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Exam Notes
Advanced Research Methods (Western Sydney University)
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Advanced Research Methods
Revision Notes
STATSTICS
TOPIC 1: Bivariate Correlation & Regression
BIVARIATE CORRELATION
• A Bivariate Correlation is the relationship between two variables
• These relationships are best shown by a scattergram or
scatterplot
• There are four different types of relationships
Type of Relationship What Happens
Positive Variables covary together
Negative Variables covary in the opposite
direction
No relationship When variables covary
independently
Perfect relationship Where one variable predicts the
other with 100% accuracy
• Correlational research looks at how variables are related
THE CORRELATION (r) AND SQUARED CORRELATION (r2) COEFFICIENT
• The statistical measure of correlation is the correlation coefficient
• It has the symbol r aka Pearson’s r
• This is looking at the strength of the relationship
• It ranges from -1.00 to +1.00
• Number is the magnitude (of relationship) and the sign indicates
the direction of the relationship
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Range of r Type of Correlation
.00 à .09 Negligible, very weak
.10 à .29 Weak, low, small
.30 à .49 Moderate, medium
.50 à .69 Strong, high, large
.70 à 1.0 Very strong, very high
• The SQUARED CORRELATION COEFFICIENT (r2) is another way to
interpret the strength of a correlation
• It indicates the proportion of variance in one variable
explained/predicted by the other
• The more the two variables share in common, the more
information about performance in one score can be explained by
the other
• Let’s say we have two variables x and y. If the correlation between
them is .50 (r) then (r2) is .25. This means that 25% of the variance
in one variable can be explained by the other, leaving 75% of the
variance in each to be explained by other factors
• R2 is also known as the coefficient of determination
ASSUMPTIONS OF A CORRELATION ANALYSIS
1. Linearity
- The relationship between the two variables must be linear
- There should be no indicator of a curvilinear relationship
- This is because it will cause an underestimation of the
degree of correlation
- Spearman’s correlation can cope with curvilinear
relationships where there is no reversal of direction
(monotonic)
- Pearson’s r can only deal with a LINEAR relationship
2. Homoscedasticity
- This means that the distribution should be equal across the
range X scores
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3. Restricted range
- There should be no restricted range on one or both
variables, as this will reduce the true correlation between
them.
- Low person correlation coefficients may arise even though
there is a strong relationship
- For example, a strong positive relationship is evident
between the two variables in the scatterplot below, but if
we restricted the scores to the upper range only (the box
within the scatterplot) there would appear to be no
relationship between the variables
4. Outliers
- Outliers are a serious problem as they distort correlations
- Usually they need to be deleted, although this action must
be reported in the results section and the researcher should
attempt to understand and evaluate why a case is an outlier
Downloaded by COLLINS WANJOHI ()
Exam Notes
Advanced Research Methods (Western Sydney University)
Studocu is not sponsored or endorsed by any college or university
Downloaded by COLLINS WANJOHI ()
, lOMoARcPSD|35435103
1
Advanced Research Methods
Revision Notes
STATSTICS
TOPIC 1: Bivariate Correlation & Regression
BIVARIATE CORRELATION
• A Bivariate Correlation is the relationship between two variables
• These relationships are best shown by a scattergram or
scatterplot
• There are four different types of relationships
Type of Relationship What Happens
Positive Variables covary together
Negative Variables covary in the opposite
direction
No relationship When variables covary
independently
Perfect relationship Where one variable predicts the
other with 100% accuracy
• Correlational research looks at how variables are related
THE CORRELATION (r) AND SQUARED CORRELATION (r2) COEFFICIENT
• The statistical measure of correlation is the correlation coefficient
• It has the symbol r aka Pearson’s r
• This is looking at the strength of the relationship
• It ranges from -1.00 to +1.00
• Number is the magnitude (of relationship) and the sign indicates
the direction of the relationship
Downloaded by COLLINS WANJOHI ()
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2
Range of r Type of Correlation
.00 à .09 Negligible, very weak
.10 à .29 Weak, low, small
.30 à .49 Moderate, medium
.50 à .69 Strong, high, large
.70 à 1.0 Very strong, very high
• The SQUARED CORRELATION COEFFICIENT (r2) is another way to
interpret the strength of a correlation
• It indicates the proportion of variance in one variable
explained/predicted by the other
• The more the two variables share in common, the more
information about performance in one score can be explained by
the other
• Let’s say we have two variables x and y. If the correlation between
them is .50 (r) then (r2) is .25. This means that 25% of the variance
in one variable can be explained by the other, leaving 75% of the
variance in each to be explained by other factors
• R2 is also known as the coefficient of determination
ASSUMPTIONS OF A CORRELATION ANALYSIS
1. Linearity
- The relationship between the two variables must be linear
- There should be no indicator of a curvilinear relationship
- This is because it will cause an underestimation of the
degree of correlation
- Spearman’s correlation can cope with curvilinear
relationships where there is no reversal of direction
(monotonic)
- Pearson’s r can only deal with a LINEAR relationship
2. Homoscedasticity
- This means that the distribution should be equal across the
range X scores
Downloaded by COLLINS WANJOHI ()
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3
3. Restricted range
- There should be no restricted range on one or both
variables, as this will reduce the true correlation between
them.
- Low person correlation coefficients may arise even though
there is a strong relationship
- For example, a strong positive relationship is evident
between the two variables in the scatterplot below, but if
we restricted the scores to the upper range only (the box
within the scatterplot) there would appear to be no
relationship between the variables
4. Outliers
- Outliers are a serious problem as they distort correlations
- Usually they need to be deleted, although this action must
be reported in the results section and the researcher should
attempt to understand and evaluate why a case is an outlier
Downloaded by COLLINS WANJOHI ()
