1. ## Chi and linear-by-linear

A quick question about the use of linear-by-linear association tests for small samples - with a structure greater than 2X2.

As we know, a chi square becomes unreliable with empty cells, or cells with very few counts. I am assuming that the same applies for linear-by-linear association tests. Is this assumption correct? If you run a linear-by-linear, and have, for example, a couple of cells with 0, 1 or 2 counts in it, it surely must be discarded as being unreliable, right?

2. ## Re: Chi and linear-by-linear

Is linear-by-linear test the same as two ordinal variables in a chi-square? If so, I would say yes. Typically with small counts one tries to use exact methods.

3. ## Re: Chi and linear-by-linear

Yes, in the sense that you have a contingency table, though one side is a range. For example Democrat/Republican on one side, and belief in god on the other side (e.g 1,2,3,4, with 1=atheist and 4 strongly believing in God, making a 2X4 table). If one's hypothesis is that Republicans will have a "more increasing" likelihood to believe in god than Democrats, then it's a linear, correlational relationship, being examined in a chi format. SPSS gives the linear-by-linear probability along with the chi statistics in crosstabs.

My assumption would be that statistically a linear-by-linear table would have the same issues with zero or small cell frequencies as chi, but I am not a hundred percent sure of this.

4. ## Re: Chi and linear-by-linear

Small values should be an issue. You should look into using Wilcoxon rank sum.

5. ## Re: Chi and linear-by-linear

hlsmith,

Thanks. Something rank-based seemed a good alternative, though there might then be an issue of having to deal with a lot of ties. I haven't found too much on the web about linear-by-linear, and I didn't want to absolutely state that empty or low-populated cells were a problem.

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