Using dummy variables when variable has been standardized

Question

I was wondering if someone can help me with the following. I am using an investor sentiment index that has been standardized to yield a mean of 0 and a standard deviation of 1. This index has been created using 50 years of data. In my sample, the mean is not close to 0. I want to create a dummy variable indicating when investor sentiment is high or low. However, as the index has been standardized I am not sure whether this is even "logical" to do. Thus my first question is, is it possible (logical) to use dummy variables on standardized values?

I ask this because when I regress, the sentiment index is significant when using the indexes as obtained. When I create dummy variables the sentiment becomes insignificant and I don't understand why. I have noticed that when I classify sentiment as high or low using dummies, low sentiment (i.e. when the index is negative) is 1/3 of the total observations. This means that 2/3 of the observations relate to high sentiment (i.e. positive investor sentiment index). Thus my second question is whether the number of observations has to do with the difference in the regression results (if the answer to question 1 is yes).

Answer 1

Using zero as a cut-off to discretize a standardized variable is equivalent to using the mean as a cut-off to discretize the raw variable. You can use a different cut-off, but it's rarely a good idea to discretize the predictor at all: see What is the benefit of breaking up a continuous predictor variable?. What kind of response would be flat against investor sentiment until a certain point & then jump up or down?

There's not enough information to say why in this case the regression t-test became insignificant (at some level or other) when using the discretized version of investor sentiment index. The kind of thing that can happen is that predictor values are concentrated about the mean, so there's not much difference in the average response for "high" and "low" groups even though further from the mean there's a clear difference in the responses.