# Graphical Analysis in Minitab Part -2

This is sequel of article named Graphical Analysis in Minitab -Part 1, (which you can read by clicking on the link). In last article we learnt analysis of single parameter. In this edition, we will learn how to use graphical analysis for analyzing relationship among multiple parameters. ## How to analyze relationship between 2 parameters

Minitab enables several graphs, which help in drawing inferences about relationship between two parameters.

### What is SCATTER PLOT?

The scatter plot is a graph that displays relationship between two continuous variables. For example, if we desire to establish relationship between Weight (Y) and height (X) of all athletes, we can use this graph. For this, we will need height (H) and weight (W) of each individual and plot these as points  (H, W) on X-Y coordinates. The pattern of this graph indicates the relationship. The adjacent graph gives following inference: "It seems if weight is high, height of individual is expected to be high". Please note some important points in this reference
1. It seems - This word indicates all graphical tests are inferential. Further analysis is needed for conclusions.
2. Relationship is non-directional - This indicates that we cannot clearly determine if  height depends on weight or weight depends on height. For any inferences, basic knowledge of process is must.
3. Strength of relationship is based on perception - How strong is the relationship depends on closeness of data points as well as slope of trend. Both are perceptional in the graph.    ### How to make Scatter Plot in Minitab?

Let us learn how to make scatter plot using Minitab. Please open given excel file Scatter-Plot-Data and paste in the Minitab. Follow the command • Graph>>Scatter Plot
• Choose - With Regression
• Under Y-variable select "Weight"
• Under X-variable select "Height"
• Click OK to get scatter plot
From the graph we can draw inference that it seems there is strong relationship at lower values of height and weight. On other hand, at higher values relationship seems to be weaker.

### How BOX PLOTS help in relating two parameters?

The box plot is a graph which is used for both one parameters and two parameter analysis. It displays relationship between a continuous variable and a discrete attribute. For example, if we desire to establish relationship between Yield from various Catalyst types, this is good method. In this we compare location (Median) as well as spread (IQR) for drawing conclusions.

### How to make Multiple Box Plots in Minitab?

Let us learn making multiple box plots using Minitab. Please open given excel file Box-Plot-for-Comparing and paste in the Minitab. Follow the command
The graph compares Yield (continuous parameter) with Catalyst Type (Discrete parameter). We can draw following inferences from the graph.
1. Catalyst-2 and Catalyst-3 seems to have lowest yield.
2. Catalyst-4 and Catalyst-5 seems to have highest yield.
3. Variation (IQR) in Yield with Catalyst-2 seems to be lowest while high with Catalyst-1, Catalyst-4 and Catalyst-5.

### What is Main Effects Plot?

Main Effects Plot also relates a continuous parameter with a discrete parameter. The Main Effect compares only location (Mean) of data (and NOT variation).

### How to make Main Effect Plot in Minitab?

Let us learn making Main Effect Plot using Minitab. Please open given excel file Main-Effects-Data and paste in the Minitab. Follow the command • Stat>>ANOVA>>Main Effects Plot....
• Choose "Yield" in Responses.
• Choose "Factors" in Responses.
• Click OK to see your Main Effects Plot.
The graph compares Yield (continuous parameter) with Catalyst Type (Discrete parameter). We can draw following inferences from the graph.
1. Catalyst-2 and Catalyst-3 seems to have lowest yield.
2. Catalyst-5 seems to have highest yield.

### What is Individual Value Plot?

Individual Value Plot also relates a continuous parameter with a discrete parameter. This Graph does comparison considering all data together without specifying any measure of location or spread.

### How to make Individual Value Plot in Minitab?

Let us learn making Individual Value Plot using Minitab. Please open given excel file Main-Effects-Data and paste in the Minitab. Follow the command • Graph>>Individual Value Plot..
• Choose One Y>>With Groups
• Choose "Yield" in graph variables
• Choose "Catalyst" in categorical variables
The graph compares Yield (continuous parameter) with Catalyst Type (Discrete parameter). We can draw following inferences from the graph.
1. Catalyst-2 and Catalyst-3 seems to have minimum Yield.
2. Catalyst 5 seems to have most of the values on higher side, while two abnormal values on lower side indicate need to look for special causes.
3. Catalyst 1 and Catalyst-4 seems to have high variation without any abnormal value.

### What is Pareto Chart?

Vilfredo Pareto was an Italian economist who noted that 20% people of Italy possessed 80% wealth (mainly land) of the country. This was translated into Pareto principle by Quality Guru, Joesh M Juran, as "In any population, there are always significant a few and insignificant too many". This principle became foundation for Pareto Chart. The purpose of Pareto Chart principally is to isolate significant few from many insignificant. Statistically, Pareto Chart relates 2 discrete data with each other. Typically, Y is frequency of events (e.g. how many defects, how many failures etc.) and X is source of this frequency (e.g. machine, cause of defects, type of defects etc.)

### How to make Pareto Chart in Minitab?

Let us learn making Pareto Chart in Minitab. Please open given excel file Pareto-data and paste in the Minitab. Follow the command • Stat>>Quality Tools>>Pareto Chart..
• Choose "Damage" in Defects or attribute data in
• Choose "Frequency" in Frequencies in
• Click OK to see your Pareto Chart.
Pareto Chart indicates 83% of damages are due to scratch only and hence we need to focus on it.

## How to analyze relationship among multiple (2 or more) parameters

Minitab enables several graphs, enabling viewing relationships among various parameters. One of the most popular graph is Multi-vari chart.

### What is Multi-vari chart?

When we need to see effect of 2 or more parameters on one out put multi-vari charts are used. They can also be referred to as overlaid Main Effects Plots, which show main effect of second parameter on each value of parameter 1.

### How to make Multi-vari Chart in Minitab?

Please open given excel file Multi-vari-data and paste in the Minitab. Follow the command
The graph compares Concentration (continuous parameter) with Machine (Discrete parameter) and Temperature (made discrete for this analysis, although continuous). We can draw following inferences from the graph.
1. Concentration seem to increase at 150 degrees temp, while it is lower at 100 ad 200 degrees.
2. Concentration seems to reduce as we move from machine 1 to 2 and 2 to 3 at 100 degree temperature.
3. Concentration is high for machine 2 and lower for machine 1 & 3 at 150 degree temperature.
4. Concentration seems to increase as we move from machine 1 to 2 and 2 to 3 at 200 degree temperature.