In a regression with a database with N=1200, I have an independent dummy variable that measures if the surveyed is unemployed or employed. The variable has the following characteristics:
Unemployment = 0 - Frecuency: 1196
Unemployment = 1 - Frecuency : 4
The regression gives me a significant coefficient, but, also, very counter intuitive (especifically, thay Life Satisfaction has a possitve association with unemployment). I think, however, that it's wrong to obtain a valid conclusion from just 4 cases in Unemployment=1. I also have other dummy variables where the situation is even less clear. For example:
Dummy = 0 - Frecuency: 1170
Dummy = 1 - Frecuency: 30
Or even more:
Categorical option A = 0 - Frecuency: 1150
Categorical option B = 1 - Frecuency: 30
Categorical option C = 2 - Frecuency: 12
Cateogorical optio D = 3 - Frecuency: 8
Can I obtain valid conlcusions from this? And, in more general terms, is there a minimun number of observations needed per category of response in each independent variable so the conslusions that arise from it are pertinent/correct? If that's the case, how can I calculate this number?
N = 1200: the entire 1,200 elements should be used as detailed study since the N (population of the database) is small. The result may be treated as learning set. Use simulation to repeat to see stable patterns.
WRONG CODING: your coding appears to be erroneous. The general convention is 1 = success and 0 = failure. in this case, EMPLOYMENT should be coded 1 and UNEMPLOYMENT should be 0. Re-code and rerun your data, the result should make sense thereafter.
SIGNIFICANCE TEST may be obtained through the DeMoivre-Laplace equation; thus:
Z = (Sx - np) / sqrt(npq)
Sx = number of employed; n = 1,200; p = (s + 1) / (n +2) where s = number of employed; and p = 1 - p. set you confidence interval, say 95% then find your critical value in Z table at 1.65. H0: Z 1.65 significant.
MINIMUM SAMPLE SIZE is not a relevant issue in this case because you have access to the entire population that is small (N = 1,200). The general rule is that where the study of the entire population is feasible, minimum sample is moot.
Suggest you see this link: https://www.google.com/search?rlz=1C1CHBF_enUS874US874&q=effect+of+dummy+coding+in+regression+interpretation&spell=1&sa=X&ved=2ahUKEwjKq9uq-PzmAhWLPM0KHS1OChQQBSgAegQIDRAm&biw=1600&bih=827
and
https://www.google.com/search?rlz=1C1CHBF_enUS874US874&ei=WHoaXsqfFov5tAatnKmgAQ&q=effect+of+dummy+coding+on+regression+interpretation+small+observations+in+one+class&oq=effect+of+dummy+coding+on+regression+interpretation+small+observations+in+one+class&gs_l=psy-ab.3...77345.95048..95761...0.2..0.237.3373.21j8j3......0....1..gws-wiz.......0i71j33i22i29i30j33i299j33i160j33i10.YzGbjn1L7Ks&ved=0ahUKEwjKq9uq-PzmAhWLPM0KHS1OChQQ4dUDCAs&uact=5
Best, D. Booth
I do not entirely agree with Paul Louangrath. First, nothing says that the database is the population. If it the case, it is a very atypical population with only around 4 thousandth of unemployed people. Second, it is not always possible to associate a dummy variable to a success versus failure scheme so coding is often arbitrary. The sign of the associated coefficient will indicate the possible direction of the effect. Third, the De Moivre-Laplace significance test that is proposed would be ok if the dummy variable would be alone. Clearly, it is not the case here so it is better to refer to the Student test which can take care of possible multicollinearity among the explanatory variables. I have doubts about the way the categorical variable was taken into account by Santiago Valdivieso. See David Eugene Booth recommendations.
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