Correlational analysis (8)

Research methods and statistics lecture 8

What does a scatterplot describe?

A scatterplot describes the association between two variables.

What are the three characteristics of the association between two variables?

The three characteristics are direction, strength and form

Direction refers to whether the association is positive or negative.

Strength indicates how closely the two variables are related, which can be weak, moderate, or strong.

Form describes the type of relationship, such as linear (straight line) or non linear

What defines a positive association?

In a positive association, as one variable increases, the other variable also increases. This relationship implies that there is a direct correlation between the two variables, meaning that higher values of one variable correspond to higher values of the other.

What defines a negative association?

In a negative association, as one variable increases, the other variable decreases. This relationship implies an inverse correlation between the two variables, meaning that higher values of one variable correspond to lower values of the other.

What does the strength of an association indicate?

The strength of an association indicates how much knowing a person's score on variable 1 provides information about variable 2.

What are the two correlation coefficients discussed?

The two correlation coefficients are Pearson product-moment correlation and Spearman rank correlation.

What data is used for the Pearson correlation coefficient?

The Pearson correlation coefficient is used for normally distributed interval or ratio level data.

When is the Spearman rank correlation used?

The Spearman rank correlation is used for ordinal level data or when interval/ratio data are not normally distributed.

How can correlation coefficients be interpreted?

A correlation coefficient can vary between -1 and +1, providing insights into the strength and direction of a relationship between two variables.

A correlation coefficient of -1 indicates a perfect negative correlation, meaning that every increase in one variable results in a proportional decrease in the other variable.

A correlation coefficient of 0 suggests no correlation between the two variables, indicating that changes in one variable do not predict any change in the other.

A correlation coefficient of +1 indicates a perfect positive correlation, where increases in one variable directly lead to increases in the other variable.

What hypothesis is tested in a correlation test?

The null hypothesis (H0) states that the correlation coefficient (r) equals 0.

What is the alternative hypothesis in a correlation test?

The alternative hypothesis (H1) states that the correlation coefficient (r) does not equal 0.

What does a significant p-value (p < .05) indicate?

A significant p-value indicates that the null hypothesis can be rejected.

What does it mean if the correlation test is not significant (p > .05)?

It means that there is not enough evidence to reject the null hypothesis.

How are degrees of freedom relevant in hypothesis testing?

Degrees of freedom indicate the number of independent observations that can vary in a statistical test.

What does a one-tailed test evaluate?

A one-tailed test evaluates whether the correlation is either positive or negative.

What is the importance of scatterplots in correlation analysis?

Scatterplots help visualize the strength and direction of correlations.

How can a one-sided test affect the interpretation of results?

Conducting a one-sided test can mislead interpretations if the non-significant results are treated as significant.

What is a spurious correlation?

A spurious correlation is a relationship where two variables seem to correlate due to a third variable influencing both.

What is the purpose of using correlation tests?

Correlation tests are used to make inferences about the correlation in a population based on a sample.

What would using a correlation table provide?

A correlation table provides a summary of correlations between multiple variables.

How is Pearson's correlation calculated?

It is calculated using the covariance of the variables and their standard deviations.

What does "line of best fit" represent in a scatterplot?

The line of best fit represents the best estimate of the linear relationship between two variables.

What can a scatterplot indicate besides correlation strength?

A scatterplot can also reveal the shape of the relationship between variables.

Why must researchers justify one-sided tests?

One-sided tests must be justified to avoid bias and maintain the integrity of the analysis.

Can correlation coefficients differ based on data type?

Yes

How is significant correlation often reported?

Significant correlation is often reported with the correlation coefficient (r) and the p-value.

What is an example of a directional hypothesis?

An example of a directional hypothesis is H1: r > 0

What does significant correlation suggest about the variables?

Significant correlation suggests there is a meaningful association that warrants further investigation.

What is one challenge in interpreting correlations?

One challenge is distinguishing real relationships from spurious correlations caused by confounding variables.