How to use scatter diagrams in statistics

To visualize or observe the relationship between variables the best method you can use is to plot them in a graph known as a scatter diagram. It uses cartesian coordinates to display the value of the variable in a data set. we need to plot dots on the horizontal and vertical axis this will inform us of the value of respective data points. We use a scatter plot in such conditions when one variable is under the control of the experiment and the other one depends on the first one. If both continuous variables are independent then we can plot the through scatter plot. We plot dependent variables on the vertical axis and independent variables on the horizontal axis. If the dependent variable is not present then either type of variable can be plotted on either axis and in this condition the scatter plot will only display the correlation between two variables no causation will be displayed in this case.

Scatter diagram 

A scatter diagram is a method of demonstrating the relationship between two variables by positioning dots. Scatter diagram is also known as scatter plot, scatter charts, scatter graphs. By just looking at the several points we can determine the degree of correlation. The degree of the relation of the variable to one another is determined by how the points are distributed over the graph. The degree of correlation depends on the scattering of points on the graph. More the points plotted lesser will be the degree of correlation. The degree of correlation is denoted by the letter r.

Different types of scatter diagrams

1.Perfect positive correlation- when r = +1. This is the condition when all the points lie on the straight line from the bottom left corner to the top right corner.

2. Perfect negative correlation- in this condition r=-1. It is when all the points lie on the straight lie but upside down i.e., they fall from the upper left to the lower right corner.
3. High degree of positive correlation- in this condition points don’t lie exactly on the line but fall near the straight line and they are said to be positive as they show the rising trends from the lower-left corner to the upper right.
4. lower degree of positive correlation- as this graph shows rising tendency it is positive but due to the highly scatter points over the graph it is termed as low degree positive correlation.
5. High degree of negative correlation- it is the extended version of negative correlation in which the point plotted falls near narrowband and shows characteristics of negative correlation.
6. low degree of negative correlation- as the graph, in this case, shows a falling tendency this is known as a negative correlation. With that in this type of graph, points are scattered over the graph which makes it a low degree of negative correlation.
7. No correlation – it is a graph in which the points are located in a chaotic order. They do not show any pattern in this case correlation tends to zero. So, r=0.

Applications of scatter diagrams

1. The first and foremost application is it tells us the relationship between two variables by the means of plotting the points in the scatter plot.
2. Another important use of scatter plot is they tell us the type of correlational relationships. In the case of independent variables points are located on the horizontal axis and in the case of the dependent variable the points lie on the vertical axis.
3. Scatter plots help us to identify the pattern of data. It can be a positive correlation, negative correlation and null mean no correlation.

Correlation as causation

In a scatter plot we study the relationship between two variables but it never means that the change in one variable is responsible for the change in the other; this means that the correlation does not imply causation. This isn’t so much a problem while making a scatter plot as it is with interpreting it. It’s possible that the correlation does not imply causation is influenced by a third variable that affects both of the plotted variables, that the causal link is reversible, or that the pattern is purely coincidental.

How to describe a pattern in a scatter plot?

We illustrate the general pattern with descriptors of direction, form, and strength in a scatterplot. Outliers are still defined as deviations from the norm. A positive (or rising) relationship indicates that an increase in one variable causes an increase in the other.

Conclusion 

A scatter plot or scatter graph or scatter chart is a diagrammatic representation that is used to display the relationship between variables. The individual values of each of the data points are represented by the dots that appear on the scatter plot. And we can even identify a pattern by looking at the diagram. The basic use of a scatter plot is to show the relationship between variables and observe the nature of the relationship. The nature of the relationship can be categorized as positive, negative, linear, non-linear, strong, or weak.