# Balance Statistic

The following article tries to explain the Balance Statistic sometimes referred to as Saldo or Saldo Statistic. It is used as a quantification method for qualitative survey question. The benefit of applying the Balance Statistic arises when the survey is repeated over time as it tracks changes in respondents answers in a comprehensible way. The Balance Statistic is common in Business Tendency Surveys.

Questions in surveys are often asking categorical values, which are of an ordinal manner. One example are business tendency surveys, where participants are asked to indicate if a certain measure of interest has increased, did not change or decreased over a certain period in time. Participants are consequently not giving a quantitative statement on how much variable in question has changed, but give a qualitative judgement on the direction of the change. The reason why questions are posed in such a way is that usually it is much easier to give a qualitative judgement about a certain variable than an exact quantitative statement. Once you start thinking about it, you will realise that it actually makes sense. The best way to so is a simple mind experiment, try to estimate how high unemployment in your country will be, lets say in one year from now. Is it not much easier to say unemplyoment will be lower, higher or the same in one year from now, than to state it will be lower by 1.54%?

However, the downside of such of questions is that answers are difficult to present to an audience, especially if the survey is on a periodical basis and the change of the variable over time is of interest.

One solution to this problem is the so-called balance statistic. In the case answers of a question are ordinal the balance statistic boils them down to one single number.

The balance statistic is thereby defined as the share of positive answers minus the share of negative answers. In a more formal way the balance statistic can be represented as $b=\frac{\sum_{i=1}^{n}I(y= + )-\sum_{i=1}^{n}I(y= - )}{n}$