Question

Falsifying Data A researcher at the Sloan-Kettering Cancer Research Center was once criticized for falsifying data. Among his data were figures obtained from 6 groups of mice, with 20 individual mice in each group. The following values were given for the percentage of successes in each group: 53%, 58%, 63%, 46%, 48%, 67%. What’s wrong with those values?

Short answer

The percentages were expected to be multiples of 5.

Step-by-step solution

Given information

The data contains observations from six groups of 20 mice each. Percentages for success in the group are 53%, 58%, 63%, 46%, 48%, and 67%.

Finding the expected counts of success

The actual count of success in each group of 20 mice can be computed using percentages.

\(\begin{aligned}{l}53\% \times 20 = 10.6\\58\% \times 20 = 11.6\\63\% \times 20 = 12.6\end{aligned}\)

\(\begin{aligned}{l}46\% \times 20 = 9.2\\48\% \times 20 = 9.6\\67\% \times 20 = 13.4\end{aligned}\)

All the counts are in the form of decimals.

Identifying the flaw of decimal counts

As the count of mice for success is always a whole number, the decimal values are incorrect.

The correct percentage values would be multiples of 5 as one mouse in a group is equivalent to 5%\(\left( {\frac{1}{{20}} \times 100} \right) = 5\% \).