MTH5P2A: Scatter Diagram

This unit explains scatter diagram

Scatter Diagram

The scatter diagram is known by many names, such as scatter plot, scatter graph, and correlation chart. This diagram is drawn with two variables, usually the first variable is independent and the second variable is dependent on the first variable.

scatter-diagram

The scatter diagram is used to find the correlation between these two variables. This diagram helps you determine how closely the two variables are related. After determining the correlation between the variables, you can then predict the behavior of the dependent variable based on the measure of the independent variable. This chart is very useful when one variable is easy to measure and the other is not.

Example

You are analyzing the pattern of accidents on a highway. You select the two variables: motor speed and number of accidents, and draw the diagram.

Once the diagram is completed, you notice that as the speed of vehicle increases, the number of accidents also goes up. This shows that there is a relationship between the speed of vehicles and accidents happening on the highway.

According to the PMBOK Guide 6th edition, the scatter diagram is, “A scatter diagram is a graph that shows the relationship between two variables. Scatter diagrams can demonstrate a relationship between any element of a process, environment, or activity on one axis and a quality defect on the other axis.”

Since this diagram shows you the correlation between the variables, it is also known as a correlation chart.

Usually the independent variable is plotted along the horizontal axis (x-axis) and the dependent variable is plotted on the vertical axis (y-axis). The independent variable is also known as the control parameter because it influences the behavior of the dependent variable.

It is not necessary for one parameter to be a controlling parameter. You can draw the scatter diagram with both variables independent to each other. In this case you can draw any variable on any axis.

Please note that the scatter diagram is different than the Ishikawa or fishbone diagram. With the Ishikawa diagram you see the effect of a cause, and in the scatter diagram you analyze the relationship between the two variables.

Type of Scatter Diagram

The scatter diagram can be categorized into several types; however, I will discuss the two types that will cover most scatter diagrams used in project management. The first type is based on the type of correlation, and the second type is based on the slope of trend.

According to the type of correlation, scatter diagrams can be divided into following categories:

  • Scatter Diagram with No Correlation
  • Scatter Diagram with Moderate Correlation
  • Scatter Diagram with Strong Correlation

Scatter Diagram with No Correlation

This type of diagram is also known as “Scatter Diagram with Zero Degree of Correlation”.

scatter-diagram-with-no-correlation

In this type of scatter diagram, data points are spread so randomly that you cannot draw any line through them.

In this case you can say that there is no relation between these two variables.

Scatter Diagram with Moderate Correlation

This type of diagram is also known as “Scatter Diagram with Low Degree of Correlation”.

scatter-diagram-with-moderate-correlation

Here, the data points are little closer together and you can feel that some kind of relation exists between these two variables.

Scatter Diagram with Strong Correlation

This type of diagram is also known as “Scatter Diagram with High Degree of Correlation”.

In this diagram, data points are grouped very close to each other such that you can draw a line by following their pattern.

scatter-diagram-with-strong-correlation

In this case you will say that the variables are closely related to each other.

As discussed earlier, you can also divide the scatter diagram according to the slope, or trend, of the data points:

  • Scatter Diagram with Strong Positive Correlation
  • Scatter Diagram with Weak Positive Correlation
  • Scatter Diagram with Strong Negative Correlation
  • Scatter Diagram with Weak Negative Correlation
  • Scatter Diagram with Weakest (or no) Correlation

Strong positive correlation means there is a clearly visible upward trend from left to right; a strong negative correlation means there is a clearly visible downward trend from left to right. A weak correlation means the trend, up of down, is less clear. A flat line from left to right is the weakest correlation, as it is neither positive nor negative and indicates the independent variable does not affect the dependent variable.

Scatter Diagram with Strong Positive Correlation

scatter-diagram-with-strong-correlation

This type of diagram is also known as Scatter Diagram with Positive Slant.

In positive slant, the correlation will be positive, i.e. as the value of x increases, the value of y will also increase. You can say that the slope of straight line drawn along the data points will go up. The pattern will resemble the straight line.

For example, if the temperature goes up, cold drink sales will also go up.

Scatter Diagram with Weak Positive Correlation

scatter-diagram-with-weak-positive-correlation

Here as the value of x increases the value of y will also tend to increase, but the pattern will not closely resemble a straight line.

Scatter Diagram with Strong Negative Correlation

scatter-diagram-with-strong-negative-correlation

This type of diagram is also known as Scatter Diagram with Negative Slant.

