correlations two

What are the two fundamental ways to test a hypothesis?

Observing what naturally happens (correlational research) or manipulating variables to observe effects (experimental research).

What defines correlational research design?

Observing naturally occurring variables without direct manipulation.

What defines experimental research design?

Systematic manipulation of one variable to observe its effect on another.

Why does correlational research provide a natural view of behaviour?

Because the researcher does not influence events or measurements.

Give an example of correlational research.

Observing pollution levels and fish populations, or smoking rates and cancer diagnoses.

In correlational research, how can variables relate to each other?

They can vary in the same way, opposite ways, or in unrelated ways.

What does covariance describe?

How two variables change together.

What does positive covariance indicate?

Both variables increase or decrease together.

What does negative covariance indicate?

As one variable increases, the other decreases.

What does zero covariance indicate?

No systematic relationship between variables.

What is the correlation coefficient (r)?

A standardised statistic measuring the direction and strength of the relationship between two variables.

What two features does r describe?

Direction and size (strength) of a relationship.

What is the range of the correlation coefficient?

From -1 to +1.

What does r = +1 indicate?

A perfect positive linear relationship.

What does r = -1 indicate?

A perfect negative linear relationship.

What does r = 0 indicate?

No linear relationship between variables.

What is the third variable problem?

The possibility that an unmeasured variable explains the relationship between two correlated variables.

Why does the third variable problem prevent causal conclusions?

Because it is unclear whether one variable causes the other or both are caused by something else.

In the ice cream sales and drowning example, what is the third variable?

Hot weather.

What is a parametric test?

A statistical test that makes assumptions about the data.

What assumptions do parametric correlation tests make?

Continuous variables, independence, linearity, and no extreme outliers.

What does independence mean in correlation analysis?

One participant’s data does not influence another participant’s data.

Why are extreme outliers problematic for parametric correlations?

They can distort the correlation coefficient.

What does linearity mean in correlation?

The relationship between variables follows a straight-line pattern.

What are non-parametric tests?

Statistical tests that make fewer assumptions about the data.

Why are non-parametric tests sometimes described as assumption-free?

They do not require normal distributions or continuous data.

Why are non-parametric tests sometimes less powerful?

They use less information by analysing ranks rather than raw scores.

What is the core principle behind non-parametric tests?

Ranking the data.

How is ranking carried out in non-parametric correlation?

Scores are ordered from lowest to highest and assigned ranks.

What does a high rank represent?

A high score in the dataset.

What does it suggest if high ranks on one variable pair with high ranks on another?

A positive relationship.

What does it suggest if high ranks on one variable pair with low ranks on another?

A negative relationship.

What does it suggest if ranks show no consistent pattern?

No relationship between variables.

Why does ranking reduce the impact of outliers?

Extreme values are compressed into nearby ranks.

How does ranking help with skewed data?

It removes the influence of uneven distributions.

What are tied ranks?

When the same score occurs more than once in a dataset.

How are tied ranks handled?

Each tied score is given the average of the ranks they would have occupied.

Why are tied ranks necessary?

To preserve fairness and accuracy in ranked data.

What types of correlation are covered in this lecture?

Pearson’s r, Spearman’s rho, Kendall’s tau, and point-biserial.

What type of test is Pearson’s r?

A parametric correlation.

What data does Pearson’s r require?

Two continuous variables measured at interval or ratio level.

Give examples of data suitable for Pearson’s r.

Test scores, height, time, temperature.

What is Spearman’s rho?

A non-parametric correlation based on ranked data.

When should Spearman’s rho be used?

When data are ordinal or violate parametric assumptions.

What is Kendall’s tau?

A non-parametric correlation often preferred for small samples.

Why might Kendall’s tau be preferred to Spearman’s rho?

It may better estimate population correlations in small samples.

How may Spearman’s correlation coefficient be reported?

rs or the Greek letter rho (ρ).

What is the formula for degrees of freedom in correlation?

df = N − 2.

Why does the correlation coefficient and p-value change depending on the test?

Different tests make different assumptions and use different data representations.

What is a categorical variable?

A variable consisting of categories rather than numerical values.

What is a dichotomous variable?

A categorical variable with two possible values.

Give examples of dichotomous variables.

Yes/No, present/absent, owns/does not own.

What is point-biserial correlation used for?

When one variable is continuous and the other is dichotomous.

Is point-biserial correlation parametric or non-parametric?

Parametric.

How is point-biserial correlation related to Pearson’s r?

It is Pearson’s r with one binary variable.

Why should the direction of a point-biserial correlation be interpreted cautiously?

It depends on how the dichotomous variable was coded.

In point-biserial correlation, what should be interpreted instead of direction?

The existence and strength of the association.

Why is data visualisation important in correlation analysis?

It helps interpret relationships and detect misleading patterns.

How can scatterplots help identify problems in correlation analysis?

They reveal outliers and non-linear relationships.

Why can numerical correlations be misleading without visualisation?

Different patterns can produce similar r values.