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Experimental Research Methods in Language Learning


Experimental Research Methods in Language Learning Chapter 11 Correlational Analysis – PowerPoint PPT presentation

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Title: Experimental Research Methods in Language Learning

Experimental Research Methods in Language
  • Chapter 11
  • Correlational Analysis

Correlational Analysis
  • Can you think of real life examples of
  • How do you express how much one thing is related
    to another thing?
  • What is a positive correlation? What is a
    negative one?

Correlational Analysis
  • Correlation allows researchers to explore a
    hypothetical relationship between variables.
  • Correlational analysis is typically used in
    non-experimental research, such as survey
    research or correlational research which aims to
    examine whether there is an association between
    variables of interest and if such an association
    exists, to what extent the variables are

Correlational Analysis
  • Correlation is fundamental to several advanced
    statistical techniques, including factor
    analysis, reliability analysis, and regression
  • One of the best strategies to start learning
    statistics for experimental research is via first
    learning how correlations are analyzed.

The Size and Sign of a Correlation Coefficient
  • There are five types of correlations introduced
    in this chapter
  • Pearson Product Moment
  • Point Biserial Correlation
  • Spearmans Rho Correlation
  • Kendalls Tau Correlation
  • Phi Correlation.

The Size and Sign of a Correlation Coefficient
  • A correlation coefficient is typically expressed
    on a scale from 0 (i.e., 0, no relationship) to
    1 (i.e., 100, perfect relationship).
  • If two variables are uncorrelated (i.e., 0),
    there is no systematic relationship between them
    and hence a prediction of one variable by the
    other is not possible.
  • A positive () correlation two variables are
    associated and move in the same direction in a
    systematic way.
  • A negative (-) correlation suggests that the two
    variables are associated with each other, but
    move systematically in the opposite direction.

Curvilinear Relationship
  • A curvilinear relationship At some level,
    something can be positive, but when it exceeds a
    certain level, it can become negative.
  • For example, we all know that some level of
    anxiety/pressure is good for test performance
    (because we will work harder and try to overcome
    it), but too much anxiety is bad for test
    performance because it takes control of our

Hypothesis Testing in Correlation
  • Researchers seek to test a hypothesis of whether
    two variables are related.
  • The null hypothesis (H0) states that there is no
    relationship between variable A and variable B
    (i.e., correlation coefficient 0).
  • The non-directional alternative hypothesis (H1)
    is that there is a relationship between variable
    A and variable B (i.e., correlation coefficient ?
  • A directional alternative hypothesis is there is
    a positive relationship between variable A and
    variable B (i.e., one-tailed).
  • The two-tailed test of significance is

Hypothesis Testing in Correlation
  • A typical p-value is taken to be 0.05. That is, a
    5 chance is acknowledged to error in rejecting
    the null hypothesis.
  • The degree of freedom (df) is determined by the
    total number of cases (or sample size) minus 1
    (i.e., N-1).

Effect Size and R-squared (R2)
  • The sign of the correlation (i.e., or -) is not
    related to the strength (or size) of the
  • A negative correlation does not mean that the
    finding is of no worth.
  • A correlation coefficient does not tell us how
    much one variable accounts for the other.
  • In some research topics, fairly weak correlations
    can be very important (i.e., they can indicate
    theoretical or practical significance) and in
    some cases even a shared variance of 10 can be
    worth acting upon.

Shared Variance
Correction for Attenuation
  • A correction for attenuation takes the
    reliability coefficients of the two measures into
    account in a Pearson correlation coefficient.
  • According to Hatch and Lazaraton (1991, p.444), a
    correction for attenuation can be computed as
  • rAB vreliability of A x reliability
    of B,
  • where rAB correlation coefficient.

Pearson Correlations
  • The Pearson Product Moment correlation (Pearsons
    r) is a parametric test for describing the
    relationship between two continuous variables.
  • Known as a simple bivariate correlation.
  • Pearson correlation can be used for numeric
    variables on continuous scales such as interval
    and ratio scales.
  • Two variables must be from the same participants.
  • A data set must be normally distributed or close
    to a normally distributed shape.

Five Statistical Assumptions for Pearson r
  • Pairs of data are related (i.e., X and Y scores
    are from the same person)
  • Continuous or interval-like data
  • Normal distribution
  • Linearity (i.e., the X-Y relationship that can be
    represented as a straight line
  • A spread of score variability
  • Assumptions 1 and 2 are easy to check.
  • Assumptions 3 and 5 can be addressed by computing
    descriptive statistics and creating a histogram.
  • Assumption 4 is checked through a scatterplot.

Point Biserial Correlations
  • Point Biserial Correlation is a non-parametric
  • Is a special case of the Pearson correlation.
  • Can be used to examine the relationship between a
    dichotomous variable (e.g. male-female, and
    yes-no) and a continuous variable (e.g., test

Spearmans Rho Correlations
  • Spearmans Rho correlation (?) is a
    non-parametric test.
  • Typically used for numeric variables on an
    ordinal or ranked scale (e.g., ranked list of
    test results, letter grades A-F, and steps on a
    Likert scale).
  • Can calculate the correlation of an ordinal score
    with an interval score.
  • Some information may be lost as continuous
    variables are ranked.

Kendalls Tau b Correlation
  • The Kendalls tau b correlation is a
    non-parametric alternative to the Spearman
  • Can be used to examine the level of agreement and
    disagreement between two sources of data.
  • For example, if a number of judges are used to
    score and rank candidates in order of performance
    outcomes, we would like to see the extent to
    which these judges agree with their ranking.

Phi Correlations
  • Phi (ø) correlation is a non-parametric test.
  • Is not used much in correlational studies.
  • Is useful for examining the relationship between
    two dichotomous variables (e.g., male or female,
    living or dead, pass or fail, agree or disagree,
    correct or wrong, homework or no homework, pair
    work or individual work).
  • These variables can be assigned as 1 or 0, or 1
    or 2, depending on how we code them in SPSS.

Factors Affecting Correlation Coefficients
  • A correlation coefficient is affected by several
    factors, some known and some unknown, including
  • Sample size
  • Correlational test being used
  • Outliers (extreme cases).
  • Reliability of the research instruments.
  • Restricted data or score range (e.g., truncated

  • Why do you think it is not suitable to use
    correlation to explain causation?
  • What is the difference between a correlation
    coefficient and a shared variance?
  • Do you think whether setting a probability value
    to be less than 0.05 is better or worse than
    setting it at 0.01? Why do you think so?
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