all)
• Presence of outliers (all)
• Subjects have only one score for each variable
• Sample size (Pearson, Alpha)

8
Multiple Regression

• Association between a criterion variable (Y1) and
  several predictor variables (X1, X2, X3, Xn,
  etc.)
• Y1 a bX1 bX2 bX3 bXn, etc.
• R
• Multiple correlation coefficient
• Strength and degree of association between the
  criterion variable and all of the predictor
  variables combined
• R2
• Variance explained by all of the predictors
  combined

9
Correlations and Measurement Validity

• Criterion
• Predictive
• Concurrent
• Discriminant/Divergent
• Degree and strength
• r gt .40, a relatively good indicator of criterion
  validity
• Others
• Content, Construct, Face

10
Correlations and Measurement Reliability Basics

• Measurement Error
• True Score Observed Score Error
• Error can consist of many things (environmental
  personal conditions, inadequate measures, lack of
  pilot test, inadequately trained judges or
  observers, data entry)
• Variability
• The presence of more variation reduces error
• How to increase variation
• More items
• More response options
• More subjects
• More judges
• Standard Error of Measure
• Expresses how similar the observed score is to
  the theoretical true score
• SEMeas SD?(1 - r)

11
Correlational Approaches for Assessing
Measurement Reliability

• Consistency over time
• test-retest (Pearson, Spearman)
• Consistency within the measure
• internal consistency (split-half, KR-20,
  Cronbachs alpha)
• Spearman Brown Prophecy formula
• 2r/(1 r)
• Among judges
• Interjudge (Cronbachs Alpha)
• Consistency across forms of a measure
• (Pearson, Spearman)
• Degree and Strength
• r .60 to .70 indicates marginal reliability
• r .70 to .85 indicates acceptable/good
  reliability
• r .85 to .99 indicates excellent reliability

12
Basics of Statistical Significance

• The probability that a result is due to chance
• p value
• Most usual criteria considered, plt.05
• Chances are 5 in 100 that the result was due to
  chance
• More conservative criteria, plt.01, plt.001
• Chances are 1 in 100 or 1 in 1000, respectively,
  that the result was due to chance
• Generally speaking, the larger the sample, the
  more likely statistical significance will be
  found
• Statistical significance does not equal Practical
  significance