different example + add it the csv tests

Author: jan-elastic

docs/reference/query-languages/esql/esql-commands.md

@@ -239,18 +239,20 @@ There must be at least 22 values for change point detection. Fewer than 1,000 is
 
 **Examples**
 
-The following example shows whether there is a day with a significant change in the number of log messages:
+The following example shows the detection of a step change:
 
 ```
-FROM kibana_sample_data_logs
-| STATS message_count=COUNT() BY day=BUCKET(@timestamp, 1 DAY)
-| CHANGE_POINT message_count ON day
+ROW key = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]
+| MV_EXPAND key
+| EVAL value = CASE(key<13, 0, 42)
+| CHANGE_POINT value ON key
 | WHERE type IS NOT NULL
+;
 ```
 
-| message_count:long | day:datetime             | type:keyword | pvalue:double          |
-|--------------------|--------------------------|--------------|------------------------|
-| 329                | 2025-05-10T00:00:00.000Z | spike        | 7.284562237089151e-198 |
+| key:integer | value:integer | type:keyword | pvalue:double |
+|-------------|---------------|--------------|---------------|
+| 13          | 42            | step_change  | 0.0           |
 
 
 ## `DISSECT` [esql-dissect]

x-pack/plugin/esql/qa/testFixtures/src/main/resources/change_point.csv-spec

@@ -1198,3 +1198,18 @@ true        | 1             | null         | null
 true        | 1             | null         | null         
 true        | 1             | null         | null         
 ;
+
+
+example for docs
+required_capability: change_point
+
+ROW key=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]
+| MV_EXPAND key
+| EVAL value = CASE(key<13, 0, 42)
+| CHANGE_POINT value ON key
+| WHERE type IS NOT NULL
+;
+
+key:integer | value:integer | type:keyword | pvalue:double
+13          | 42            | step_change  | 0.0          
+;