For example, there is a correlation between summer temperatures and ice cream sales. When one goes up, so does the other. Two variables are said to be. Scatter plots can be used for finding out the correlation between 2 variables. Given below are the data for height and weight. From the chart you can clearly see they are positively correlated. This works well on smaller dataset. If you need to analyze lots of data then it is not easy to interpret the results from the scatter plot.
What we need is a descriptive statistic which summarizes huge quantities of data into a single number. Correlation coefficient is used for this purpose. A correlation of 1 between two variables indicates that the change in one variable will result in equivalent change in the other variable in the same direction. A correlation of -1 indicates that the change in one variable results in a equivalent change in other variable in the opposite direction.
I am taking this example from the book Naked Statistics. Using the same height and weight example, let us calculate the correlation coefficient. The value of 0. Do not worry if you do not get the math. As long as you understand what the value means you should be good. There are tools available to do the math. In the book Naked Statistics the author writes. At the most basic level, Netflix is exploiting the concept of correlation.
First, I rate a set of films. Netflix compares my ratings with those of other customers to identify those whose ratings are highly correlated with mine. Those customers tend to like the films that I like. Once that is established, Netflix can recommend films that like-minded customers have rated highly but that I have not seen. The actual methodology is much more complex. Strong correlation between two variables does not mean that the change in one variable is causing the change in other.
Let me give an example taken from the book The Halo Effect. A famous statistician once showed a precise correlation between arrests for public drunkenness and the number of Baptist preachers in nineteenth-century America. The correlation is real and intense, but we may assume that the two increases are causally unrelated, and that both arise as consequences of a single different factor: a marked general increase in the American population.
This is an important concept and we confuse correlation and causation a lot in our life. In the book Thinking Statistically the author writes.
Does this mean that, say, eating ice-cream causes significant groups of children to go sugar-crazy and fall in a lake? Or, even more bizarrely, that while people are drowning they suddenly consume a lot of ice-cream? Well, unsurprisingly, no. Public health experts in the s noticed a correlation between polio cases and ice-cream consumption; they recommended cutting out ice-cream to protect against the disease.
It later turned out that, you guessed it, polio outbreaks were more common in summer, and ice-cream eating was more common in summer, and polio and ice-cream had nothing to do with each other.
If you ask the CEO the following question. One of the answers we often hear is our employees are happy and hence there is a low employee turnover which caused the success. Is that a correlation or causation? Excerpt from the book The Halo Effect.
Now the challenge is to untangle the direction of causality. Does lower employee turnover lead to higher company performance? Perhaps, since a company with a stable workforce might be able to provide more dependable customer service, spend less on hiring and training and so forth.
Or does higher company performance lead to lower employee turnover? Saul McLeod , updated Correlation means association - more precisely it is a measure of the extent to which two variables are related.
There are three possible results of a correlational study: a positive correlation, a negative correlation, and no correlation. A correlation can be expressed visually. This is done by drawing a scattergram also known as a scatterplot, scatter graph, scatter chart, or scatter diagram. A scattergram is a graphical display that shows the relationships or associations between two numerical variables or co-variables , which are represented as points or dots for each pair of score.
A scattergraph indicates the strength and direction of the correlation between the co-variables. When you draw a scattergram it doesn't matter which variable goes on the x-axis and which goes on the y-axis.
Remember, in correlations we are always dealing with paired scores, so the values of the 2 variables taken together will be used to make the diagram. Decide which variable goes on each axis and then simply put a cross at the point where the 2 values coincide. The correlation coefficient r indicates the extent to which the pairs of numbers for these two variables lie on a straight line.
Values over zero indicate a positive correlation, while values under zero indicate a negative correlation. A correlation of —1 indicates a perfect negative correlation, meaning that as one variable goes up, the other goes down. There is no rule for determining what size of correlation is considered strong, moderate or weak. The interpretation of the coefficient depends on the topic of study.
When studying things that are difficult to measure, we should expect the correlation coefficients to be lower e. When we are studying things that are more easier to measure, such as socioeconomic status, we expect higher correlations e.
In these kinds of studies, we rarely see correlations above 0. For this kind of data, we generally consider correlations above 0. When we are studying things that are more easily countable, we expect higher correlations. For example, with demographic data, we we generally consider correlations above 0. Causation means that one variable often called the predictor variable or independent variable causes the other often called the outcome variable or dependent variable.
Experiments can be conducted to establish causation.
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