An Argument for Statistics (Part 2)

Most people who know anything about statistics understand descriptive ones: numbers used to summarize and describe data. I feel strongly that as traders, we need to understand inferential statistics too.

Inferential statistics are used to reach conclusions that extend beyond the immediate data alone. These might be used to infer from a sample characteristics about the whole population.

Inferential statistics are also used to determine whether an observed difference between groups is dependable or simply a chance occurrence. This is called hypothesis testing.

I said one could lie with descriptive statistics by including certain things and excluding others.

Inferential statistics may also mislead by including/excluding certain differences/similarities in experimental design. Even before hypothesis testing begins, validation of experimental design is essential albeit beyond the scope of today’s post.

Hypothesis testing begins by defining the hypotheses. The null hypothesis (H_o) generally states that both (all) groups are the same. The value of a group is often given in terms of an average (e.g. arithmetic mean) and standard deviation. The null hypothesis represents the status quo. The alternative hypothesis (H_A) generally states the groups are not equal. H_A may or may not go one step farther and state which group is thought to be greater than the other.

The next step is to consider the statistical assumptions being made about the sample(s) involved. For example, a given statistical test may require the samples be independent (e.g. not affecting each other) or that the distribution (shape) of a sample be “normal” (bell curve, which has a specific mathematical definition), etc. If the assumptions for a statistical test are not met then the test should not be used or the caveats/limitations should be discussed to put reasonable context around any conclusions.

I will continue next time.