The Oneway Analysis red triangle menu contains testing, fitting, and display options. Options include analysis of variance (ANOVA), nonparametric tests, equivalence tests, and multiple comparisons methods to evaluate differences across groups. Probability density function (PDF) and cumulative distribution function (CDF) plots enable you to visualize the distribution of your response by the X categories. Options add visualizations to the scatterplot, provide statistical reports, or launches an additional analysis.
When a blocking variable is used, a one-way ANOVA model with blocking is fit to the data. Additional analysis options are limited.
Note: The Fit Group menu appears only if you have specified multiple Y or X variables. Use the Fit Group menu options to arrange reports or order them by RSquare. See “Fit Group Options” in Fitting Linear Models.
The Oneway Analysis red triangle menu contains the following options:
Quantiles
Shows or hides box plots on the Oneway plot and shows or hides a quantile report. See Quantiles Report.
Means/Anova
(Available only when the X variable has more than two levels.) Shows or hides mean diamonds on the Oneway plot and shows or hides an ANOVA report. See Means/Anova/Pooled t Report.
Means/Anova/Pooled t
(Available only when the X variable has exactly two levels.) Shows or hides mean diamonds on the Oneway plot and shows or hides an ANOVA report. The ANOVA report includes a pooled t test report that assumes that the two groups have equal variances.
Means and Std Dev
Shows or hides mean lines, error bars, and standard deviation lines on the Oneway plot and shows or hides a summary statistics table. The standard errors for the means use individual group standard deviations. For more information about these graph elements, see Mean Lines, Error Bars, and Standard Deviation Lines.
t test
(Available only when the X variable has exactly two levels.) Shows or hides a t test report assuming that the variances are not equal. See t Test Report.
Analysis of Means Methods
Contains options for comparing multiple groups using Analysis of Means (ANOM) methods. See Analysis of Means Reports. For more information about ANOM methods, see Nelson et al. (2005).
Note: If you specify a Block variable in the launch window and there are equal counts for each combination of Block and X variable level, the ANOM chart is the only Analysis of Means chart available. If you specify a Block variable in the launch window and there are unequal counts, none of the Analysis of Means options are available.
ANOM
Shows or hides an ANOM decision chart to compare group means to the overall mean. This method assumes that your data are approximately normally distributed. See Example of Analysis of Means.
ANOM with Transformed Ranks
Shows or hides an ANOM with transformed ranks decision chart for a nonparametric comparison of group means. ANOM with Transformed Ranks compares each group’s mean transformed rank to the overall mean transformed rank. The ANOM test applies the usual ANOM procedure and critical values to the transformed observations.
Tip: Use this method if your data are clearly nonnormal and cannot be transformed to normality.
ANOM for Variances
(Available only when the X variable has more than two levels and each group has at least four observations.) Shows or hides an ANOMV decision chart to compare group standard deviations (or variances) to the root mean square error (or mean square error). This method assumes that your data is approximately normally distributed. For more information about the ANOM for Variances test, see Wludyka and Nelson (1997) and Nelson et al. (2005). For an example, see Example of Analysis of Means for Variances.
ANOM for Variances with Levene (ADM)
Shows or hides an ANOMV-LEV decision chart that is robust to non-normality to compare group variances. This method compares the group means of the absolute deviations from the median (ADM) to the overall mean ADM. For more information about the ANOM for Variances with Levene (ADM) test, see Levene (1960) or Brown and Forsythe (1974).
Tip: Use ANOM for Variances with Levene (ADM) if you suspect that your data are not normal and cannot be transformed to normality. ANOM for Variances with Levene (ADM) is robust to outliers and non-normality.
ANOM for Ranges
(Available only for balanced designs and specific group sizes.) Shows or hides an ANOM for Ranges decision chart to compare group ranges to the mean of the group ranges. This is a test for scale differences based on the range as the measure of spread. See Wheeler (2003). See Restrictions for ANOM for Ranges Test.
Compare Means
Contains options for multiple comparisons between specified sets of group means. See Means Comparisons Reports.
Each Pair, Student’s t
Shows or hides a Fisher’s LSD multiple comparison of all pairs of means report and shows or hides comparison circles on the Oneway plot.
All Pairs, Tukey HSD
Shows or hides a Tukey-Kramer multiple comparison of all pairs of means report and shows or hides comparison circles on the Oneway plot.
With Best, Hsu MCHB
Shows or hides a Hsu’s multiple comparison with the best report and shows or hides comparison circles on the Oneway plot.
With Control, Dunnett’s
Shows or hides a Dunnett’s multiple comparison with a control report and shows or hides comparison circles on the Oneway plot.
