## 25.5 Statistical validity conditions: Comparing odds

As usual, these results hold under certain conditions. The CI computed above is statistically valid if

- All
*expected*counts are at least five.

Some books may give other (but similar) conditions.

In addition to the statistical validity condition, the CI will be

**internally valid**if the study was well designed; and**externally valid**if the sample is a simple random sample and is internally valid.

The statistical validity condition is a bit tricky to understand
(but is explained further in Sect. 31.3).
SPSS will let you know if the expected count condition is not met,
underneath the *first* output table
in Fig. 25.3.
In jamovi,
the *expected* counts must be explicitly requested
to see if this condition is satisfied.

**Example 25.2 (Statistical validity) **In Fig. 25.3
(for the uni-students data),
the text under the *first table* table of SPSS output
(labelled **Chi-Square Tests**)
says

0 cells (0.0%) have expected count less than 5.

That is, *all* the cells have expected counts of at least five,
so the statistical validity condition is satisfied.
Notice from
Table 25.1
that the *observed* counts are not all greater than five
(one cell has a count of 2).
The statistical validity condition is about the
*expected* counts though,
not the *observed* counts.

In jamovi, the expected counts must be requested explicitly (Fig. 25.4), but again none are less than five.

In either case, the conclusion is statistically valid.**Example 25.3 (Car crashes in China) **In Example 25.1,
all the *observed* counts are larger than five.

The *expected* counts are shown below.
Since all *expected* counts are larger than five, the CI will be statistically valid.

Type of crash | 2011 | 2015 |
---|---|---|

Involving pedestrians | 15.11 | 36.88 |

Involving vehicles | 34.88 | 85.12 |

These counts are what we would *expected* to find if there was no relationship between the type of crash in 2011 and 2015;
that is, if the proportion of crashes involving pedestrians was the same in 2011 and 2015.

*very*close to these

*expected*counts, meaning that what we observe is very close to what we expected if there was no relatiionship.