Correlation

Reading time

Ellistat offers the Correlation submenu, which contains several statistical tools. These tools can be used to carry out correlation studies of several responses in a dataset, to reduce the size of a dataset or to monitor processes with several variables simultaneously.

In the examples below we present the tools:

⇒ Correlation matrix :

⇒ ACP

⇒ T² card

The dataset used in these examples can be found on the following page.

Independent Data 🇺🇸/ Données indépendantes🇫🇷 

Example 1: Find the correlation between several Y responses, using the correlation matrix

Visit correlation matrix is an essential statistical tool used to understand the relationships between several variables in a data set.

  • In the example, we want to find the correlation between responses Y1="Delta", Y2="Force" and Y3="Pressure".
  • Click on the "Inferential statistics".
  • In the zone 1Select the Y columns Y1="Delta", Y2="Force" and Y3="Pressure".
  • In zone 2, select your data type. By default, if the selected columns contain quantitative values, Ellistat will plot the correlation curves between all the responses in pairs. In addition to the Correlation sub-menu, you can also choose the "Proportion" or "Population" sub-menus. 📝: select "Correlation matrix".
  • In zone 3In the upper half, above the diagonal, we obtain the correlation matrix containing all the correlation graphs of two answers in pairs. The diagonal of this matrix shows the names of the responses, while the lower half shows the coefficients of determination R² and the significance level (P-value).

The diagram below shows the correlation graph, R² and P-value for both Delta and Pressure responses.

💡 When you click on a graph, you'll find a report of an XY Analysis of the two correlated responses:

💡 In the lower half of the correlation matrix there are two values :

R² (P-value).

Example 2: Find the correlation between several Y variables, using the PCA.

Principal Component Analysis (PCA) is a statistical method used to reduce the dimensionality of a dataset while retaining as much information as possible. This technique is particularly useful when working with multivariate data (i.e. data containing several variables).

  • In the example, we want to perform a PCA analysis on the data: Y1="Delta", Y2="Force", Y3="Pressure", Y4="Pressure 2", Y5="Pressure 3".
  • Click on the "Inferential statistics".
  • In the zone 1Select the Y columns Y1="Delta", Y2="Force" and Y3="Pressure", Y4="Pressure 2", Y5="Pressure 3".
  • In zone 2, select your data type. Press the "correlation" sub-menu and select "correlation".ACP". In addition to this sub-menu, you can also select the "Proportion" or "Population" sub-menus. 📝: select "ACP"
  • In zone 3we obtain the projection of the various responses in the plane composed of the principal vectors C1 (x-axis) and C2 (ordinate).

💡 In the upper part of the zone 3There are two tools used to select one of the spreadsheet factors:

⇒ With the "Label" tool: There is the possibility of seeing the variation of individuals according to the chosen factor . this would make it possible to apply a color code to individuals according to the chosen variable. the following case presents the results obtained in the case of label = "Delta". we can see that the individuals with a strong delta are in orange/yellow and the individuals with a weak delta are in blue.

⇒ The "other variable" tool is used to plot a factor without taking it into account when determining the main vectors. For this feature to work, the factor must not be checked in zones 1 and 3 at the same time. It must only be ticked in zone 3. Here, the example of the "Delta" factor (see figure below). This variable can be either a quantitative or a qualitative variable.

Whether you choose the "Label" option or the "Other variable" option, the variables selected can be quantitative or qualitative.

💡 In the middle part of the zone 3you can select several tabs:

⇒ "Synthesis" tab: This tab contains the graph, menus for displaying individuals in the graph, classification settings and the table of main vectors.

⇒The Pareto tab: This tab shows the Pareto diagram, expressing the contribution of each main vector.

⇒"Variable" tab: This tab shows the degree of correlation significance between the variables and the different main axes (C1, C2,...). A P-value<0.05 means that the correlation between the variable and the main vector is significant. (see table below)

⇒"Individual values" tab: This tab shows the coordinates of individuals in the space of principal vectors.

Example 3: Hotelling's T² card

Hotelling's T² chart is a statistical tool used to calculate multivariate quality control and data analysis, enabling processes with several variables to be monitored simultaneously. It is a multivariate extension of Shewhart control charts, which focus on a single variable. Hotelling's T² is often used in contexts where several quality characteristics need to be monitored at the same time, for example in manufacturing, biology and engineering.

  • In the example, we want to monitor the following data simultaneously: Y1="Delta", Y2="Force", Y3="Pressure", Y4="Pressure 2", Y5="Pressure 3".
  • Click on the "Inferential statistics".
  • In the zone 1Select the Y columns Y1="Delta", Y2="Force" and Y3="Pressure", Y4="Pressure 2", Y5="Pressure 3".
  • In zone 2, select your data type. Press the "correlation" sub-menu and select "correlation".T²". In addition to this sub-menu, you can also select the "Proportion" or "Population" sub-menus. 📝: select "T²"
  • In zone 3we obtain the control chart T² with individual values and control limits.
  • In the zone 4Here you'll find options such as general map settings, display options and control limit calculation.

💡 In the middle part of the zone 4Several options can be set:

⇒ The "General" option: With this option you can choose the type of control chart calculation (classic, Sullivan, and Chi-2), select the alpha risk level and determine the data for training.

⇒ The "Display" option: With this option you can transform the ordinate into a logarithmic scale and apply a Label to the data.

⇒ The "Limits" option: With this option you can change the control limit by setting it manually.