Tip: You can add a Control Level column property to the factor column to avoid specifying the control group each time you select With Control, Dunnett’s. See “Control Level” in Using JMP.
Each Pair Stepwise, Newman-Keuls
Shows or hides a Newman-Keuls stepwise paired comparison report. The Newman-Keuls test does not control the familywise error rate.
Nonparametric
Contains options for nonparametric comparisons of group locations. See Nonparametric Test Reports.
Wilcoxon / Kruskal-Wallis Test
Shows or hides one or more tests that are based on Wilcoxon rank scores. The Wilcoxon rank scores are the simple ranks of the data. The Wilcoxon test is the most powerful rank test for errors with logistic distributions.
If the X variable has exactly two levels, the Wilcoxon test is equivalent to the Mann-Whitney test. In this situation, the report contains a table for the Wilcoxon two-sample normal approximation test that uses a 0.5 continuity correction and a table for the Kruskal-Wallis chi-square approximation test that does not use a continuity correction.
If the X variable has more than two levels, the test based on simple ranks is called the Kruskal-Wallis test.
For information about the report, see Wilcoxon Kruskal-Wallis, Median, Friedman Rank, and Van der Waerden Test Reports. For an example, see Example of the Nonparametric Wilcoxon Test.
Median Test
Shows or hides a test based on median rank scores. The median rank scores are either 1 or 0, depending on whether a rank is above or below the median rank. The median test is the most powerful rank test for errors with double-exponential distributions. For information about the report, see Wilcoxon Kruskal-Wallis, Median, Friedman Rank, and Van der Waerden Test Reports.
van der Waerden Test
Shows or hides a test based on Van der Waerden rank scores. The Van der Waerden rank scores are the ranks of the data divided by one plus a score value. The score value is the number of observations transformed to a normal score by applying the inverse of the normal distribution function. The Van der Waerden test is the most powerful rank test for errors with normal distributions. For information about the report, see Wilcoxon Kruskal-Wallis, Median, Friedman Rank, and Van der Waerden Test Reports.
Kolmogorov Smirnov Test
(Available only when the X variable has exactly two levels.) Shows or hides a test based on the empirical distribution function, which tests whether the distribution of the response is the same across the groups. For information about the report, see Kolmogorov-Smirnov Two-Sample Test Report.
Friedman Rank Test
(Available only when a Block variable with an equal number of observations within each block is specified in the launch window.) Shows or hides a test based on Friedman Rank scores. The Friedman Rank scores are the ranks of the data within each level of the blocking variable. The parametric version of this test is a repeated measures ANOVA. For information about the report, see Wilcoxon Kruskal-Wallis, Median, Friedman Rank, and Van der Waerden Test Reports.
Note: The Friedman Rank Test red triangle menu contains an option for the Nemenyi test. This test is a nonparametric version of the Tukey-Kramer multiple comparisons test. When the Friedman Rank Test is statistically significant, use the Nemenyi test to evaluate which pairs of items differs.
Notes:
– For the Wilcoxon, Median, Van der Waerden, and Friedman Rank tests, if the X variable has more than two levels, a chi-square approximation to the one-way test is performed
– If you specify a Block variable in the launch window and there are equal counts for each combination of Block and X variable level, the Friedman Rank Test is the only Nonparametric option available. If you specify a Block variable in the launch window and there are unequal counts, none of the Nonparametric options are available.
Jonckheere Terpstra Test
Shows or hides a trend test of ordered differences among categories. This test is appropriate when the categories have an ordering of interest, such as dosages of a drug. The alternative hypothesis is the ordering of categories.
Exact Test
Contains options for performing exact tests. See Exact Test Reports.
Wilcoxon Exact Test
Shows or hides a test of Wilcoxon scores using exact methods. See Example of the Nonparametric Wilcoxon Test.
Median Exact Test
Shows or hides a test of median scores using exact methods.
Van Der Waerden Exact Test
Shows or hides a test of Van der Waerden normal scores using exact methods.
Kolmogorov Smirnov Exact Test
(Available only when the X variable has exactly two levels.) Shows or hides a test based on the empirical distribution function, which tests whether the distribution of the response is the same across the groups.
Caution: Exact tests might take a long time to compute for large sample sizes. If you cancel an exact test, the corresponding non-exact test report is provided.
Nonparametric Multiple Comparisons
Contains options for nonparametric multiple comparisons of group locations.
Wilcoxon Each Pair
Shows or hides the Wilcoxon test on each pair. This procedure does not control for the overall alpha level. This is the nonparametric version of the Each Pair, Student’s t option found on the Compare Means menu. See Wilcoxon Each Pair, Steel-Dwass All Pairs, and Steel with Control Reports.
