Hi everyone! I hope someone can help me determine if it’s better to use the chi square test or anova for comparing two variables with three categories each. The categories are not trust (1), neutral (2) and trust (3) for my “trust” dependent variable and not organized (1), neutral (2), organized (3) for my “organization” independent variable.
The goal is to test the null hypothesis that there is no relationship between organization and trust.
In addition, I have two groups a control and experiment group. I usually just split the file in SPSS by group and run the crosstabulation/chi-square in order to get the results by group. Is this okay or do I need to do the Anova instead?
Also, just to give you some background knowledge the no, neutral and yes type categories above were based on a likert scale that had 1 to 5 with 1 being strongly disagree and 5 being strongly agree. I basically combined 1 and 2 into no, 3 as neutral and 4 and 5 into yes. I did this for both variables.
Is it better to leave the likert scale 1-5 and do an anova or is it okay to just do the crosstabulation in SPSS with the Chi-square or Fisher‘s test? I am hoping that the chi square can be used or if there is an argument in favor of using it but I am open to doing the Anova if it is better.
By the way, my sample size is 72.
Thank you in advance for your assistance and I hope to hear from all of you soon.
ANOVA is bettter. Chi 2 will have most likely insufficient power with n=72.
Argument for Chi2 would: be not normal distribution of your DV.
Nevertheless even then non-parametric ANOVA available in SPSS would be better option.
Good Luck
If you are asking whether the two variables are related, then ANOVA can't really be used at all; that is not its function (ANOVA is for comparing scores across groups). You can either run a chi-square test (or some variant thereof) or a correlation coefficient. If the latter, then definitely retain the 5-point rating system, because you want all the variability preserved. If the former, then having just 3 categories might be better.
The fact that your sample contains two groups raises a different issue. Should you lump them together or treat them separately? Offhand, I'd say to keep them separate, but then you'd only have 36 people per analysis and power would be sharply reduced.
ANOVA could be used to compare the ratings across groups, though with just two groups you might as well run t-tests. If the groups aren't different to a statistically significant degree, that would help you to justify lumping them together for the chi-square or correlational analyses.
Thank you for the responses!
Dear Marcin Sklad: I checked the dependent variable and it is not normally distributed, this might be a good reason for using the chi-square test. Although, I will check into the non-parametric ANOVA. Do you have any other arguments in favor of using chi-square that you can think of?
Dear Stephen Joy: I am looking at both groups separately and together. I am also using Fisher's test if there are less than 5 per cell. I did run a t-test to test one of my hypotheses, however I am using the chi-square to test the other hypotheses of whether there is a relationship or not between the variables. Therefore, it seems based on your response that ANOVA may not be appropriate. Also I just wanted to confirm that you meant to keep the 5-point rating system for the correlation coefficient and 3 categories for the chi-square.
Thank you again and I look forward to additional responses.
I think so. In general, a greater range of possible ratings/scores means more information, which is better for most purposes (such as correlation coefficients). But as you note, with chi-square tests one hopes to have at least 5 cases per cell. With N=72, a 3x3 matrix gives you an average of 8 per cell, while a 5x5 matrix would mean slightly fewer than 3 in the average cell.
Dear Jennifer,
although likert-scales are often treated as 'continuous' variables that have equal distance between each level (i.e. for example "strongly disagree" - "disagree" is the same 'distance' as "neutral" - "agree"), it would be more appropriate to assume only an ordinal scale. Thus it is better to use Spearman (rank) correlation.
If you want to compare the correlations between the groups you should use Fisher-Z transformation; on http://comparingcorrelations.org/ you can find a very convenient tool for this comparison, you simply enter your correlation coefficients and sample sizes.
Cheers, Gunnar
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