Is the "empty" methodology NULL or a blank string? If NULL, then the comparison <> should be IS NOT ...
Secondly, should not the order by and ProjID constraint not be in the subselect?
```
SELECT ProjID,
Updated_By,
InsertDate,
var,
oldv,
newv
FROM (
SELECT ProjID,
Updated_By,
InsertDate,
'Methodology' as var,
(
SELECT Methodology
FROM Project_List
WHERE ProjID = o.ProjID
AND InsertDate < o.InsertDate
ORDER BY InsertDate DESC
LIMIT 1
) AS oldv,
Methodology as newv
FROM Project_List as o
WHERE ProjID = 'PR0000014752'
ORDER BY InsertDate ASC
)
WHERE oldv IS NOT newv;
```