Index not being used in SELECT query
According to your current explanation indexes are not going to help much (if at all) with your current query.


  So there are 3.25M rows with a project key.


That's also the total number of rows, so this predicate is true for (almost) every row ... and not selective at all. But there is no useful index for the jsonb column "references". Including it in the btree index on ("createdAt", "references", type) is just pointless.

Even if you had a generally more useful GIN index on "reference" like:

CREATE INDEX stats_references_gix ON stats USING gin ("references");


... Postgres would still have no useful statistics about individual keys inside the jsonb column. 




  There are only 5 distinct values for the type


Your query selects all of one type and an unknown fraction of another type. That's an estimated 20 - 40 % of all rows. A sequential scan is most certainly going to be fastest plan. Indexes start to make sense for around 5 % of all rows or less.

To test, you can force a possible index by setting for debugging purposes in your session:

SET enable_seqscan = off;


Reset with:

RESET enable_seqscan;


You'll see slower queries ...



You group by project values:


  GROUP  BY "references"-&gt;&gt; 'project'


And:


  There are exactly 400,000 distinct values for the project reference.


That's 8 rows per project on average. Depending on value frequencies we still have to retrieve an estimated 3 - 20 % of all rows if we only picked min and max per project in a LATERAL subquery ...

Try this index, it makes more sense than what you have now:

CREATE INDEX stats_special_idx ON stats (type, ("references" -&gt;&gt; 'project'), "createdAt")
WHERE "references" ? 'project';


Postgres might still fall back to a sequential scan ...

More might be done with a normalized schema / more selective criteria / a smarter query that only picks min and max "createdAt" ...

Query

I would write your query like this:

SELECT EXTRACT(EPOCH FROM (MAX("createdAt") - MIN("createdAt"))) 
FROM   stats
WHERE  "references" ? 'project'
AND   (type = 'event1' OR
       type = 'event2'
   AND "createdAt" &gt;= '2015-11-02 00:00:00+08:00'  -- I guess you want this
   AND "createdAt" &lt;  '2015-12-04 00:00:00+08:00'
      )
GROUP  BY "references"-&gt;&gt; 'project';  -- don't cast


Notes


Don't cast here:

stats."references"::jsonb ? 'project'

The column is jsonb already, you gain nothing. If the predicate was selective, index usage might be prohibited by the cast.
Your predicates on "createdAt" are probably incorrect at lower and upper bound. To include whole days consider my suggested alternative.
references is a reserved word, so you have to always double-quote it. Don't use it as identifier. Similar for double-quoted CaMeL-case names like "createdAt" either. Allowed, but error prone, needless complication.
type


  type character varying(255) NOT NULL,
  
  The type is a simple string no longer than 50 characters.
  
  There are only 5 distinct values for the type field, this would probably be no more than a few hundred in production.


None of this seems to make sense.


varchar(255) in itself hardly ever makes any sense. 255 characters is an arbitrary limit without significance in Postgres. 
If it's no longer than 50 chars, then the limit of 255 makes even less sense.
In a properly normalized design you would have a small integer column type_id (referencing a small type table) which occupies only 4 bytes per row and makes indexes smaller and faster.

Ideally, you would have a project table, listing all projects and another small integer FK column project_id in stats. Would make any such query faster. And for selective criteria, much faster queries would be possible - even without the suggested normalization. Along these lines:
Optimize GROUP BY query to retrieve latest record per user