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"He has pointed out flaws in your arguments ..."

If you truly believe that then you're clearly as stupid as he!

As much as it pains me ....

Pat would like to have us believe that because a parameter in the analysis presented by Leventhal must be estimated that the analysis is flawed, speculative, or arbitrary.

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Aside

As is typical of Pat he doesn't actually *say* such thing, preferring instead the neutral statement, "You will note that Leventhal's calculations of the probabilities of Type II errors depend on arbitrary assumptions". But Pat forgets that this is *not* a pedantic debating club or a forum for fans of Logic 101 and hence his silliness betrays only a limited intelligence, i.e. he appears unaware that he antics are as transparent as air.

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The parameter in question, (p), is defined by Leventhal as, "... the listener's true ability to hear the differences under test (p)", and he goes on to say:

"Since one really never knows p, and one can only speculate on how to increase it (e.g., by carefully selecting musical selections and ancillary equipment to be used in the listening test), one can reduce with certainty the risk of Type 2 error in a practical listening test only by increasing either N or the risk of Type 1 error. (Remember, Type 1 error risk can be deliberately increased by selecting a larger significance level for the significance test which simultaneously reduces Type 2 error risk.)"

In other words the *uncertainty* of the value of (p) is precisely one of the reasons for increasing N (number of trial).

Moreover Leventhal's table provides columns for multiple values of (p) which he then uses for driving home the consequences (applied rudimentary statistic theory) of low-N testing:

"Suppose an investigator wishes to use the table to analyze the results of a 16-trial (N16) listening study. What is the minimum number of correct identifications (r) that the investigator should require of the listener before concluding that performance is statistically significant (i.e., that differences are audible)? The table shows that the probability of Type 1 error (falsely concluding that inaudible differences are audible) will be .0384 if the investigator requires a minimum r of 12. If the probability of Type 1 error is not to exceed .05, our investigator must choose an r of 12 for the listener to meet or exceed.

But, with the selection of an r of 12, the table shows that the probability of Type 2 error (concluding that audible differences are inaudible) will be .8334, if audible differences between the two components are so slight that the listener can correctly identify the components only 60% of the time (p = .6). If audible differences were slightly larger and the listener can correctly identify the components 70% of the time (p = .7), then the probability of Type 2 error will be .5501, and so on. (The p values should be interpreted as the proportion of correct identifications the listener will provide when given an infinite number of trials under the conditions of the listening study, even if those conditions are not ideal for making correct identifications.)"

Hence it is trivially clear that the allowance has been made for the speculative value of (p) and to claim the analysis is in any way invalidated because of the nature of (p) is nothing more than the product of a colossal stupidity!


No Guru, No Method, No Teacher

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