Do I have enough respondents for analysing three groups?

[Sibbens]

Hi all,

I am doing a study on customer loyalty and I have collected data from 180 respondents after cleaning data.

Through a cluster analysis I have separated respondents into four groups where three is to be used in the PLS analysis. The groups are: Ambassadors (very loyal and recommending the products), tacit loyals (very loyal but no recommendation to others) and "the rest" (no significant loyalty nor no aversion against buying the same again).

I would like to do three PLS analysis, one for each of the three groups. I end up with groups that have n=84, n=33 and n=32. My problem is that I am in doubt whether I can use that small amounts of respondents.

I have read that a rule of thumb is, that I need 10 times the largest amount of indicator variables linked to a LV. The largets amount of indicator variables in my model is 4 and therefore two of the groups are just short of the recommendation given by the rule of thumb.

Can I use the data for measuring the three groups anyway?? (of course I guess I would only be able to conclude anything about quite strong path coefficients)

Any help would be very appreciated!


Kind regards

Sune

[Diogenes]

Hi Sune,


1) The better way to compute the sample size is using the G*Power 3 (http://www.psycho.uni-duesseldorf.de/ab ... d-register)
Using:
Alpha err. prob. = 5%
Power = 80%
Predictors = 4
Effect size (f2) = 0.15 (medium)
The sample size should be equal 85 cases.

2) With a 32 sample size, just effects above 0.444 (R2 = 0.31) will be detected as significant (sensitivity analysis in the G*Power 3).
With small sample size, a nonsignificant coefficient could be caused by the low power and not because the coefficient is zero in the population.

3) If you want to compare the coefficients (to test the three group difference), you should do another test in the Power*3 (differences between slopes).


I hope this help you.

Best regards,

Bido

[Sibbens]

Thanks for your reply! I will for sure look into G Power 3. If I choose to move on with SmartPLS will it then be OK to use the quite low sample sizes for two of the groups, anyway?

Also, another question has arisen that I thought you might be able to help with. It is quite hard for me to decide whether my approach is okay or way off.

I am doing three different analyses in SmartPLS, one for each of the three groups stated above (let's call them ambassadors, tacit loyals and latent loyals). I want to compare the effects in each of the PLS analyses with each other in order to detect similarities and differences in what drives customer loyalty between these clusters. Therefore, the LV "Customer Loyalty" needs to be the same construct with same IVs in all three analyses. As the clusters are created by clustering the total sample using the three IVs measuring the LV "Customer Loyalty" the reliability and validity of this construct varies greatly across the three analyses.

My problem is therefore that I need the LV "Customer Loyalty" to be the same in order to maintain construct validity and the basis of comparing the three analyses, despite the low reliability (i.e. a Cronbach's alpha of -0,29). Is it in this case okay to work with reliability and validity values that are too low and in a few cases negative due to the fact that the analysis compare the same conceptual model on different data from different clusters of respondents?

Again, your help is very valuable - thanks a lot!

[Diogenes]

Hi,

negative alphas is a problem with the correlation between indicators (some of them have positive and other negative correlation in the same LV). Are there some reversed scale?
This issue must be solved before any future analysis.
Best regards,
Bido

[Sibbens]

In the case with the cluster of tacit loyals, their loyalty is characterized by a high willingness to buy again in the future, but a low willingness to recommend the product to others. The cluster of ambassadors have both a high willingness to buy again in the future and a high willingness to recommend the product to others. Therefore, the three MVs that define the "Customer Loyalty"-construct, when the model is feeded with data from the cluster of tacit loyals, do not correlate positively. One MV is positive with a high loading, while the two others (which ask whether the customer recommends the product to others) have negative loadings. This makes Cronbach's alpha negative. So yes, these MVs are reverse compared to the first MV. But I need the model to be comparable to the results from the model that is feeded with data from the cluster of ambassadors. If I reverse the two MVs that make problems, my "Customer Loyalty"-construct would no longer be the same in the two analyses.

Do you have any recommendations on how to go about this problem? Again, I should emphazise that the target of the analysis is to compare what drives customer loyalty between the three clusters that I have identified. Therefore, I guess I need the same "Customer Loyalty"-construct, right?

I am looking forward to hearing your thoughts on this.

[jmbecker]

Maybe your Loyalty construct is not measured reflective but formative?

It sound more like you have some indicators that form a latent construct, i.e., loyalty constitutes of willingness to buy again+ willingness to recommend + ...

and not that if loyalty increases/decreases all facets of the construct increase/decrease, i.e., w. to buy again AND w. to recommend AND ...