Steel-Dwass All Pairs
Shows or hides the Steel-Dwass test on each pair. This is the nonparametric version of the All Pairs, Tukey HSD option found on the Compare Means menu. See Wilcoxon Each Pair, Steel-Dwass All Pairs, and Steel with Control Reports.
Steel With Control
Shows or hides the Steel test to compare each level of the grouping variable to a control level. This is the nonparametric version of the With Control, Dunnett’s option found on the Compare Means menu. See Wilcoxon Each Pair, Steel-Dwass All Pairs, and Steel with Control Reports.
Dunn All Pairs for Joint Ranks
Shows or hides a comparison of each pair using the Dunn method. The Dunn method computes ranks for all the data, not just the pair being compared. The reported p-value reflects a Bonferroni adjustment. It is the unadjusted p-value multiplied by the number of comparisons. If the adjusted p-value exceeds 1, it is reported as 1. See Dunn All Pairs for Joint Ranks and Dunn with Control for Joint Ranks Report.
Dunn With Control for Joint Ranks
Shows or hides a comparison of each level of the grouping variable to a control level using the Dunn method. The Dunn method computes ranks for all the data, not just the pair being compared. The reported p-value reflects a Bonferroni adjustment. It is the unadjusted p-value multiplied by the number of comparisons. If the adjusted p-value exceeds 1, it is reported as 1. You can add a Control Level column property to the factor column to avoid specifying the control group each time you select Steel With Control or Dunn With Control for Joint Ranks. See “Control Level” in Using JMP. See Dunn All Pairs for Joint Ranks and Dunn with Control for Joint Ranks Report.
Note: The choice of a nonparametric test is dependent on your data. For guidance on test selection for a hypothesis about all pairs see Boos and Duan (2021)
Unequal Variances
Shows or hides four tests for equality of group variances and Welch’s ANOVA test for equal means with unequal standard deviations. The tests for equality of group variances are O'Brien, Brown-Forsythe, Levene, and Bartletts. See Unequal Variances Reports.
Equivalence Tests
Contains methods to test for equivalence, superiority, or noninferiority. See Equivalence Test Reports. Such tests are useful when you want to detect similarities that are of practical or clinically significant interest. Parametric and nonparametric tests are available.
Means
Launches a window with options for equivalence, superiority, or noninferiority tests for means. Specify variance assumptions and the critical difference.
Standard Deviations
Launches a window with options for equivalence, superiority, or noninferiority tests for standard deviations. Specify the critical ratio.
Robust
Contains options for a robust mean estimates. Robust methods reduce the influence of outliers on your analysis. Robust estimates are more efficient than least squares estimates for distributions with heavy tails. See Robust Fit Reports.
Robust Fit
Shows or hides robust mean lines on the Oneway plot and shows or hides a Robust Fit report that includes Huber estimates of the group means.
Cauchy Fit
Shows or hides robust mean lines on the Oneway plot and shows or hides a Cauchy Fit report that includes estimates of the group means assuming a Cauchy error distribution. This robust method is appropriate for extreme outliers.
Power
Enables you to run power calculations for the ANOVA analysis. See Power Reports. For more information about power calculations as well as examples, see “Power Calculations” in Fitting Linear Models.
Set α Level
Enables you to specify an α level. You can select from a list of common alpha levels or specify a level by selecting Other.
Note: The alpha level is applied across analyses and reports. This includes confidence limits, mean diamonds, comparison circles, and multiple comparison analyses. The alpha levels for equivalence tests are set separately.
Normal Quantile Plot
Contains options for plotting the quantiles of the data in each group. See Example of a Normal Quantile Plot.
Plot Actual by Quantile
Shows or hides a quantile plot to the right of the Oneway Analysis plot. The quantile plot shares the Oneway Analysis vertical axis for the Y variable. The cumulative probabilities for each group are on the horizontal axis. The plot shows quantiles computed within each level of the X variable.
Plot Quantile by Actual
Shows or hides a quantile plot with the Y variable on the horizontal axis and cumulative probabilities on the vertical axis. The plot shows quantiles computed within each level of the categorical X variable.
Line of Fit
(Available only when a quantile plot is open.) Shows or hides a reference line fit to the data for each level of the X variable on each open quantile plot.
Normal Quantile Label
(Available only when a quantile plot is open.) Shows or hides the normal quantile scale on each open quantile plot.
CDF Plot
Shows or hides the cumulative distribution function (CDF) for all of the groups in the Oneway report. See Example of a CDF Plot.
Densities
Contains options for visualizing densities across groups. See Example of the Densities Options.
Compare Densities
Shows or hides a plot of overlaid probability density functions for each group.
Composition of Densities
Shows or hides a plot of the summed densities, weighted by the count of each group. Across the range of the X variable, the Composition of Densities plot shows how each group contributes to the total density.
