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Note: For a < 1, log a < 0, and the differential entropy is negative. Hence, unlike discrete entropy, differential entropy can be negative. However, 2h(X) = 2log a = a is the volume of the support set, which is always nonnegative, as we expect. Example 8.1.2 (Normal distribution) Let X (x) = Then calculating the differential entropy in nats, we obtain h( ) = = = ln (x) x2 ln 2 2 2 2

way to determine the proportion of clients who bene ted from the treatment (Jacobson et al, 1984) Thus, in addition to testing for the statistical signi cance of a treatment, it is also important to assess to what extent the therapy-induced change is of practical importance for the client Many researchers have thus advocated using clinical signi cance as a criterion for evaluating the effectiveness of psychotherapy However, there has been much disagreement in the eld in regard to what constitutes clinical signi cance.

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Some suggestions have included: improvement shown by a large proportion of the clients (Hugdahl & Ost, 1981); a change that is large in magnitude (Barlow, 1981); an improvement in the everyday functioning of the client (Kazdin & Wilson, 1978); an elimination of the presenting problem (Kazdin & Wilson, 1978); and attaining a level of functioning that is indistinguishable from that of the nondeviant population (Kazdin & Wilson, 1978; Kendall & Norton-Ford, 1982) One common approach has been to calculate the percentage of clients in each condition who show an operationally de ned amount of improvement on a speci ed set of measures (also termed responder status) This measure of clinically signi cant change is often arbitrarily set at 20% (ie, clients achieved a 20% change from their scores at pretherapy).

4. Let S1 , S2 {X (1) , X (2) , . . . , X (k) }. If (s1 , s2 ) A(n) (S1 , S2 ), then p(s1 |s2 ) = 2 n(H (S1 |S2 ) 2 ) .

Delay for (2BE-1) unit backoff periods (2)

Investigators differ in how many posttherapy measures are considered in evaluating whether a given client is a responder, although most commonly investigators require that a client show 20% improvement on the majority of main outcome measures Responder status is an effective means of communicating how many clients displayed at least some response to treatment However, it is a fairly weak means of assessing clinically signi cant change If reported, it should be combined with the more stringent criterion of high end-state functioning, which is de ned as the percentage of clients from each condition that is now functioning at so-called normal levels on a majority of main outcome measures Here, normal is typically de ned as a posttherapy or follow-up score falling within the normal or functional range.

In 6 we discussed the various behavioral adaptations that enable animals to secure the food that is essential for their survival. However, there is a ip side to this coin remember that in many of the examples we considered animals preyed upon one another. We are used to thinking in terms of the evolutionary arms race that has resulted in the coevolution of plants and the herbivores that consume them. The plants have evolved to minimize the damage herbivores can in ict upon them and the animals in turn adapt to overcome these defences. For example, many plants possess chemicals that render them unpalatable or even poisonous. But many species of insect have evolved a way to

Operationally de ned normal functioning is often a score falling within one standard deviation of normative means or, in the absence of normative data, a score deemed normal on the basis of its face validity (eg, a daily diary anxiety score of 20 or less on a 0 100 point scale, where 20 was labeled as slight anxiety) However, as Jacobson, Roberts, Berns, and McGlinchey (1999) point out, the criteria chosen for such face valid measures are often arbitrary (eg, Jansson & Ost, 1982) or highly subjective (eg, Barlow & Mavissakalian, 1981) Jacobson et al (1984) have proposed three potential operational de nitions of clinically signi cant change in.

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