Basic Analysis • Oneway Analysis • Additional Examples of the Oneway Platform
Previous
 • 
Next
Additional Examples of the Oneway Platform
This section contains additional examples of selected options and reports in the Oneway platform.
Example of an Analysis of Means Chart
1.
Select Help > Sample Data Library and open Analgesics.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select pain and click Y, Response.
4.
Select drug and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Analysis of Means Methods > ANOM.
Example of Analysis of Means Chart
For the example in Example of Analysis of Means Chart, the means for drug A and C are statistically different from the overall mean. The drug A mean is lower and the drug C mean is higher. Note the decision limits for the drug types are not the same, due to different sample sizes.
Example of an Analysis of Means for Variances Chart
This example uses the Spring Data.jmp sample data table. Four different brands of springs were tested to see what weight is required to extend a spring 0.10 inches. Six springs of each brand were tested. The data was checked for normality, since the ANOMV test is not robust to non-normality. Examine the brands to determine whether the variability is significantly different between brands.
1.
Select Help > Sample Data Library and open Spring Data.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select Weight and click Y, Response.
4.
Select Brand and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Analysis of Means Methods > ANOM for Variances.
7.
From the red triangle menu next to Analysis of Means for Variances, select Show Summary Report.
Example of Analysis of Means for Variances Chart
From Example of Analysis of Means for Variances Chart, notice that the standard deviation for Brand 2 exceeds the lower decision limit. Therefore, Brand 2 has significantly lower variance than the other brands.
Example of the Each Pair, Student’s t Test
This example uses the Big Class.jmp sample data table. It shows a one-way layout of weight by age, and shows the group comparison using comparison circles that illustrate all possible t-tests.
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select weight and click Y, Response.
4.
Select age and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Compare Means > Each Pair, Student’s t.
Example of Each Pair, Student’s t Comparison Circles
The means comparison method can be thought of as seeing if the actual difference in the means is greater than the difference that would be significant. This difference is called the LSD (least significant difference). The LSD term is used for Student’s t intervals and in context with intervals for other tests. In the comparison circles graph, the distance between the circles’ centers represent the actual difference. The LSD is what the distance would be if the circles intersected at right angles.
Example of Means Comparisons Report for Each Pair, Student’s t
In Example of Means Comparisons Report for Each Pair, Student’s t, the LSD threshold table shows the difference between the absolute difference in the means and the LSD (least significant difference). If the values are positive, the difference in the two means is larger than the LSD, and the two groups are significantly different.
Example of the All Pairs, Tukey HSD Test
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select weight and click Y, Response.
4.
Select age and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Compare Means > All Pairs, Tukey HSD.
Example of All Pairs, Tukey HSD Comparison Circles
Example of Means Comparisons Report for All Pairs, Tukey HSD
In Example of Means Comparisons Report for All Pairs, Tukey HSD, the Tukey-Kramer HSD Threshold matrix shows the actual absolute difference in the means minus the HSD, which is the difference that would be significant. Pairs with a positive value are significantly different. The q* (appearing above the HSD Threshold Matrix table) is the quantile that is used to scale the HSDs. It has a computational role comparable to a Student’s t.
Example of the With Best, Hsu MCB Test
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select weight and click Y, Response.
4.
Select age and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Compare Means > With Best, Hsu MCB.
Examples of With Best, Hsu MCB Comparison Circles
Example of Means Comparisons Report for With Best, Hsu MCB
The Comparison with Max and Min report compares the mean of each level to the maximum and the minimum of the means of the remaining levels. For example, the mean for age 15 differs significantly from the maximum of the means of the remaining levels. The mean for age 17 differs significantly from the minimum of the means of the remaining levels. The maximum mean could occur for age 16 or age 17, because neither mean differs significantly from the maximum mean. By the same reasoning, the minimum mean could correspond to any of the ages other than age 17.
Example of the With Control, Dunnett’s Test
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select weight and click Y, Response.
4.
Select age and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Compare Means > With Control, Dunnett’s.
7.
Select the group to use as the control group. In this example, select age 12.
Alternatively, click on a row to highlight it in the scatterplot before selecting the Compare Means > With Control, Dunnett’s option. The test uses the selected row as the control group.
8.
Click OK.
Example of With Control, Dunnett’s Comparison Circles
Using the comparison circles in Example of With Control, Dunnett’s Comparison Circles, you can conclude that level 17 is the only level that is significantly different from the control level of 12.
Example Contrasting All of the Compare Means Tests
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select weight and click Y, Response.
4.
Select age and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select each one of the Compare Means options.
Although the four methods all test differences between group means, different results can occur. Comparison Circles for Four Multiple Comparison Tests shows the comparison circles for all four tests, with the age 17 group as the control group.
