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Hello, I’m 2-Click Clovis, a passionate advocate for data analysis and, above all, time efficiency. Throughout my career in the semiconductor and manufacturing sectors, JMP has been an indispensable tool. Since joining the JMP team, I’ve discovered a wealth of new techniques that could have saved me countless hours in my data analysis workflow! My goal is to share this knowledge with fellow JMP users, helping you reclaim valuable time.
Prepare to witness how JMP drastically simplifies routine data manipulation and analysis compared to other platforms, and I’ll guide you to the most efficient methods within JMP itself.
ANOVA and the Power to Compare Means
In my time providing JMP training and demonstrations across diverse industries, I’ve observed a recurring theme. Despite varied datasets and terminologies, engineers and scientists consistently seek the same fundamental statistical analyses.
A cornerstone of these universal analyses is the one-way Analysis of Variance (ANOVA), particularly its capability to Compare Means across multiple independent groups.
One-way ANOVA is a powerful statistical test used to determine if there are statistically significant differences between the means of two or more independent groups. It operates by testing the null hypothesis that all group means are equal. Conversely, the alternative hypothesis posits that at least two group means exhibit a statistically significant difference.
It’s crucial to understand that while one-way ANOVA identifies if differences exist among group means (when considering three or more groups), it doesn’t pinpoint which specific groups differ. Fortunately, JMP offers not only robust ANOVA functionality but also post hoc tests to identify these specific group differences when a statistically significant ANOVA result is found. In today’s example, we will utilize Tukey’s Honestly Significant Difference (HSD) post hoc test, assuming equal population variances across groups.
I recall the days of manual calculations, painstakingly troubleshooting errors for hours. Having a platform like JMP, where complex analyses are executed with simple drag-and-drop actions, is transformative. I’m thrilled to share this time-saving knowledge with you!
Effortlessly Compare Means Using Fit Y by X in JMP
Let’s consider an example involving three typewriter brands – Regal, Speedtype, and Word-O-Matic – tested for typing speed. Our dataset comprises two columns: “brand” (categorical factor) and “speed” (continuous response). You can download the dataset attached to this post to follow along.
To perform a one-way ANOVA and compare mean typing speeds, navigate to Analyze > Fit Y by X in JMP. Then, simply drag-and-drop the continuous response variable, “speed,” into the Y role and the categorical factor variable, “brand,” into the X role. Click OK to proceed. The initial report displays a scatter plot visualizing speed against brand.
To delve deeper into mean comparison, click the red triangle next to “Oneway Analysis of Speed By brand” and select Means/ANOVA. The enhanced report now includes mean diamonds overlaid on the scatter plot, a Summary of Fit table, an ANOVA test with its associated p-value, and summary statistics for each brand group.
Within the mean diamonds, the central horizontal line represents the group mean, and the vertical span depicts the 95% confidence interval for that mean. A quick visual inspection reveals that Speedtype exhibits a notably higher mean typing speed compared to Regal and Word-O-Matic. The ANOVA section confirms this observation with a statistically significant p-value of 0.0004. This low p-value allows us to reject the null hypothesis, concluding that not all group means are equal; at least one mean is significantly different.
Remember, the ANOVA test signals that a difference exists among means, but not specifically which means differ. To pinpoint these differences, we employ a post hoc test. Let’s implement a Tukey-Kramer multiple comparison to compare all pairs of means. Click the red triangle again, navigate to Compare Means, and select All Pairs, Tukey HSD.
The report now expands to include comparison circles to the right of the scatter plot. These interactive circles offer a visual interpretation of group mean comparisons. Circles representing significantly different means will either not intersect or exhibit only a slight intersection. Click on the circle associated with Word-O-Matic. Notice how both Word-O-Matic and Regal circles are highlighted in red. Red highlighting indicates groups whose means are not significantly different from each other. The Speedtype circle remains gray and importantly, does not intersect with the red circles. This visual cue signifies that the mean typing speed of Speedtype is significantly different from the means of both Regal and Word-O-Matic.
For a more quantitative perspective on mean comparison, scroll down to the Ordered Differences Report. This section provides the difference between each pair of means, the standard error of the difference, the confidence interval for the difference, and the crucial p-value for each pairwise comparison.
Observe that the p-values for the Speedtype vs. Word-O-Matic and Speedtype vs. Regal comparisons are highlighted in orange. Both p-values are significantly below the 0.05 threshold, confirming that these pairwise differences are statistically significant. This quantitative result aligns perfectly with the visual interpretation provided by the comparison circles.
This streamlined workflow, achievable in just a few clicks within JMP’s user interface, is broadly applicable across diverse datasets and industries. Whether you are in manufacturing, healthcare, or research, JMP empowers you to efficiently compare means and extract meaningful insights from your data.
With that,
2-Click Clovis is signing off!
Typing Data.jmp
