You don't really say how the tests were done or what you tested for so the only answer that I can give is that it depends.  I would certainly say that they are not necessarily in conflict depending on what you did.

Hello David. Thank you for the reply, I had 50 observations (N=50) for 26 variables (IV) which were assessed and ranked according to 3 t levels  (  the assessment of the 26 variables was also scored for statistical comparisons among groups ).  The DV represents a categorical variable with resulting outcomes (above defined limit, below defined limit, Not detected). I am interested in knowing whether the factors represented by the IV affect the presence / level of DV. ( i am not sure though if the tests i have performed were the right approach). So, I used multinomial regression and have entered into the model the IVs that showed highest contribution to the variation in the total assessment score). Eventually, i ended  up with a significant regression model with a number of IV explaining 51% of the variance in DV and correctly classified 75% of the cases. Running chi-square to check the association between the DV and those IV, did not give statistical significance. Probably using DV ranked to 3 levels may cause loss of precision as it did not necessarily contained all the information in the underlying measurement?

Two things. First, in  some regression books you find a rule of thumb that says that you need 5-10 observations per predictor to be safe in running the analysis. You are way below that. Second, were all the 26 predictors included in the contingency table you used in the Chi-square test? If not, how many were and were any of the cells empty?

Maybe i misunderstood the term "cases per predictor" ? i somehow considered I have 50 cases (observations) per each IV. 

Chi square test was performed for the same number of variables entered into multinomial regression (17). I had the curiosity to run the test and check if results would be the same. Not all same variables were significant in both tests (chi squre adn regression).

the other IVs were excluded either because very few had cases ranked  as "not observed", or having being shown not to have a major contribution to the overall assessment score (calculated total score of the 26 variables).

May be i  better adopt simple non parametric correlation or chi-square test?  I thought having a sample size N=50 would allow performing the regression analysis. I have read that " Multinomial logistic regression does necessitate careful consideration of the sample size and examination for outlying cases, And you noted , Sample size guidelines for multinomial logistic regression indicate a minimum of 10 cases per independent variable".

Re.empty cells. In few cases  1 cell was empty and in others 4-5 cells empty. 

All tests have specific rules that you need to fulfill: sampling distribution, sampling size, type of variable, etc. The interpretation depends on if the analysis is with categorical or quantitative variables. Do you employ logistic regression or linear regression? or Do you employ another multinomial model? The statistical tests can complemented between, but We can obtain different results.

Dima, Thank you. The requirement to use the approximation for the test stat to be Chi-sq. is at least 5 obs per cell. With empty cells you can't trust the Chi-sq. test. If you have less than 5 obs. per IV you can't trust the regression. I would guess that these two things are causing you to observe the problem. Remember too that you must be testing the same hypothesis in both cases so if all of the IVs in your regression aren't signif. you probably should drop the nonsignif. ones out of the chi-sq test. I hope this helps a bit. Finally remember that the Chi-sq is a test of independence so you want a large p-value if you want the Chi-sq test to compliment the regression. Best wishes

Thank you so much David !!I greatly appreciate your thorough clarification. Will try again with your suggestions.

Thanks for the input .Though not very clear.so must the output of both tests (multinomial regression model and chisquare) test be the same?If so how do you discuss the different results?which conclusion do you make?