How does the scale of data affect your choice between covariance and correlation?

It does depend on the relative measure both of the variables have. Since it is a multiplicative measure the one who is relative bigger or smaller will drop the other variable down. Honestly it really depends on the purpose of the research, for example I’ve identify that centering the variables works in most cases but in time series it could be better just differentiate the variables or transform it into logs.

Covariance is like a statistical tango: it reveals how two random variables move together. If both increase or decrease together, the covariance is positive. If one goes up while the other goes down, the covariance is negative. But like a good dance partner, the covariance needs adjustments for different scales. Imagine comparing height in centimeters with weight in kilograms! The covariance would be huge, but that doesn't mean the relationship between height and weight is any stronger than if you measured height in meters.

Use correlation rather than covariance when your data have various scales; it will make comparisons easier. Clear relationships can be shown via correlation without having to worry about the size of your data set.

It is true, however it is not sensity to outliers, so extreme values in one of the variables may bias the coefficient and distort at least the linear relationship assumption. As well as the derived conclusions.

Correlation, standardizes covariance by dividing it by the product of the standard deviations of the variables. This standardization makes correlation values range from -1 to 1, making them easier to interpret regardless of the data scale. A correlation coefficient close to 1 or -1 indicates a strong relationship, while values near 0 suggest a weak relationship. This feature is particularly useful when comparing variables of different units or scales.

Pearson's correlation coefficient, used to measure the relationship between two variables, goes beyond covariance by normalizing it, adjusting to different scales. This normalization results in a value between -1 and 1, where: > 1 indicates a perfect positive linear relationship: the variables increase together proportionally. > -1 indicates a perfect negative linear relationship: as one variable increases, the other decreases by the same amount. > 0 indicates no linear relationship: the variables do not show a pattern of joint increase or decrease.

In terms of data science we always look for controlling external effects, so I do agree that correlation provide better insights when it comes to large datasets since allows to have a unique standard to compare the association degree of serveral variables.

The scale of your data significantly influences the choice between covariance and correlation. For large-scale data with varying units and magnitudes, correlation is often preferred because it provides a unit-free measure of relationship strength. Covariance can be misleading in such cases as it is sensitive to the scale of the variables. For instance, when analyzing global economic indicators, correlation allows for meaningful comparisons between countries with vastly different GDPs.

The choice between covariance and correlation to analyze the relationship between two variables depends on the scale of your data. For small data sets with consistent units, covariance can provide quick insights without the need for normalization. This makes it a useful tool for initial explorations. However, as data sets increase in size and complexity, and especially when variables have different scales or units, correlation becomes more appropriate. It standardizes values, allowing a fair comparison between different data sets and ensuring that results are not skewed by the scale of the data itself.

The scale of data significantly impacts the choice between covariance and correlation in analytical decisions. When dealing with variables on disparate scales, covariance may obscure true relationships due to its reliance on units of measurement. Instead, correlation standardizes these variations, providing a consistent metric for assessing relationships. This standardization is critical for ensuring accurate comparisons and insights across diverse units. Consequently, correlation is often favored for its capacity to offer a clearer and more interpretable understanding of variable relationships

When choosing between covariance and correlation, consider the nature of your data and your analysis objectives. Correlation should be your go-to if you need a standardized measure that can be easily compared across different datasets. Covariance is useful when dealing with raw co-movements and when the variables are on a similar scale. In my experience, starting with correlation to get a broad sense of relationships, then delving into covariance for more detailed analysis, is a practical approach.