Q 614. Correlation is an indicator or relationship between two variables (X and Y). While potentially the coefficient of correlation can range from -1 to +1, could there be a situation where it is zero i.e. No Correlation for a known cause and effect? Provide examples to support your answer.

 

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Zero Correlation Definition

Zero correlations indicating there is no linear relation ship between the compared 2 variables.

 

Could there be situation where correlation is zero?

Yes there could be situations where 2 variables can have zero correlation.

 

Examples 

Salary earned Vs Hair on the Head.

Age Vs Nails length

Amount of Food eaten Vs Crime rate

Bike cost Vs Shoe size

Cholesterol level Vs Intelligence 

Calendar Year Vs Pass Rate

Finger size Vs Head shape

No: of children Vs Financial Success

Blood group Vs Shirt Color

Correlation shows the direction (positive or negative) and strength (strong, weak or null) of relationship between two variables. It is represented using correlation coefficient. Its value lies between -1 to +1; higher the magnitude, stronger the relationship between variables. Types of correlation coefficient are as follows:

 

 

There can be cases wherein the correlation coefficient is zero for a known cause and effect relationship - this is because of the following reasons:

 

1. Non linear relationship between variables 
    One assumption while working with Correlation coefficient and regression is that there is a linear relationship between variables. If this assumption is violated, the correlation coefficient values can vary significantly.

 

2. Interaction effect
    Interaction between the variables in consideration and other external variables can cause the correlation coefficient to be zero.

 

(Example) In ecommerce, customer satisfaction is poor for slow deliveries. As delivery time improves, the customer satisfaction improves significantly at first. Beyond a certain point any improvement in delivery time will not impact the customer satisfaction - satisfaction will be affected by other variables like quality, customer support, pricing etc. thereby dropping the coefficient value close to zero despite a known cause and effect relationship

There could be potentially zero correlation between known cause and effects, meaning when one variable is set to some value, the other variable may still fall or rise.

We can explain it with an example.

 

There is a male boy of 6 years with autism. As the age of the boy increases to 7, the level of autism or ASD CARS(childhood autism rating scale) may rise or fall even though there is a cause and effect assumption that autism rate will diminish as the child grows because the neurons or hyperactivity tend to settle down/burnt out with age.

 

Further there is global data available that shows boys have more autism than girls. But still in principle or reality could be opposite due to uncollected or not analysed data. This in no way would means that if boys keep increasingly diagnosed with autis

, the rate at which girls are detected would come down. That would be a wrong assumption to make.

 

i would like to explain with another example too using the same autism spectrum disorder (ASD).

 

In order to control the hyperactivity, there is a medicine used called Risperidone. Now if we were to give 1ml or 20 drops to a child aged 5, would mean he must be more settled than his peers with same level of ASD. If we increase the dosage to 1.5ml or to 30 drops in a day, it can be both adverse or favourable. So there is no correlation between childhood age autism and dosage of medicine.

correlation coefficient -its is a way of verifying the relation between 2 variables.

It can be best described by regression analysis

They are 3 types.

1-Positive co-relation

2-Negative co-relation

3- Linear co-relation

Positive co-relation 0 to +1

1 means strong positive co-relation

we can find the co-relation line directing NE in the graph.

Negative co-relation -1 to 0

-1 means strong negative relation

we can find the co-relation line directing NW in the graph

Formula

0 means Linear co-rrelation or poor co-relation.

Coefficient of correlation= co efficient of variance(variables)/Product of standard deviation of variables.

 

  Coefficient of determination is an indicator which set up a relative relationship between two variables where one variable is called dependent and other independent denoted by “Y” and “X” respectively.  Coefficient of determination can be computed with the help of below formula ( symbolized by “r”)

 

There are three type of correlation, as stated below:
Positive Correlation : when one variable increases then other will also increase, called positive correlation between two variables.
Negative Correlation: When one variable decreases then other will also decrease. Called negative correlation between two variables.
No Correlation: when one variable increases or decrease, there is no change in other variable is called no-correlation between two variables.
To compute the strength of correlation, we find range from +1 to -1 ( with the help of above formula).  If coefficient of determination value is closed to 1 is called strong correlation ( on either positive or negative side), if r-value is zero, it indicates that there is no relation between both variables.

We can splinter coefficient of determination range as per below table for more articulation :

 

 

Example of +ve correlation between Semiconductor device and leakage current: higher the wattage, higher the leakage current. It's shows positive strong relation.

 

Example of -ve relationship, increasing device thickness reduces leakage current. showing -ve correlation.

 

No Correlation for a known cause and effect?

No correlation between both variables, device leakage current with device temperature. All shown parameters are important for device reliability but it does not mean that all parameters have direct relation to each other in the reference of above +ve and -ve relationship examples.

 

In case, when gauge happens to be out of order and dependent variable is not being changed by changing independent variable, relation between both variable get lost ( coefficient of determination r=0). while both parameters have strong positive relationship.

 

The question was for variables that are in known cause and effect relationship. While, some of the answers have highlighted cases where correlation is zero but that is between two unrelated things. Correlation coefficient can be zero between 2 variables (that in a known cause and effect relationship) if they have a non-linear relationship.

The best answer has been provided by Keerthi Vasan. Well done!