Best Analysis to Run on Jmp When You Have One Nominal and All Numeric Continuous Stats

Computing an Analysis of Variance with Summary Statistics in JMP® Software

In some instances, an experimenter may want to perform an Analysis of Variance (ANOVA), but only the summary statistics are available. Most statistical programs are designed to compute ANOVA models with the full, complete set of data. However, David A. Larson describes a method to generate surrogate data from the summary statistics which can be used to fit the ANOVA of interest(1). That is, if the analysis is comparing k categories, and only the summary statistics (n_i, mean_i,s² _i i= 1, 2, 3,..., k) are available, then data can be generated to perform the desired analysis.

Utilizing Larson's ideas, JMP can perform this type of analysis. The following is an example demonstrating the appropriate steps taken to fit this ANOVA within JMP. If you have only two means to compare, JMP (beginning with version 11) provides an option in the Sample Data Index that can be used. Select Help ► Sample Data. In the Teaching resources section, open Calculators and click on Hypothesis Test for Two Means. Here, choose Summary Statistics and complete the dialog.

Now, for more than two means, suppose all the information available is the summary statistics below:

The first step is to create a JMP data table with the above data (Table 1).

Table 1: The JMP data table

According to Larson, two new columns need to be generated. So, create two columns named "Xi's" and "Xn's" having the Formula Column Property. Then, using JMP's Formula Editor, define these formulas:

Once these columns are created, they need to be "stacked." From the Tables menu, select Stack and select the columns "Xi's" and "Xn's" to be stacked, and also, change the name of the stacked column from the default "_Stacked_" to "Y" (Figure 1).

Figure 1: The "Stack" dialog box

The last item necessary to run the model is an appropriate frequency column added to the stacked data table. Using the If function (found in the Formula Editor's Conditional function list), create one more column named "Frequency" with the formula shown in Figure 2 below.

Figure 2: The "if" selection and the formula for "Frequency"

The final data table should appear as shown in Table 2.

Table 2: Final data table

The surrogate data has been generated so the ANOVA can now be performed. From the Analyze menu, choose Fit Y by X. Specify "Treatment" as "X", "Y" as "Y", and "Frequency" as "Freq," then click OK to run the analysis. The first item seen in the output is a scatterplot of the points. From the Oneway Analysis red triangle menu, click on Means/Anova to produce the resulting output seen in Figure 3.

Figure 3: ANOVA results

Oneway ANOVA
Summary of Fit

Rsquare	0.690838
Adj Rsquare	0.625752
Root Mean Square Error	1.751986
Mean of Response	15.85833
Observations (or Sum Wgts)	24

Analysis of Variance

Source	DF	Sum of Squares	Mean Square	F Ratio	Prob > F
Treatment	4	130.31833	32.5796	10.6141	0.0001
Error	19	58.31965	3.0695
C. Total	23	188.63798

Means for Oneway ANOVA

Level	Number	Mean	Std Error	Lower 95%	Upper 95%
A	4	15.2000	0.8760	13.367	17.033
B	6	12.8000	0.7152	11.303	14.297
C	6	19.0000	0.7152	17.503	20.497
D	5	17.1000	0.7835	15.460	18.740
E	3	14.5000	1.0115	12.383	16.617

Std Error uses a pooled estimate of error variance.

As you see, the means are exactly those that were specified in the initial summary statistics. The standard errors given are estimated using a pooled estimate of the error variance. To compare all results, Table 3 gives the actual data from which the summary data is generated. The results from an analysis of variance using the actual data align perfectly to the output given with the summary statistics.

Table 3: Actual data

In conclusion, if only the summary statistics are available for an oneway analysis, the method described above can be followed to generate surrogate data in JMP to complete the desired analysis of variance.

REFERENCES

Larson, David A. (1992), "Analysis of Variance With Just Summary Statistics as Input," American Statistician, 46, 151-152.

Operating System and Release Information

Product Family	Product	System	SAS Release
			Reported	Fixed*
JMP Software	JMP software	Microsoft Windows 8.1 Enterprise 32-bit
		Microsoft Windows 8 Pro x64
		Microsoft Windows 8 Pro 32-bit
		Microsoft Windows 8 Enterprise x64
		Microsoft Windows 8 Enterprise 32-bit
		Microsoft® Windows® for x64
		Macintosh on x64
		Macintosh
		Microsoft Windows 8.1 Enterprise x64
		Windows 7 Ultimate x64
		Windows 7 Professional x64
		Windows 7 Ultimate 32 bit
		Windows 7 Home Premium 32 bit
		Windows 7 Home Premium x64
		Windows 7 Professional 32 bit
		Windows 7 Enterprise 32 bit
		Windows 7 Enterprise x64
		Microsoft Windows 8.1 Pro 32-bit
		Microsoft Windows 8.1 Pro x64
		Microsoft Windows 10

* For software releases that are not yet generally available, the Fixed Release is the software release in which the problem is planned to be fixed.

winntheye1957.blogspot.com

Source: https://www.jmp.com/support/notes/35/253.html

Share this post