# Help Manual

### Contents

• Introduction
• Project
• Analytics Templates
• Change Templates
• Lean Templates
• Graph Templates
• Projects Templates
• Stats Templates
• Analysis
• Miscellaneous

Sigma Magic Help Version 17

# Correlation

## Overview

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

The correlation coefficient varies from -1 to +1. A value of +1 indicates a positive perfect correlation, -1 indicates a negative perfect correlation, and 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.

Two methods exist to compute the correlation coefficient available in the Sigma Magic software. The first method is Pearson's correlation coefficient, and the second is Spearman's. 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. It can be used for ordinal data and does not make any assumptions about 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:
OptionDescription
ContinuousContinuous data can take any arbitrary value (like the temperature of the room example, 34.53 degrees centigrade).
OrdinalOrdinal 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.
OptionDescription
PearsonUse the pearson's correlation coefficient. Typically used for continuous data.
SpearmanUse 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:
OptionDescription
SignificantOnly display the scatter plot for statistically significant variables.
AllDisplay 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:
OptionDescription
HideDo not display the best-fit line on the scatter plot.
ShowShow 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

You will see the following dialog box if you click the Data button. 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 speed up the search for the right data 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 has no 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 crucial that you not only specify the column name but also the table name.
3
Add or View Data: Click on this button to add more data to 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 the Data Editor dialog box, where you can import more data into your workbook. You can also 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, select only numeric columns. You can choose numeric and text columns if the code begins with a T. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, you must select a minimum of 2 columns of data and a maximum of 4 columns 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 choose 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 choose the data is to double-click on the columns in the list of Available Data. Finally, you can 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: The list box header will be black if the right number of data columns is specified. If sufficient data has not been specified, then the list box header will be displayed in 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 in the Setup tab.
OptionDescription
1If 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 two columns of data for this analysis.
2If you have more than two 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 specified for this analysis. The data can be viewed in a tabular format or a graphical summary.

### Charts

You will see the following dialog box if you click the Charts button.

### Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. The software checks 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, they are shown as green-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. The verification checks are shown in the orange exclamation mark if the verification checks result in a warning. Finally, any checks required to be performed by the user are shown as blue info icons.
 1 Item: The left-hand side shows the major tabs and the items checked within each section 2 Status: The right-hand side shows the status of the checks. 3 Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

## 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.
CoefficientStrength
0.0-0.2Very Weak Correlation - practically, these variables are not correlated with each other.
0.2-0.4Weak Correlation
0.4-0.6Moderate Correlation
0.6-0.8Strong Correlation
0.8-1.0Very Strong Correlation
The analysis calculates the text output of the model. This includes a summary of the inputs used for the analysis, 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 specified in your input dialog box. If you want to add the best-fit line, right-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 have specified more than two variables, the software will calculate the correlation between each factor.

## Notes

Here are a few pointers regarding this analysis:
• You can simultaneously compute the correlation coefficients for up to 20 variables.
• The order of specification of the variables is not important for this analysis.

## Examples

The following examples are in the Examples folder.
• For the data in the reference file, determine if any of the variables are correlated. (Correlation 1.xlsx).