Multi-group analysis with WarpPLS: Comparing means of two or more groups

Comparing means of two groups is something that behavioral researchers often do. In fact, this is the most widely used quantitative analysis approach. This is also a form of multi-group analysis, where the number of groups is two. Common tests for comparing means are the t and and one-way ANOVA tests.

There is an arguably much better way of doing comparison of means test, with WarpPLS. Follow the steps below. This is a two-group test. Multi-group tests can be done in a similar way, through multiple two-group tests where conditions (i.e., groups) are compared pair by pair.

- Create a dummy variable (G) with numbers associated with each of the two groups - e.g., 0 for one group, and 1 for the other group. This dummy variable should be implemented as a LV with 1 indicator.

- Define your dependent (or criterion) construct (T) as you would normally do; in this case, I think that would be as a reflective LV with 3 indicators.

- Create a link between G and T, with G pointing at T.

- Estimate the model parameters with WarpPLS; this will calculate the beta and P values for the link. The P value is analogous to the P value you would obtain with a t test.

The following article goes into some detail about this procedure, contrasting it with other approaches:

Kock, N. (2013). Using WarpPLS in e-collaboration studies: What if I have only one group and one condition?  International Journal of e-Collaboration, 9(3), 1-12.

This type of WarpPLS test has a number of advantages over a standard t test or a one-way ANOVA test (which are essentially the same thing). For example, it allows for the use of LVs as dependent variables; and it is a robust test, which does not require that the dependent variables be normally distributed.

Multi-group tests, with more than two groups, can also be conducted by assigning different values to each of the groups. The key here is to decide what values to assign to each group. This choice is often somewhat arbitrary in exploratory analyses. The “Save grouped descriptive statistics into a tab-delimited .txt file” option may be helpful in this respect. This is a special option that allows you to save descriptive statistics (means and standard deviations) organized by groups defined based on certain parameters. For more details, see the user manual for WarpPLS, which is available from Warppls.com.

Starting in version 6.0 of WarpPLS, the menu options “Explore multi-group analyses” and “Explore measurement invariance” allow you to conduct analyses where the data is segmented in various groups, all possible combinations of pairs of groups are generated, and each pair of groups is compared. In multi-group analyses normally path coefficients are compared, whereas in measurement invariance assessment the foci of comparison are loadings and/or weights. The grouping variables can be unstandardized indicators, standardized indicators, and labels. These types of analyzes can now also be conducted via the new menu option “Explore full latent growth”, which presents several advantages (as discussed in the WarpPLS User Manual).

Related YouTube videos:

Explore Multi-Group Analyses in WarpPLS

Explore Measurement Invariance in WarpPLS

Standard deviation is not the same as range of variation

Means and standard deviations can be generated and saved through the “Save grouped descriptive statistics into a tab-delimited .txt file” option of WarpPLS. You can choose a grouping variable, number of groups, and the variables to be grouped. This option is useful if one wants to conduct a comparison of means analysis using the software, where one variable (the grouping variable) is the predictor, and one or more variables are the criteria (the variables to be grouped).

In comparisons of means analyses, research results are normally expressed in means and standard deviations. For example, in the study reviewed in this post, it is stated that the weight of participants in a 12-week weight loss study varied from: 87.9 plus or minus 15.4 kg (at baseline, or before the 12-week intervention) to 81.7 plus or minus 16.2 kg (after the 12-week intervention).

The 87.9 and 81.7 are the average weights (a.k.a. “mean” weights), in kilograms, before and after the 12-week intervention. However, the 15.4 and 16.2 are NOT the range of variation in weights around the means before and after 12-week intervention. They are actually the ranges around the means encompassing approximately 68 percent of all of the values measured (see figure below, from www.electrical-res.com).

In the figure above, the minus and plus 15.4 and 16.2 values would be the “mean(x) – s” and “mean(x) + s” points on the horizontal axis of histograms of weights plotted before and after the 12-week intervention. This assumes that the distributions of weights are normal, or quasi-normal (i.e., similar to a bell-shaped, or normal, curve); a common assumption in this type of research.

The larger the standard deviation, the wider is the variation in the measures, and the flatter is the associated histogram (the bell-shaped curve). This property has a number of interesting implications, some of which will be discussed in other posts.

Sometimes another measure of dispersion, the variance, is reported instead of the standard deviation. The variance is the standard deviation squared.

The reason why standard deviations are reported instead of ranges of variation is that outliers (unusually high or low values) can dramatically widen the ranges. The standard deviation coefficient is much less sensitive to outliers.

Saving and using grouped descriptive statistics in WarpPLS

When the “Save grouped descriptive statistics into a tab-delimited .txt file” option is selected, a data entry window is displayed. There you can choose a grouping variable, number of groups, and the variables to be grouped. This option is useful if one wants to conduct a comparison of means analysis using the software, where one variable (the grouping variable) is the predictor, and one or more variables are the criteria (the variables to be grouped).

The figure below (click on it to enlarge) shows the grouped statistics data saved through the “Save grouped descriptive statistics into a tab-delimited .txt file” option. The tab-delimited .txt file was opened with a spreadsheet program, and contained the data on the left part of the figure.

That data on the left part of the figure was organized as shown above the bar chart; next the bar chart was created using the spreadsheet program’s charting feature. If a simple comparison of means analysis using this software had been conducted in which the grouping variable (in this case, an indicator called “ECU1”) was the predictor, and the criterion was the indicator called “Effe1”, those two variables would have been connected through a path in a simple path model with only one path. Assuming that the path coefficient was statistically significant, the bar chart displayed in the figure, or a similar bar chart, could be added to a report describing the analysis.

The following article goes into some detail about this procedure, contrasting it with other approaches:

Kock, N. (2013). Using WarpPLS in e-collaboration studies: What if I have only one group and one condition? International Journal of e-Collaboration, 9(3), 1-12.

Some may think that it is an overkill to conduct a comparison of means analysis using an SEM software package such as this, but there are advantages in doing so. One of those advantages is that this software calculates P values using a nonparametric class of estimation techniques, namely resampling estimation techniques. (These are sometimes referred to as bootstrapping techniques, which may lead to confusion since bootstrapping is also the name of a type of resampling technique.) Nonparametric estimation techniques do not require the data to be normally distributed, which is a requirement of other comparison of means techniques (e.g., ANOVA).

Another advantage of conducting a comparison of means analysis using this software is that the analysis can be significantly more elaborate. For example, the analysis may include control variables (or covariates), which would make it equivalent to an ANCOVA test. Finally, the comparison of means analysis may include latent variables, as either predictors or criteria. This is not usually possible with ANOVA or commonly used nonparametric comparison of means tests (e.g., the Mann-Whitney U test).