# Is Zero a Frequency? Miller G.A, Frick F.C. Statistical Behavioristics 1949

• EasilyConfuse
In summary, Miller and Frick (1949) discuss the use of an equation to measure sequence variability in response production. This equation takes into account the number of possible sequences and the relative frequency of each sequence. However, a potential issue arises when a particular sequence is not produced, leading to an indeterminate solution. The authors suggest either ignoring such sequences or using the limit of xlog(x) as x approaches 0, which is 0 for any base.

#### EasilyConfuse

I've been playing with an equation that purports to provide a measure of sequence variability
Miller G.A, Frick F.C. Statistical behavioristics and sequences of responses. Psychological Review. 1949;56:311–324

If a person is asked to produce a sequence of responses and there are say 16 possible sequences the statistic is

-∑_(i=1)^16 ([RF)_i*log_2 (RF_i)])/(log_2 (16)) , where 16 equals the number of possible sequences and RFi is the relative frequency of any given sequence.

1 mean they've produced each sequence equally often, and zero that they've produced just one sequence.

So here's my problem, if someone doesn't produce a particular sequence I'm then faced with the conundram do I use a relative frequency of zero? If I do I'm then faced with the problem of trying to calculate log base 2 of zero and also multiply that by zero in the numerator - the solution to this is indeterminate and I can't solve it. So either I ignore sequences that weren't produced when summing across relative frequencies - if I do then I can avoid trying solve for log 2 (0), and I can solve this problem - or at least get estimates of U that are bigger when . But this seems very inelegant. Any thoughts on this would be helpful.

Lim (x->0) of xlog(x) = 0, for any base.

## 1. Is zero considered a frequency in statistical behavioristics?

Yes, in Miller and Frick's 1949 study on statistical behavioristics, they define zero as a frequency. They explain that zero represents the absence of a certain behavior or event, and therefore it can be considered a frequency in the context of their research.

## 2. Why is it important to consider zero as a frequency?

Considering zero as a frequency allows for a more comprehensive understanding of a particular behavior or event. It acknowledges the possibility of no occurrence, which can impact the interpretation of data and statistical analyses.

## 3. Can zero be used in calculations and statistical analyses?

Yes, zero can be included in calculations and statistical analyses. It is a valid data point that should not be ignored or excluded. In fact, excluding zero can skew the results and lead to inaccurate conclusions.

## 4. Are there any limitations to considering zero as a frequency?

One limitation of considering zero as a frequency is that it does not differentiate between the complete absence of a behavior and a low frequency of occurrence. Therefore, it is important to consider other factors and data points in addition to zero when analyzing behavior.

## 5. How does considering zero as a frequency relate to other statistical concepts?

Considering zero as a frequency is closely related to the concept of probability. It represents the likelihood of a certain behavior or event not occurring. It also relates to the concept of outliers, as zero may be considered an outlier in certain data sets.