Tube testers do not always tell the full story.  Below is an excerpt taken from the RCA Receiving Tube Manual (RC-30).  Now in a time where we often find ourselves consumed with test results, RCA provides an important perspective from the golden age of tube electronics.  The limitations of tube testers are discussed and very insightful.

RCA Tubes – Radio Corporation of America

Found in the manual version RC-30 (page 103).

Tube Tester Limitations
“The tube tester can only indicate the difference between a tube characteristic and those which are standard for that type. Because the operating conditions imposed upon the tube may vary within wide limits it is impossible for a tube tester to evaluate tubes for all applications.

Commercially available tube checkers vary widely in purpose performance and significance of results. They range from relatively inexpensive portable units to costly laboratory quality instruments. Design trade-offs are made by tube checker manufacturers to provide a product simple to operate, capable of testing a wide variety of tube types, and in some cases, low in cost. Accuracy of readings, completeness of testing, and even proper testing conditions for certain types are sometimes sacrificed in these trade-offs. Recognition of individual tester limitations is absolutely necessary before valid judgments on tube quality can be made from test results.

Tube checkers generally make two types of evaluations: tests for inter-element shorts (leakage) and an electrical test of quality that is either and AC cathode emission test or a more complex large signal transconductance test.

The shorts or leakage tests are often more sensitive than those of the tube manufacturer and also in some cases more stringent than circuit application requirements. Leakage sensitivity of 100 megohms between elements is available in some tube checkers. Some can be adjusted by the user to even higher sensitivities. Many tube checkers tie several elements together to test many parallel paths in a single test position. As a result multiple paths having individual inter-element leakage resistances which are acceptable result in parallel combinations which caused the tube to read as defective.

Quality test interpretations must be tempered by knowledge of the character of the quality test. Large signal transconductance often does not correlate with small signal transconductance, that require this characteristic. Cathode emission, as read on many tube checkers, is a function of both the emitting capability of the cathode and the mechanical spacing of the tubes internal parts. While high cathode emitting capability is generally desirable for all tubes, a high emission reading obtained by close mechanical spacing of parts can result in a false indication of good quality. In addition, high or low indications in a tube checker are often caused by compromised test conditions rather than the quality of the tube being tested.

The setup instruction and charts furnished by the tester manufacturer establish the conditions and limits which the tester manufacturer considers adequate for the tube types evaluated. These conditions and limits are usually established independently of the tube manufacturer and without consideration of application requirements.

A tube testing device can only indicate the difference between a given tube’s characteristics and those which are standard for that particular type. Since the operating conditions imposed upon a tube of a given type may vary within wide limits, it is impossible for a tube testing device to evaluate tubes in terms of performance capabilities for all applications. The tube tester, therefore, cannot be looked upon as a final authority in determining whether or not a tube is always satisfactory. An actual operating test in the equipment in which the tube is to be used will give the best possible indication of a tube’s worth.”