# 17 - Statistical Plots

## 1.0 Introduction

This tutorial demonstrates the use of statistical plots (e.g., **Plot Histogram**, **Plot Scatter**, **Plot Cumulative**) to fit distributions and perform linear regression on quantitative Grid Data.

**Topics Covered in this Tutorial:**

- Grid Data
- Histogram Plot and Best Fit Distribution
- Scatter Plot and Regression Line
- Cumulative Plot

**Finished Product:**

The finished product of this tutorial can be found in the *Tutorial 17 Statistical Plots.dips8* file, located in the **Examples > Tutorials **folder in your Dips** **installation folder.

## 2.0 Model

If you have not already done so, run Dips** **by double-clicking on the **Dips** icon in your installation folder. Or from the **Start** menu, select **Programs > Rocscience > Dips > Dips**.

If the Dips** **application window is not already maximized, maximize it now, so that the full screen is available for viewing the model.

Dips comes with several example files installed with the program. These example files can be accessed by selecting **File > Recent Folders > Examples Folder** from the Dips** **main menu. This tutorial will use the *Orthogonal Sets**.dips8 *file to demonstrate the basic plotting features of Dips.

- Select
**File >****Recent Folders > Example Folder**from the menu. - Open the
file. Since we will be using the*Orthogonal Sets**.dips8*file in other tutorials, save this example file with a new file name without overwriting the original file.*Orthogonal Sets**.dips8* - Select
**File >****Save As**from the menu. - Enter the file name
**Tutorial 17 Statistical Plots**and**Save**the file.

You should see the **Stereonet Plot View** shown in the following figure.

- Switch to the
**Grid Data view**of the file using the view tabs in the lower left of the window.

The file contains 1683 measurements from 47 televiewer linear borehole cores.

The file uses the following columns:

- The two mandatory Orientation columns
- A Traverse column
- A Set column
- A Distance column
- Three location X, Y, Z columns
- A Persistence columns
- 2 extra columns

## 3.0 Statistical Plots

In Dips, **statistical plots** (e.g., histogram plot, scatter plot, cumulative plot) can be generated for any quantitative column in the Grid Data.

### 3.1 Histogram Plot

A histogram plot is a graphical representation that displays the distribution of a dataset. It consists of a series of bars, where the height of each bar corresponds to the frequency or relative frequency of data falling within a particular interval or bin. A statistical distribution can also be fitted to the dataset. The following distributions are available in Dips:

To plot a histogram of Persistence:

- Select
**Statistics > Plot Histogram**from the menu . - In the
**Histogram Plot Parameters**dialog:- Set the
**Data Type = Persistence**. - Enter
**Number of Intervals = 30**. - Select
**Attach Markers to Distribution**checkbox. - Select
**Best Fit Distribution (Kolmogorov-Smirnov Test)**checkbox to fit a distribution to the data.Histogram Plot Parameters with Dataset set to Persistence - Click
**OK**to generate the histogram plot.

- Set the

The **Histogram Plot** view shows the **Relative Frequency **on the y-axis and **Persistence **on the x-axis. The **Best Fit Distribution **is fit with an Exponential Distribution through the data.

The SAMPLED and FIT distributions show the following:

- Mean = 3.889
- Standard Deviation = 2.467
- Min = 1
- Max = 10

**Best Fit Distribution**can be used to set up the distributions for Random Variables in other programs such as

**SWedge**,

**UnWedge**and

**RocSlope**since we have the Distribution Type, Mean, Standard Deviation (if applicable), and (absolute) Minimum and Maximum values. Note that in the listed programs the Relative Minimum and Relative Maximum are used to define the distribution. The Relative Minimum = Mean - Minimum. The Relative Maximum = Maximum - Mean.

### 3.2 Scatter Plot

A **scatter plot** is a graphical representation that displays the relationship between two variables. A linear regression can be fitted through the dataset to see if there is a correlation between the two variables plotted.

To plot a scatter plot of **Z (Elevation)** vs **PHIR**:

- Select
**Statistics >****Plot Scatter**from the - In the
**Scatter Plot Parameters**dialog:- Set the
**X Axis Dataset = Z (Elevation)**. - Set the
**Y Axis Dataset = PHIR**. - Select
**Show Regression Line**checkbox to fit a linear regression through the data.Scatter Plot Parameters dialog with X Axis Dataset set to Z (Elevation) and Y Axis Dataset set to PHIR - Click
**OK**to generate the scatter plot.

- Set the

The **Scatter Plot** view shows the **Z (Elevation)** values on the x-axis vs. **PHIR **values on the y-axis. The **Regression Line** is fit through the data.

The residual friction angle (i.e., PHIR) is loosely negatively correlated with the Z (Elevation) as indicated by the **Correlation Coefficient **of **-0.511.** The alpha and beta values represent the y-intercept and slope of regression line, respectively.

### 3.3 Cumulative Plot

A **cumulative plot** is a graphical representation that shows the cumulative distribution of a dataset.

To plot a cumulative plot of **Processed Dip**:

- Select
**Statistics > Plot Cumulative**from the menu. - In the
**Cumulative Plot Parameters**dialog:- Set the
**Data Type = Processed Dip**. - Enter
**Number of Intervals = 30**. - Select the
**Attach Markers to Distribution**checkbox. - Click
**OK**to generate the cumulative plot.

NOTE: In this example, Orient 1 and Processed Dip are equivalent since all measurements are either Dip/Dip Direction according to the Global Orientation or recorded along a Linear BH Televiewer Traverse with Dip/Dip DirectionCumulative Plot Parameters dialog with Data Type set to Processed Dip - Set the

The **Cumulative Plot** view shows the **Cumulative Probability** values on the y-axis and **Processed Dip** on the x-axis.

To view a subset of the data, we can apply a filter to the Cumulative Plot View.

- From the
**Filter**drop down in the toolbar, select the**Bedding**filter.

Only data in the Bedding filter will be used to generate the cumulative plot.

The footer at the bottom of the chart indicates that the **Current Filter Applied to Data** is the **Bedding **filter, which includes all poles in **Set 1**.

**Dips**, can have filters applied to the Grid Data. See the Filter Data topic for more information about filters.

This concludes the tutorial.