Crosstabulation
a tabular method for summarizing the distributional characteristics of the data for two variables simultaneously.
Crosstabulation takes the form of:
- Contingency table: qualitative data
- Correlation table: quantitative data
- A mix of qualitative and quantitative data
Covariance definition
Covariance is a measure of how much two random variables vary together. It’s similar to variance, but where variance tells you how a single variable varies, co variance tells you how two variables vary together.
Correlation definition
Absence of correlation
- The absence of correlation between X and Y (ρ = 0) is always due to the covariance (sxy = 0).
- Nul covariance can be attributed to:
- Perfect independence between the variables
- Nonlinear relationship between the variables
Spurious relationship
when the correlation between two phenomena taken alone is basically nonsense.
chi-square statistic
The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.
Crosstabulation: an example of a contingency table
Crosstabulation: an example of a correlation table
It can be shown (after some algebra) that if X and Y are independent, the ij frequency must be equal to:
Theoretical independent frequencies definition
the frequencies that would be observed in case
of perfect independence between X and Y
Measure of association:
