Sigma Magic Help Version 15

Correlation

Overview

Correlation analysis is a statistical measure of the relationship between two or more variables. If two variables are positively correlated, it means that if one variable increases, we find that the other variable also increases. On the other hand, if the two variables are negatively correlated, that means that when one variable increases the other variable decreases and finally, no correlation between the two variables means that there is no observable pattern between the changes in these two variables. We can use a scatter plot to visually look at these variables but when you want to quantify using a statistical approach, we can use the correlation analysis. Note that correlation does not imply causation. Just because two variables have a positive correlation between them, we cannot conclude that one variable causes the other variable to change.

The correlation coefficient varies from -1 to +1. A value of +1 indicates a positive perfect correlation, a value of -1 indicates a negative perfect correlation and a value of 0 implies no correlation. Of course, the correlation coefficient can take any value between -1 and +1. The following table provides a general guideline between the absolute values of the correlation coefficient and the degree of strength of correlation between the two variables.

There are two methods to compute the correlation coefficient that is available in the Sigma Magic software. The first method is Pearson's correlation coefficient and the second method is Spearman's correlation coefficient. Pearson's correlation should be used for continuous data and when there is a linear relationship between the two variables. Spearman's correlation coefficient is based on ranks rather than original measurements and can be used for ordinal data and it does not make any assumption on the linear relationship between the variables. Hence, if you have outliers in your data, you should be using Spearman's correlation coefficient. When a scatter diagram shows a linear relationship between the two quantitative variables, both methods will give similar values. The following flowchart shows a high-level view of when to use which analysis. This tool can be added to your active workbook by clicking on Stats and then selecting Correlation Analysis.

Inputs

Click on Analysis Setup to open the menu options for this tool.

Setup

A sample screenshot of the setup menu is shown below.

1	Data Type: Specify the type of input data. The following options are available: Option Description Continuous Continuous data can take any arbitrary value (like the temperature of the room example 34.53 deg centigrade). Ordinal Ordinal data has more than two categories and they can be compared with each other and ranked (like the grades in an exam A > B > C). Make sure that ordinal data are entered in a numeric format for this analysis.
2	Method: Specify the methodology to compute the correlation coefficients. Option Description Pearson Use the pearson's correlation coefficient. Typically used for continuous data. Spearman Use the spearman's correlation coefficient. Typically used for rank data (statistical dependence between the rankings of two variables).
3	Show Graphs: Specify what graphs you want to plot. The available options are: Option Description Significant Only display the scatter plot for variables that are statistically significant. All Display all pairs of scatter plots.
4	Best Fit Line: Specify if you want to display a best fit line to your data points. The available options are: Option Description Hide Do not display the best fit line on the scatter plot. Show Show the best fit line on the scatter plot.
5	Flowchart: Click on this button to open the flowchart for this analysis.
6	Help Button: Click on this button to open the help file for this topic.
7	Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
8	OK Button: Click on this button to save all changes and compute the outputs for this analysis.

Data

If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis.

1	Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and to speed up finding the right data to use for analysis. Enter a few characters in the search field and the software will filter and display the filtered data in the Available Data box.
2	Available Data: The available data box contains the list of data available for analysis. If your workbook does not have any data in tabular format, this box will display "No Data Found". The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is important that you not only specify the column name but also the table name.
3	Add or View Data: Click on this button either to add more data into your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens up the Data Editor dialog box where you can import more data into your workbook, or you can switch from the list view to a table view to see the individual data values for each column.
4	Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, then you will need to select only numeric columns. If the code starts with a T, then you can select both numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data in this box. If the minimum value is 0, then no data is required to be specified for this box.
5	Select Button: Click on this button to select the data for analysis. Any data you select for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to select the data is to double click on the columns in the list of Available Data. Finally, you can also drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
6	Selected Data: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the red color. Note that you can double-click on any of the columns in this box to remove them from the box. The data you specify for this analysis depends on the options you have specified in the Setup tab. Option Description 1 If you want to compute the correlation between two columns of data you would enter the two columns of data under Analysis Variables. Note that you need at least 2 columns of data for this analysis. 2 If you have more than 2 columns of data, you can enter them under Analysis Variables and the software will compute the correlation coefficients between each pair of variables.
7	View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in a tablular format or in a graphical summary.

Charts

If you click on the Charts button, you will see the following dialog box.

0	Pick Charts: Select the charts you would like to display for this analysis.
1	Title: The system will automatically pick a title for your chart. However, if you would like to override that with your own title you can specify a title for your chart here. Note that this input is optional.
2	Sub Title: The system will automatically pick a subtitle for your chart. However, if you would like to override that with your own subtitle you can specify a subtitle for your chart here. Note that this input is optional.
3	X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your own label for the x-axis you can specify a different label here. Note that this input is optional.
4	Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your own label for the y-axis you can specify a different label here. Note that this input is optional.
5	X Axis: The system will automatically pick a scale for the x-axis. However, if you would like to override that with your values for the x-axis, you can specify them here. The format for this input is to specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20 then the minimum x-axis scale is set at 10 and the maximum x-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the x-axis increment is set at 2. Note that this input is optional.
6	Y Axis: The system will automatically pick a scale for the y-axis. However, if you would like to override that with your values for the y-axis, you can specify them here. The format for this input is to specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20 then the minimum y-axis scale is set at 10 and the maximum y-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the y-axis increment is set at 2. Note that this input is optional.
7	Horizontal Lines: If you want to add a few extra horizontal reference lines on top of your chart you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15 then two horizontal lines are plotted at Y = 12 and Y = 15 respectively. Note that this input is optional.
8	Vertical Lines: If you want to add a few extra vertical reference lines on top of your chart you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5 then two vertical lines are plotted at X = 2 and X = 5 respectively. Note that this input is optional.

Verify

If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the dialog box is shown in the figure below. The objective of this analysis as well as any checks that are performed is listed in this dialog box. For example, the software may check if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.

Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. The following table shows a rough guideline for interpreting the correlation coefficients.

Coefficient	Strength
0.0-0.2	Very Weak Correlation - practically these variables are not correlated with each other.
0.2-0.4	Weak Correlation
0.4-0.6	Moderate Correlation
0.6-0.8	Strong Correlation
0.8-1.0	Very Strong Correlation

The analysis calculates the text output of the model. This includes a summary of the inputs used for the analysis and some checks for you to consider before performing the analysis and finally, the correlation coefficients (indicated by Rho) and the significance test results (P values). The graphs will show the scatter plot between the variables as specified in your input dialog box. If you want to add the best-fit line, right mouse click on the plot and select add trendline. The conclusion will state if any significant correlations have been found between the input variables.

If you had specified more than 2 variables, then the software will calculate the correlation between each of the factors.

Notes

Here are a few pointers regarding this analysis:

• You can compute the correlation coefficients for up to 20 variables at a time.
• The order of specification of the variables is not important for this analysis.

Examples

Following examples can be found in the Examples folder.

• For the data given in the reference file determine if any of the variables are correlated with each other? (Correlation 1.xlsm).