Week 4 - non-parametric correlations Flashcards
How do we test for normality?
Independent samples t-test:
- Between subjects design
- Test the normality of each of the two groups of data
- Divide Skewness by Std error skewness
- Divide Kurtosis by Std error Kurtosis
Repeared measures t-test:
- Calculate the score differences
- Test the normality of different between scores
For data to be normal all these values must be between plus and minus 1.96
- If one of them is greater than 1.96 (>1.96) OR
- If one of them is less than -1.96 (<-1.96) The data is not normally distributed and you need to use a non-parametric alternative
How many Histograms?
Between-groups: TWO
Within-groups: ONE
What are mean, median, standard deviation and interger scales rounded to/reported?
- Mean, median & standard deviation are generally reported to two decimal places
- However, where data is measured on an INTERGER scale, means etc. are reported to
one decimal place.
What does a correlation coefficient represent?
The amount of association between two variables.
- The correlation coefficient measures the strength and direction of the linear relationship between two variables
- Values range from -1 to 1 where:
1 indicates a perfect positive relationship.
-1 indicates a perfect negative relationship.
0 indicates no linear relationship.
What does a correlation coefficient measure?
The relationship between two continuous variables.
What does the value of a correlation coefficient represent?
The strength of the association, as the correlation coefficient primarily represents the strength of the association between two variables.
The sign ( +/- ) indicates the direction of the relationship (positive or negative).
The coefficients absolute value provides information about the strength of the association
How are variables affected in a Positive/Negative correlation?
POSITIVE CORRELATION: As one variable goes up the other variable also goes up
NEGATIVE CORRELATION: As one variable goes up the other variable goes down
What is the difference between parametric and non-parametric tests?
Typical PARAMETRIC TESTS can only assess continuous data and the results can be significantly affected by outliers.
NONPARAMETRIC TESTS can handle ordinal data, ranked data, and not be seriously affected by outliers.
Pearson’s R is a parametric test. What certain assumptions does it have to meet to use its data?
- Variables must be normally distributed: Pearson’s r assumes that the variables are normally distributed.
-
The relationship between variables should be linear: Pearson’s r measures the strength and direction of a linear relationship between two variables. If the relationship is not linear, the
correlation coefficient may not accurately reflect the association. - Variables must be continuous: Pearson’s r is intended for continuous variables, as it measures the linear relationship between them. Using ordinal or categorical data violates this assumption, and an alternative test is needed.
Not an Assumption: The correlation distribution must not contain outliers
- While outliers can impact the value of Pearson’s r, the test itself does not assume the absence of outliers.
What is Spearman’s rank correlation coefficient calculated on?
The rank differences.
Spearman’s rank correlation coefficient is calculated based on the differences between the ranks of the variables.
The steps involve converting the original scores to ranks, calculating the differences between
these ranks (d=x-y), squaring these differences (d2),
and then
using these squared differences in the final formula.
Non-parametric correlations, such as Spearman’s rank correlation, can be run on data that is normally distributed.
When are non-parametirc methods used?
Non-parametric methods are often used when data does not meet the assumptions required for parametric tests,
but they can still be applied to normal data if desired.
Name a parametric test?
- t-test (both paired and unpaired),
- Pearson’s R
Name a non-parametric test
- Mann-Whitney U
- Wilcoxon signed
- Chi-square test
- Kendall’s tau
Which test is most accurate with tied ranks?
Kendall’s Tau
This test is the most accurate with tied ranks. It is particularly well-suited for data with tied ranks. It calculates the correlation based on the concordance and discordance of pairs, making it more
robust and accurate in the presence of ties
What is needed to calculate Kendall’s tau?
Concordant Pairs
Kendall’s tau is calculated based on the number of concordant and discordant pairs of observations.
Which tests cannot be run with correlation outliers?
Wilcoxon’s W.
- Wilcoxon’s W is a non-parametric test used to compare two related samples or paired observations to assess whether their population mean ranks
differ. - It is not a correlation test and doesn’t involve the
measurement of relationships between variables, - hence why it isn’t applicable for correlation outliers
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