Chi-Square: Is effect A larger than effect B?

grey

New Member
#1
Dear All,

I would like to test hypotheses like the following example: Effect A is weaker than effect B.

For Effects A and B, I have a 2 (error: present vs. absent) x 2 (group: control vs. experimental) contingency table, thus getting chi and e.g. a phi-coefficient.

My question is: How can I find out whether the resulting effect A is stronger than B?

I'll be grateful for any help!
Thanks for your consideration :)
 
#2
Hi Grey,

Look into logistic regression. I think most people would agree that a larger Odds Ratio (OR>3), typically represents a stronger association.

Take care, Mike
 

hlsmith

Less is more. Stay pure. Stay poor.
#3
If you just have a single dependent variable (present/absent) and a single independent variable (control/experiment), you do not necessarily need to use logistic regression. You can just do the calculations based on your 2x2 contingency table.

Given your study design (prospective [incidence] or retrospective[prevalence]) you can either calculate relative risk or odds ratio (respectively). The important follow-up action would be also calculating the confidence interval and ensuring it does not include "1" or no difference in the comparison (ratio).

The magnitude of the effect is context and situation specific. In some situations a 1% greater relative risk could be very important, while in others perhaps you want a 300% or greater relative risk as noted in post #2.
 

grey

New Member
#4
Many thanks for your answers!!

I just became aware that I forgot to mention an important aspect: The data is to some extent dependent. I'll try to illustrate it with the following example:

Hypothesis: We expect a weaker misinformation effect for the central compared to the peripheral item.

To calculate this "misinformation effect", i compare the error rate of the control (CG) and the experimental (EG) group. Let's assume the error rate for the central item is 50% in the EG and 20% in the CG (difference = 30%). I analyse whether this difference is statistically significant by means of a 2 (EG/CG) x 2 (answer correct/incorrect) contingency table. I do the same thing for the peripheral item (let's assume a difference of 50%).

I am interested in whether the difference (i.e. misinformation effect) of 30% for the central item is significantly lower than the difference of 50% for the peripheral item. BUT: All participants answered the peripheral and the central item question, i.e. this part of the experiment was manipulated within subjects. Does that change anything? And is there a possibility to directly compare two chi-square results without using e.g. odds ratios?