SLAT7806 Research Methods

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SLAT7806 Research Methods

• Correlations
• Week 6

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Key terms

• Causation Correlation
• Positive correlation Pearsons r
• Negative correlation Outlier
• Crossed lag panel Strength of association
  Regression

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Causation versus Correlation

• The effect on Variable A on Variable B versus how
  Variable A is related to Variable B.

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Causal relationship between two variables

• A relationship in which the independent variable
  (IV) Y has a causal effect on the dependent
  variable (DV) X. Changes in the IV will be
  systematically reflected in changes on the DV.

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Describe the causal relationship here.

• Doughty (1991) studied of acquisition of relative
  clauses by three learner groups.
• 1. The Control group received input only
• 2. Meaning group received lexical and semantic
  enhancements
• 3. Form group received formal enhancements
• gtgt Both meaning and form groups outperformed the
  control group on test of relative clause
  knowledge.

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Correlational relationship

• A correlation is the strength of association
  between two variables. Variable pairs X and Y
  are correlated when they change together, that
  is, a change in the value of X in mirrored in a
  change on the value of Y or vice versa. The
  changes can be positive or negative.

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Correlational research

• Correlational techniques are typically used in
  studies where values are observed and do not
  involve the manipulation of variables. Also
  known as ex post facto data. Common in SLA
  research where naturally occurring variable are
  studied, e.g., age,length of exposure,
  proficiency level.

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• Correlational research ...allows the researcher
  to determine simultaneously the degree and
  direction of a relationship with a single
  statistic. Elmes et al p 104

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Linear relationships Correlations can vary in
strength and direction. Strong negative
Strong positive
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• Weak positive Weak
  negative

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Pearsons product moment correlation

• aka Pearsons r
• Commonly used statistical method for calculation
  the correlation between two variables. The r
  represents the correlation coefficient between
  the two variables. The magnitude of the
  correlation indicates the degree of
  relationshipIt ranges from 1.0 for perfect
  positive relationship, to 0 for no relationship,
  to
• -1.0 for a perfect negative relationship.

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The correlation coefficient

• The magnitude of the correlation indicates the
  degree of relationship, with the larger numbers
  reflecting stronger relations. The sign
  represents the direction of the relationship.
• The coefficient ranges from 1.0 for perfect
  positive relationship, to 0 for no relationship,
  to -1.0 for a perfect negative relationship.

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Interpreting the correlation coefficient.

• Interpreting the magnitude of an obtained
  correlation coefficient depends on many factors.
  However, general guidelines have been suggested
  by researchers. One commonly used framework
• .10 a weak or small association
• .30 moderate correlation
• .50 strong or large correlation
• Cohen, J. (1988).Statistical power analysis for
  the behavioural sciences (2nd ed.) New York
  Academic Press.

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• Correlations
• VOCAB GRAMMAR WORKMEM
• VOCAB Pearsons r 1 .654 .291
• Sig. (2-tailed) . .000 .132
• N 28
• GRAMMAR Pearsons r .654 1 .425
• Sig. (2-tailed) .000 . .024
• N 28 28 28
• WORKMEM Pearson Correlation .291 .425 1
• Sig. (2-tailed) .132 .024 .
• N 28 28 28
• Correlation is significant at the 0.01 level
  (2-tailed).
• Correlation is significant at the 0.05 level
  (2-tailed).

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Correlations between measures of English
vocabulary, grammar and working memory capacity
by university ESLsubjects (N28).

• VOCAB GRAMMAR WORKMEM
• VOCAB 1 .654 .291
• Sig. (2-tailed) . .000
  .132
• GRAMMAR .654 1
  .425
• Sig. (2-tailed) .000 .
  .024
• WORKMEM .291 .425
  1
• Sig. (2-tailed) .132 .024
  .
• N 28 28
  28
• Correlation is significant at the 0.01 level
  (2-tailed).
• Correlation is significant at the 0.05 level
  (2-tailed).
• From Harrington, Horiba Yoshida, 2003

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Scatterplot for ESL Vocabulary and Grammar scores
(r .65)
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Scatterplot for ESL Grammar and Working Memory
scores (r .42)
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Scatterplot for ESL Grammar and Working Memory
scores (r .29)
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Non-linear relationships

• A correlation is used to assess linear
  relationships. If the relationship is curvilinear
  the correlation will be low, even though there is
  a systematic relationship between the variables.

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A curvilinear relationship between age and memory
(Estes, et al., p 111)
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Correlation does not imply causation

• There does not have to be a causal link between X
  and Y in order to produce a correlation.
• Correlation Correlation Correlation
• X Y X Y X Y
• Causal link W
  No causal link
• Third variable
  Unknown direction

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Regression analysis

• Used to predict scores on one variable (Y) on the
  basis of information about X. Y can also be
  called the dependent variable or criterion, while
  X is called the independent variable or the
  predictor.
• For example, we might want to see if the length
  of study aboard in the target culture increasing
  proficiency test scores.

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Linear regression (least squares)

• The simplest way to predict Y is with an equation
  that produces a straight line. For example,
• Y bYXX aYX
• Y predicted score on Y
• bYX slope of the line, also called the
  regression coefficient for predicting Y (
  average rate of change in Y score per unit
  increase in X score)
• aYX Y-intercept, or the value of Y when X 0
  ( the Y value at which the line crosses the
  Y-axis)

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The regression line.

• 
  Regression line for
• Y
  predicting Y
• X Prediction of Y given score on X

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Least squares regression line

• Represents the line fitted to a set of points
  (representing the intersection of two variables)
  such that the sum of squares of the distances of
  all points from the line is minimised.

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A perfect linear relationship
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A (more realistic) positive relationship
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A curvilinear correlation
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• SLAT7806 week 6 end