Summarizing the Observed Data
For the first mechanism they built, they found a 3/7 split and decided that the mechanism had a built in bias and that they should build another.
Let’s analyze the data more formally. In particular, we will determine the probability of 3 successes and 7 failures in a binomial process
- The observational units are the individual drops, with n = 10.
- The variable is whether the toast lands "top" down, a binary variable.
- The null model is that a drop is equally likely to land top/bottom side down.
Terminology detour
We will also differentiate between a statistic and a parameter.
- A statistic is a numerical value that summarizes the observed results.
- A parameter is also a numerical summary, but applied to the underlying random process that generated the data (whose value is usually unknown).
In Lab 1, the statistic was the number (14) or proprotion (0.875) of infants who chose the helper toy, the parameter was the long-run probability of an infant picking the helper toy.
(a) Define (in words) the parameter and the statistic of interest in this study.
As is often we the case, can compute a value for the statistic from the observed data, and then we use it to estimate or make decisions about the unknown value of the parameter.
