Confidence interval (bias corrected)

[Choukri]

Hi everyone,

I would like to make a multigroup analysis between lower and higher income groups, I got the following results for the relationship between satisfaction and trust

Group 1: Confidence interval (bias corrected) [Lower= 0.522; Upper= 0.693]; Path coefficient= 0.599

Group 2: Confidence interval (bias corrected) [Lower= 0.615; Upper= 0.784]; Path coefficient= 0.693

According to Sarstedt et al. (2011), the path coefficient of group 1 does not overlaps with the confidence interval of group 2.

The path coefficient of group 2 (0.693) does not overlaps with the confidence interval of group 1 [0.522; 0.693], but it is equal to the upper value.

Could I conclude that the relationship between satisfaction and trust is different between the two groups?

Thank you

[jmbecker]

The two confidence intervals do overlap, because group1 Upper= 0.693 is larger than group 2 Lower= 0.615, i.e., there is an area between 0.615 and 0.693 where they overlap. Hence, the two groups are not significantly different for this parameter.

[Choukri]

Thank you Dr. Jan-Michael Becker for the respond

I think that there is a problem (for me) of how to evaluate the parameters;

According to Sarstedt et al. (2011), we should check if the path coefficient of the first group falls in the corresponding interval (lower and upper) of the second group, for example in my case the path coefficient of the first group (0.599) does not overlap with the confidence interval [Lower= 0.615; Upper= 0.784] of the second group, and vice versa.

If what I said was not correct, please show me the right way how can I evaluate my results (significant or not significant ).

I will be grateful to know your answer

Thank you

[jmbecker]

Hi Choukri,
ok, the Sarstedt et al. 2011 paper says that the path coefficient of one group should not be in the confidence interval (CI) of the second group and vice versa. Hence, following Sarstedt 2011 you are correct with your assessment.
I was not aware that they suggest it this way, because I had other papers in mind that say that the CI boundaries should not overlap.

This made me curious and I searched myself for the right way to do it. I found something interesting in Geoff Cummings Book (Understanding The New Statistics), where he discusses the use of CIs intensively and there is no definite answer. More precisely, both approaches are not quite correct. The one is a bit too conservative (mine) and the other (Sarstedt’s) is a bit too liberal.
Cumming shows for a simple mean comparison that if the bootstrapp CIs just touch (i.e., upper bound of group 1 = lower bound of group two) it is a situation equivalent to a p-value of 0.01 (1%). If the boundary of one CI is equal to the parameter estimate of the other group the situation is similar to a p-value of 0.10 (10%). If the CIs overlap only by half of their arm length, then the situation is similar to a p-value of 0.05 (5%). Hence, CI can overlap to some degree, but they should not overlap too much. Using the parameter estimate to judge the overlap is probably too liberal (10% significance level) and disregarding overlap at all is quite conservative (1% significance level).
These considerations must not match a PLS estimate one-to-one, but it might be a good indicator for understanding the situation.

Back to your case: It actually seems that your difference could be significant in a p=5% sense, because your CIs overlap only to a very small degree (i.e., probably less than half of the arm length).

[AAljabr]

Hi all,

I have one question regarding using the approach proposed by Sarstedt et al. 2011. The question is that when checking whether the path coefficient of one group falls in the confidence interval of the another group, should I use the path coefficient of the original sample (O) or the path coefficient of the Sample mean (M)?

Thanks