In negative slant, the correlation will be negative, i.e. as the value of x increases, the value of y will decrease. The slope of a straight line drawn along the data points will go down.

For example, if the temperature goes up, sales of winter coats goes down.

Scatter Diagram with Weak Negative Correlation

scatter-diagram-with-weak-negative-correlation

Here as the value of x increases the value of y will tend to decrease, but the pattern will not be as well defined.

Scatter Diagram with no Correlation

In this type of chart, you are not able to see any kind of relationship between the two variables. It might just be a series of points with no visible trend, or it might simply be a straight, flat row of points. In either case, the independent variable has no effect on the second variable (it is not dependent).

Limitations of a Scatter Diagram

The following are a few limitations of a scatter diagram:

  • Scatter diagrams are unable to give you the exact extent of correlation.
  • Scatter diagram does not show you the quantitative measure of the relationship between the variable. It only shows the quantitative expression of the quantitative change.
  • This chart does not show you the relationship for more than two variables.

Benefits of a Scatter Diagram

The following are a few advantages of a scatter diagram:

  • It shows the relationship between two variables.
  • It is the best method to show you a non-linear pattern.
  • The range of data flow, i.e. maximum and minimum value, can be easily determined.
  • Observation and reading is straightforward.
  • Plotting the diagram is relatively simple.

Summary

Scatter diagrams are very useful to determine the relation between two variables. Usually the first variable is independent and the second is dependent on the first variable. To analyze the pattern of the relationship, you make changes to the independent variable and monitor the changes in the dependent variable.

Please keep in mind that the scatter diagram is different than the Ishikawa diagram. The Ishikawa diagram shows you only the variables; it does not show you the relationship between these variables. However, the Ishikawa diagram can help you draw the scatter diagram; for example, you can find the two variables (cause and effect), and then draw the scatter diagram to analyze the relationship between them.

Here is where this blog post on the scatter diagram ends. If you have something to share or any questions, you can do so through the comments section.

Definition: The Scatter Diagram Method is the simplest method to study the correlation between two variables wherein the values for each pair of a variable is plotted on a graph in the form of dots thereby obtaining as many points as the number of observations. Then by looking at the scatter of several points, the degree of correlation is ascertained.

The degree to which the variables are related to each other depends on the manner in which the points are scattered over the chart. The more the points plotted are scattered over the chart, the lesser is the degree of correlation between the variables. The more the points plotted are closer to the line, the higher is the degree of correlation. The degree of correlation is denoted by “r”.

The following types of scatter diagrams tell about the degree of correlation between variable X and variable Y.

  1. Perfect Positive Correlation (r=+1): The correlation is said to be perfectly positive when all the points lie on the straight line rising from the lower left-hand corner to the upper right-hand corner.Scatter diagram-1
  2. Perfect Negative Correlation (r=-1): When all the points lie on a straight line falling from the upper left-hand corner to the lower right-hand corner, the variables are said to be negatively correlated.Scatter diagram-2
  3. High Degree of +Ve Correlation (r= + High): The degree of correlation is high when the points plotted fall under the narrow band and is said to be positive when these show the rising tendency from the lower left-hand corner to the upper right-hand corner.Scatter diagram-3
  4. High Degree of –Ve Correlation (r= – High): The degree of negative correlation is high when the point plotted fall in the narrow band and show the declining tendency from the upper left-hand corner to the lower right-hand corner.Scatter diagram-4
  5. Low degree of +Ve Correlation (r= + Low): The correlation between the variables is said to be low but positive when the points are highly scattered over the graph and show a rising tendency from the lower left-hand corner to the upper right-hand corner.Scatter diagram-5
  6. Low Degree of –Ve Correlation (r= + Low): The degree of correlation is low and negative when the points are scattered over the graph and the show the falling tendency from the upper left-hand corner to the lower right-hand corner.Scatter diagram-6
  7. No Correlation (r= 0): The variable is said to be unrelated when the points are haphazardly scattered over the graph and do not show any specific pattern. Here the correlation is absent and hence r = 0.Scatter diagram-7

Thus, the scatter diagram method is the simplest device to study the degree of relationship between the variables by plotting the dots for each pair of variable values given. The chart on which the dots are plotted is also called as a Dotogram.

ASSIGNMENT : Scatter Diagram Assignment MARKS : 50  DURATION : 1 week, 3 days

 

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