Comparison Circles for Four Multiple Comparison Tests
From Comparison Circles for Four Multiple Comparison Tests, notice that for the Student’s t and Hsu methods, age group 15 (the third circle from the top) is significantly different from the control group and appears gray. But, for the Tukey and Dunnett method, age group 15 is not significantly different, and appears red.
Example of the Unequal Variances Option
Suppose you want to test whether two variances (males and females) are equal, instead of two means.
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select height and click Y, Response.
4.
Select sex and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Unequal Variances.
Example of the Unequal Variances Report
Since the p-value from the 2-sided F-Test is large, you cannot conclude that the variances are unequal.
Example of an Equivalence Test
This example uses the Big Class.jmp sample data table. Examine if the difference in height between males and females is less than 6 inches.
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select height and click Y, Response.
4.
Select sex and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Equivalence Test.
7.
Type 6 as the difference considered practically zero.
8.
Click OK.
Example of an Equivalence Test
From Example of an Equivalence Test, notice the following:
•
The test at the Upper Threshold is the lower one-tailed test for the null hypothesis that the mean difference is 6.
•
The test at the Lower Threshold is the upper one-tailed test for the null hypothesis that the mean difference is -6.
•
For both tests, the p-value is small. Therefore, you can conclude that the difference in population means is significantly located somewhere from 6 to -6. For your purposes, you can declare the means to be practically equivalent.
Example of the Robust Fit Option
The data in the Drug Toxicity.jmp sample data table shows the toxicity levels for three different formulations of a drug.
1.
Select Help > Sample Data Library and open Drug Toxicity.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select Toxicity and click Y, Response.
4.
Select Formulation and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Means/Anova.
7.
From the red triangle menu, select Robust > Robust Fit.
Example of Robust Fit
If you look at the standard Analysis of Variance report, you might wrongly conclude that there is a difference between the three formulations, since the p-value is 0.0319. However, when you look at the Robust Fit report, you would not conclude that the three formulations are significantly different, because the p-value there is 0.21755. It appears that the toxicity for a few of the observations is unusually high, creating the undue influence on the data.
Example of the Power Option
1.
Select Help > Sample Data Library and open Typing Data.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select speed and click Y, Response.
4.
Select brand and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Power.
7.
Within the From row, type 2 for Delta (the third box) and type 11 for Number.
8.
Within the To row, type 6 for Delta, and type 17 in the Number box.
9.
Within the By row, type 2 for both Delta and Number.
10.
Select the Solve for Power check box.
Example of the Power Details Window
11.
Click Done.
Note: The Done button remains dimmed until all of the necessary options are applied.
Power is computed for each combination of Delta and Number, and appears in the Power report.
To plot the Power values:
12.
From the red triangle menu at the bottom of the report, select Power Plot.
Example of the Power Report
13.
You might need to click and drag vertically on the Power axis to see all of the data in the plot.
Power is plotted for each combination of Delta and Number. As you might expect, the power rises for larger Number (sample sizes) values and for larger Delta values (difference in means).
Example of a Normal Quantile Plot
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select height and click Y, Response.
4.
Select sex and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Normal Quantile Plot > Plot Actual by Quantile.
Example of a Normal Quantile Plot
From Example of a Normal Quantile Plot, notice the following:
•
The Line of Fit appears by default.
•
The data points track very closely to the line of fit, indicating a normal distribution.
Example of a CDF Plot
1.
Select Help > Sample Data Library and open Analgesics.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select pain and click Y, Response.
4.
Select drug and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select CDF Plot.
Example of a CDF Plot
The levels of the X variables in the initial Oneway analysis appear in the CDF plot as different curves. The horizontal axis of the CDF plot uses the y value in the initial Oneway analysis.
Example of the Densities Options
1.
Select Help > Sample Data Library and open Big Class.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select height and click Y, Response.
4.
Select sex and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Densities > Compare Densities, Densities > Composition of Densities, and Densities > Proportion of Densities.
Example of the Densities Options
Example of the Matching Column Option
This example uses the Matching.jmp sample data table, which contains data on six animals and the miles that they travel during different seasons.
1.
Select Help > Sample Data Library and open Matching.jmp.
2.
Select Analyze > Fit Y by X.
3.
Select miles and click Y, Response.
4.
Select season and click X, Factor.
5.
Click OK.
6.
From the red triangle menu, select Matching Column.
7.
Select subject as the matching column.
8.
Click OK.
Example of the Matching Column Report
The plot graphs the miles traveled by season, with subject as the matching variable. The labels next to the first measurement for each subject on the graph are determined by the species and subject variables.
The Matching Fit report shows the season and subject effects with F tests. These are equivalent to the tests that you get with the Fit Model platform if you run two models, one with the interaction term and one without. If there are only two levels, then the F test is equivalent to the paired t-test.
Note: For details about the Fit Model platform, see the Fitting Linear Models book.