Proportion of Densities
Shows or hides a plot of the contribution to the density made by each level of the X variable. The contribution is shown as a proportion of the total density across the range of the X variable.
Matching Column
Shows or hides a matched fit line and a corresponding fit line on the Oneway plot based on a specified matching variable. Use this option when the data in your analysis come from matched (paired) data, such as when observations in different groups come from the same participant. See Matching Column Report.
Save
Saves the following quantities as new columns in the current data table:
Save Residuals
Saves values computed as the Y variable minus the mean of the Y variable within each level of the X variable.
Save Standardized
Saves standardized values of the Y variable for each level of the X variable. The standardized value is the centered response divided by the standard deviation within each level.
Save Normal Quantiles
Saves normal quantile values computed within each level of the X variable.
Save Predicted
Saves the predicted mean of the Y variable for each level of the X variable.
Display Options
Adds or removes elements from the plot. Some options might not appear when they are not relevant.
All Graphs
Shows or hides the Oneway plot.
Points
Shows or hides data points on the Oneway plot.
Box Plots
Shows or hides outlier box plots for each group. See “Outlier Box Plot”. For an example, see Conduct the Oneway Analysis.
Mean Diamonds
Shows or hides mean diamonds on the Oneway plot. Each mean diamond spans a 95% confidence interval for the corresponding group mean, with a horizontal line at the mean. The 95% confidence intervals are calculated using the pooled standard deviation. See Mean Diamonds and X-Axis Proportional.
Mean Lines
Shows or hides a line at the mean of each group. See Mean Lines, Error Bars, and Standard Deviation Lines.
Mean CI Lines
Shows or hides lines at the upper and lower 95% confidence levels for each group. The 95% confidence levels are calculated using the pooled standard deviation.
Mean Error Bars
Shows or hides the mean of each group with error bars that are one standard error above and below the mean. See Mean Lines, Error Bars, and Standard Deviation Lines.
Grand Mean
Shows or hides the overall mean of the Y variable.
Std Dev Lines
Shows or hides lines that are one standard deviation above and below the mean of each group. See Mean Lines, Error Bars, and Standard Deviation Lines.
Comparison Circles
(Available only when a multiple comparison report is open.) Shows or hides comparison circles. See Statistical Details for Comparison Circles. For an example, see Conduct the Oneway Analysis.
Connect Means
Shows or hides straight lines that connect the group means.
Mean of Means
Shows or hides the mean of the group means.
X-Axis Proportional
(Not available when the Matching Column option is selected.) Specifies the spacing on the horizontal axis. When selected, the spacing is proportional to the number of observations at each level. See Mean Diamonds and X-Axis Proportional.
Points Spread
Specifies the spread of the data points. When selected, the data points are spread across the width of the interval.
Points Jittered
Specifies the type of random noise that is added to the spread of the data points. This option contains multiple types of jitter that help avoid overlapping markers. See “Points” in Essential Graphing for descriptions of the jitter types that are available.
Matching Lines
(Available only when the Matching Column option is selected.) Shows or hides lines that connect the means of each level of the matching variable.
Matching Dotted Lines
(Available only when the Matching Column option is selected and values of the matching variable are all missing for a level of the X variable.) Shows or hides dotted lines that connect the means through missing levels of the matching variable. The values used in place of the missing cell means are obtained using a two-way ANOVA model.
Histograms
Shows or hides side-by-side histograms to the right of the original plot.
Robust Mean Lines
(Available only when a Robust option is selected.) Shows or hides a line at the robust mean of each group.
Legend
Shows or hides a legend for the normal quantile, cumulative distribution function (CDF), and probability density function (PDF) plots.
See “Local Data Filters in JMP Reports”, “Redo Menus in JMP Reports”, “Group Platform”, and “Save Script Menus in JMP Reports” in Using JMP for more information about the following options:
Local Data Filter
Shows or hides the local data filter that enables you to filter the data used in a specific report.
Redo
Contains options that enable you to repeat or relaunch the analysis. In platforms that support the feature, the Automatic Recalc option immediately reflects the changes that you make to the data table in the corresponding report window.
Platform Preferences
Contains options that enable you to view the current platform preferences or update the platform preferences to match the settings in the current JMP report.
Save Script
Contains options that enable you to save a script that reproduces the report to several destinations.
Save By-Group Script
Contains options that enable you to save a script that reproduces the platform report for all levels of a By variable to several destinations. Available only when a By variable is specified in the launch window.
Note: Additional options for this platform are available through scripting. Open the Scripting Index under the Help menu. In the Scripting Index, you can also find examples for scripting the options that are described in this section.