I run factor analysis with likert data and I took 3 new scale variables with positive and negative values (save as variables in spss...). When I used one of them to run an one-way anova with a categorical variable (3 levels) I was obliged to compare opposite means (Bonferroni test shew statistical significance between two groups. But the first mean was positive and the other negative). Which is bigger? The positive or negative one?
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You cannot tell this a priori because it depends on the interpretation of the factors themselves.
The first thing you have to do, thus, is to find a reasonable interpretation of the factors (or factor if you have only one common factor) by looking at the loadings, and perhaps trying different rotation methods (varimax, promax, etc.). Then estimate the rotated factor scores. Now you can tell what it means to have higher (lower) values on the factor scores in terms of your original variables by looking at the signs of the loadings.
For instance, if you find out that the loadings for the first factor on the relevant variables are all of the same sign, then this means that those original variables are positively correlated with that factor. This is because the sign of the loadings determines the direction of the correlation between factors and original variables. All this implies that individuals with higher (lower) values on this factor will have higher (lower) values on the associated original variables.
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1$\begingroup$ That is a reasonable advice unless OP becomes more specific. +1. $\endgroup$ Commented Jan 13, 2023 at 5:42
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$\begingroup$ Ι run factor analysis already (varimax method). The questions were in 3 and 5 level likert scale-correlation matrix). I took 3 common factors and their factor scores (standardized-mean=0&standard deviation=1) came up automatically from spss (scores-save as variables). One of the factors was "the perception of passengers about the safety of planes" (+ and - values). So i used it as scale variable in one-way anova analysis (the independent variable was "age"-3 levels). Bonferroni test shew statistical significance between two groups. How can i compare a mean of "-0.34" with a mean of "0.2"? $\endgroup$– J.S.Commented Jan 13, 2023 at 6:39
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$\begingroup$ @J.S. the interpretation of the factor scores depends not only on the magnitude of the loadings but also on their sign. Indeed, the sign of the loadings determines the direction of the correlation of the factor scores with the original variables. Thus, with the information you have provided, you can only say IF age groups are different in terms of the "safety perception" factor. But it is not obvious what higher the safety perceptions values actually mean, they are not measured. To tell this you have to look at the sign of the loadings. $\endgroup$– utobiCommented Jan 13, 2023 at 7:52