Before you perform a statistical analysis, you can use graphs to explore data and assess relationships between the variables. Also, you can use graphs to summarize data and to help interpret statistical results.

You can access Minitab’s graphs from the Graph and Stat menus. Built-in graphs, which help you interpret results and assess the validity of statistical assumptions, are also available with many statistical commands.

Minitab graphs include the following features:

- Pictorial galleries to help you choose a graph type
- Flexibility in customizing graphs
- Graph elements that you can change
- Option to be automatically updated

This chapter explores the shipping data worksheet that you opened in the previous chapter. You use graphs to check normality, compare means, explore variability, and examine the relationships between variables.

For more information about Minitab graphs, go to Graphs in the Minitab Help index. To access the Minitab Help index, open Minitab, choose , then click the Index tab in the left pane.

Before you perform a statistical analysis, first create graphs that display important characteristics of the data. For the shipping data, you want to know the mean delivery time for each shipping center and how the data vary within each shipping center. You also want to determine whether the shipping data follow a normal distribution, so that you can use standard statistical methods for testing the equality of means.

To determine whether the shipping data follow a normal distribution, create a paneled histogram of the time lapse between order date and delivery date.

- If you are continuing from the previous chapter, go to step 4. If not, start Minitab.
- Choose .
- Double-click the Getting Started folder, then double-click ShippingData.MTW.
- Choose .
- Click With Fit, then click OK.
- In Graph variables, enter
`Days`. - Click Multiple Graphs.
- On the By Variables tab, in By variables with groups in separate panels, enter
`Center`. - Click OK in each dialog box.

To select variables in most Minitab dialog boxes, use one of the following methods:

- Double-click the variables in the variables list box.
- Highlight the variables in the list box, and then click Select.
- Type the variables’ names or column numbers.

The histograms seem to be approximately bell-shaped and symmetric about the means, which indicates that the delivery times for each center are approximately normally distributed.

For the graph that you created, you want to rearrange the three panels so that comparing the means and variation is easier.

- Right-click the histogram, then choose Panel.
- On the Arrangement tab, in Rows and Columns, select Custom. In Rows, enter
`3`. In Columns, enter`1`. - Click OK.

The mean delivery times for each shipping center are different:

- Central: 3.984 days
- Eastern: 4.452 days
- Western: 2.981 days

The histogram shows that the Central and Eastern centers are similar in both mean delivery time and spread of delivery time. In contrast, the mean delivery time for the Western center is shorter and the distribution is less spread out. Analyzing Data shows how to detect statistically significant differences between means using ANOVA (analysis of variance).

If your data change, Minitab can automatically update graphs. For more information, go to Updating graphs in the Minitab Help index. To access the Minitab Help index, open Minitab, choose , then click the Index tab in the left pane.

To help your supervisor quickly interpret the histogram, you want to change the title and add a footnote.

- Double-click the title, Histogram of Days.
- In Text, enter
`Histogram of Delivery Time`. - Click OK.
- Right-click the histogram, then choose .
- In Footnote, enter
`Western center: fastest delivery time, lowest variability`. - Click OK.

The paneled histogram now has a more descriptive title and a footnote that provides a brief interpretation of the results.

Graphs can help you identify whether relationships exist between variables, and the strength of any relationships. Knowing the relationship between variables can help you determine which variables are important to analyze and which additional analyses to choose.

Because each shipping center serves a region, you suspect that distance to delivery location does not greatly affect delivery time. To verify this suspicion and to eliminate distance as a potentially important factor, you examine the relationship between delivery time and delivery distance for each center.

To examine the relationship between two variables, you use a scatterplot. You can choose a scatterplot from the Graph menu or you can use the Minitab Assistant. The Assistant guides you through your analyses and helps you interpret the results with confidence. The Assistant can be used for most basic statistical tests, graphs, quality analyses, and DOE (design of experiments).

Use the Assistant in the following situations:

- You need assistance to choose the correct tool for an analysis.
- You want dialog boxes that have less technical terminology and that are easier to complete.
- You want Minitab to check the analysis assumptions for you.
- You want output that is more graphical and explains in detail how to interpret your results.

- Choose .
- Under Graph relationships between variables, click Scatterplot (groups).
- In Y column, enter
`Days`. - In X column, enter
`Distance`. - From Number of X columns, select 1.
- In X1, enter
`Center`. - Click OK.

Use Minitab’s graph layout tool to arrange multiple graphs on one page. You can add annotations to the layout and edit the individual graphs within the layout.

To show your supervisor the preliminary results of the graphical analysis of the shipping data, arrange the summary report and the paneled histogram on one page.

- Ensure that the scatterplot summary report is active, then choose . The scatterplot summary report is already included in the layout.
- To arrange two graphs on one page, in Rows, enter
`1`. - Click the summary report and drag it to the right side of the layout.
- Click the right arrow button to place the paneled histogram in the left side of the layout.
- Click Finish.

If you edit the data in the worksheet after you create a layout, Minitab cannot automatically update the graphs in the layout. You must recreate the layout with the new graphs.

You want to add a descriptive title to the graph layout.

- To ensure that you have the entire graph layout selected, choose .
- Choose .
- In Title, enter
`Graphical Analysis of Shipping Data`. - Click OK.

You can print any Minitab window, including a graph or a layout.

- Choose , and then choose .
- Click OK.

Minitab data are saved in worksheets. You can also save Minitab projects, which contain all of your work, including worksheets, Session window output, graphs, history of your session, and dialog box settings.

- Choose .
- Browse to the folder that you want to save your files in.
- In File name, enter
`MyGraphs`. - Click Save.

The graphical output indicates that the three shipping centers have different delivery times for book orders. In the next chapter, you display descriptive statistics and perform an ANOVA (analysis of variance) to test whether the differences among the shipping centers are statistically significant.

Go to Analyzing Data.